model dependent and model in dependent considerations on two photon exchange
DESCRIPTION
Model dependent and model in dependent considerations on two photon exchange. Egle Tomasi-Gustafsson IRFU, SPhN- Saclay , and IN2P3- IPN Orsay France. Plan. Introduction Generalities . Model in dependent considerations Space-like Time-like. Model dependent considerations. - PowerPoint PPT PresentationTRANSCRIPT
Model dependent and model independent considerations
on two photon exchange
Egle Tomasi-GustafssonIRFU SPhN-Saclay
and IN2P3- IPN Orsay France
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
Plan
bull Introduction bull Generalities
bull Model independent considerationsbull Space-likebull Time-like
bull What do data saybull Which alternative for GEp problem
bull Conclusions
bull Model dependent considerations
Egle Tomasi-Gustafsson Gatchina July 10 2012
Two-Photon exchange
bull 1g-2g interference is of the order of a=e24p=1137 (in usual calculations of radiative corrections one photon is lsquohardrsquo and one is lsquosoftrsquo)
bull ldquoInvent a mechanismrdquo to enhance this contributionbull In the 70rsquos it was shown [J Gunion and L Stodolsky V Franco FM Lev VN Boitsov L Kondratyuk and VB Kopeliovich R Blankenbecker and J Gunion] that at large momentum transfer due to the sharp decrease of the FFs if the momentum is shared between the two photons the 2g- contribution can become very large
bull The 2g amplitude is expected to be mostly imaginarybull In this case the 1g-2g interference is more important in time-like region as the Born amplitude is complex
Egle Tomasi-Gustafsson Gatchina July 10 2012
Qualitative estimation of 2g exchange
From quark counting rules Fd ~ t-5 and FN~t-2 At t = 4 GeV2
For d 3He 4He 2g effect should appear at ~1 GeV2for protons ~ 10 GeV2
q2 q2
For ed elastic scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
Two-Photon exchange in ed-scatterng
bull Discrepancy between the results fromndash Hall A [LC Alexa et al PRL 82 1374 (1999)] ndash Hall C [D Abbott et al PRL 82 1379
(1999)]
bull Model-independent parametrization of the 2g- contribution
bull Applied to ed-elastic scattering data
M P Rekalo E T-G and D Prout Phys Rev C60 042202 (1999)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Crossing Symmetry
Scattering and annihilation channels
- Described by the same amplitude
- function of two kinematical variables
p2 rarr ndash p1
k2 rarr ndash k2
- which scan different kinematical regions
Egle Tomasi-Gustafsson Gatchina July 10 2012
1g
1g-2g interference
2g1g
M P Rekalo E T-G and D Prout Phys Rev C (1999)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The 1g-2g interference destroys the linearity
of the Rosenbluth plot
What about data
Egle Tomasi-Gustafsson Gatchina July 10 2012
1g-2g interference
M P Rekalo E T-G and D Prout Phys Rev C60 042202 (1999)
CA DA
Egle Tomasi-Gustafsson Gatchina July 10 2012
From the data deviation from linearity ltlt 1
Parametrization of 2g-contribution for e+p
E T-G G Gakh Phys Rev C 72 015209 (2005)
)(11)( 2)(2 QfQF a
-
222222
]1[ a
Dγ(a)
m[GeV]QGC
)(Qf
e+4He scattering
Spin 0 particle F(q2) in Born approximation
2g exchange F1(sq2)F2(sq2)=F(q2) +f(sq2)
F(q2)~a0 F1(sq2)~a
Egle Tomasi-Gustafsson Gatchina July 10 2012
GI Gakh and E T-G NuclPhys A838 (2010) 50-60
Linear fit to e+4He elastic scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
GI Gakh and E T-G NuclPhys A838 (2010) 50-60
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull One-photon exchange - Two form factors (real in SL complex in TL) - Functions of one variable (t)
16 amplitudes in the general caseP- and T-invariance of EM interaction
helicity conservation
Interaction of 4 spin frac12 fermions
bullTwo-photon exchange
- Three (complex) amplitudes - Functions of two variables (st)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Space-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
Possible but difficult
Egle Tomasi-Gustafsson Gatchina July 10 2012
Determination of EM form factors in presence of 2g exchange
-electron and positron beams
- longitudinally polarized - in identical kinematical
conditions
M P Rekalo E T-G EPJA (2004) Nucl Phys A (2003)
Model independent considerations foreplusmn N scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
Model independent considerations foreplusmn N scattering
Determination of EM form factors in presence of 2g exchange- electron and positron beams
- longitudinally polarized - in identical kinematical conditions
Generalization of the polarization method (A Akhiezer and MP Rekalo)
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
bull Ay unpolarized leptons transversally polarized target or Py outgoing nucleon polarization with unpolarized leptons unpolarized target
bull Depolarization tensor (Dab) dependence of the
b-component of the final nucleon polarization on the a-component of the nucleon target with longitudinally polarized leptons
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Very difficult experimentsThree T-odd polarization observableshellipExpected small of the order of a triple spin correlations buthellip Model independent way
This ratio contains the lsquoTRUE lsquoform factors
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellipor five T-even polarization observableshellip among dsdW Px(le) Pz(le) Dxx Dyy Dzz Dxz
Again very difficult experiments
Only Model independent ways (without positron beams)M P Rekalo and E T-G Nucl Phys A740 (2004) 271
M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
Time-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
much easier
Time-like observables | GE| 2 and | GM| 2
As in SL region- Dependence on q2 contained in FFs- Even dependence on cos2q (1g exchange)- No dependence on sign of FFs- Enhancement of magnetic term
but TL form factors are complex
A Zichichi S M Berman N Cabibbo R Gatto Il Nuovo Cimento XXIV 170 (1962)B Bilenkii C Giunti V Wataghin Z Phys C 59 475 (1993)G Gakh ET-G Nucl Phys A761120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
Unpolarized cross section
bull Induces four new termsbull Odd function of q bull Does not contribute at q =90deg
Two Photon Exchange
MP Rekalo and E T-G EPJA 22 331 (2004)GI Gakh and E T-G NPA761 120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullProperties of the TPE amplitudes with respect to the transformation cos q = - cos q ie q - q
(equivalent to non-linearity in Rosenbluth fit)
bullBased on these properties one can remove or single out TPE contribution
Symmetry relations
E T-G G Gakh NPA (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullDifferential cross section at complementary angles
Symmetry relations (annihilation)
The DIFFERENCE enhances the 2g contribution
The SUM cancels the 2g contribution
Egle Tomasi-Gustafsson Gatchina July 10 2012
What do data say
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Return (ISR)
s
m
x
sin
xxx
)xs(W
s
m
s
Ex)m)(ppee()xs(W
sm
cosddm)ppee(d
eq
-
q
-a
q
-sqq
gs g--
222
122
2
2
2
2
e+ +e- p + p + g
B Aubert ( BABAR Collaboration) Phys Rev D73 012005 (2006)
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
Plan
bull Introduction bull Generalities
bull Model independent considerationsbull Space-likebull Time-like
bull What do data saybull Which alternative for GEp problem
bull Conclusions
bull Model dependent considerations
Egle Tomasi-Gustafsson Gatchina July 10 2012
Two-Photon exchange
bull 1g-2g interference is of the order of a=e24p=1137 (in usual calculations of radiative corrections one photon is lsquohardrsquo and one is lsquosoftrsquo)
bull ldquoInvent a mechanismrdquo to enhance this contributionbull In the 70rsquos it was shown [J Gunion and L Stodolsky V Franco FM Lev VN Boitsov L Kondratyuk and VB Kopeliovich R Blankenbecker and J Gunion] that at large momentum transfer due to the sharp decrease of the FFs if the momentum is shared between the two photons the 2g- contribution can become very large
bull The 2g amplitude is expected to be mostly imaginarybull In this case the 1g-2g interference is more important in time-like region as the Born amplitude is complex
Egle Tomasi-Gustafsson Gatchina July 10 2012
Qualitative estimation of 2g exchange
From quark counting rules Fd ~ t-5 and FN~t-2 At t = 4 GeV2
For d 3He 4He 2g effect should appear at ~1 GeV2for protons ~ 10 GeV2
q2 q2
For ed elastic scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
Two-Photon exchange in ed-scatterng
bull Discrepancy between the results fromndash Hall A [LC Alexa et al PRL 82 1374 (1999)] ndash Hall C [D Abbott et al PRL 82 1379
(1999)]
bull Model-independent parametrization of the 2g- contribution
bull Applied to ed-elastic scattering data
M P Rekalo E T-G and D Prout Phys Rev C60 042202 (1999)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Crossing Symmetry
Scattering and annihilation channels
- Described by the same amplitude
- function of two kinematical variables
p2 rarr ndash p1
k2 rarr ndash k2
- which scan different kinematical regions
Egle Tomasi-Gustafsson Gatchina July 10 2012
1g
1g-2g interference
2g1g
M P Rekalo E T-G and D Prout Phys Rev C (1999)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The 1g-2g interference destroys the linearity
of the Rosenbluth plot
What about data
Egle Tomasi-Gustafsson Gatchina July 10 2012
1g-2g interference
M P Rekalo E T-G and D Prout Phys Rev C60 042202 (1999)
CA DA
Egle Tomasi-Gustafsson Gatchina July 10 2012
From the data deviation from linearity ltlt 1
Parametrization of 2g-contribution for e+p
E T-G G Gakh Phys Rev C 72 015209 (2005)
)(11)( 2)(2 QfQF a
-
222222
]1[ a
Dγ(a)
m[GeV]QGC
)(Qf
e+4He scattering
Spin 0 particle F(q2) in Born approximation
2g exchange F1(sq2)F2(sq2)=F(q2) +f(sq2)
F(q2)~a0 F1(sq2)~a
Egle Tomasi-Gustafsson Gatchina July 10 2012
GI Gakh and E T-G NuclPhys A838 (2010) 50-60
Linear fit to e+4He elastic scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
GI Gakh and E T-G NuclPhys A838 (2010) 50-60
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull One-photon exchange - Two form factors (real in SL complex in TL) - Functions of one variable (t)
16 amplitudes in the general caseP- and T-invariance of EM interaction
helicity conservation
Interaction of 4 spin frac12 fermions
bullTwo-photon exchange
- Three (complex) amplitudes - Functions of two variables (st)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Space-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
Possible but difficult
Egle Tomasi-Gustafsson Gatchina July 10 2012
Determination of EM form factors in presence of 2g exchange
-electron and positron beams
- longitudinally polarized - in identical kinematical
conditions
M P Rekalo E T-G EPJA (2004) Nucl Phys A (2003)
Model independent considerations foreplusmn N scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
Model independent considerations foreplusmn N scattering
Determination of EM form factors in presence of 2g exchange- electron and positron beams
- longitudinally polarized - in identical kinematical conditions
Generalization of the polarization method (A Akhiezer and MP Rekalo)
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
bull Ay unpolarized leptons transversally polarized target or Py outgoing nucleon polarization with unpolarized leptons unpolarized target
bull Depolarization tensor (Dab) dependence of the
b-component of the final nucleon polarization on the a-component of the nucleon target with longitudinally polarized leptons
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Very difficult experimentsThree T-odd polarization observableshellipExpected small of the order of a triple spin correlations buthellip Model independent way
This ratio contains the lsquoTRUE lsquoform factors
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellipor five T-even polarization observableshellip among dsdW Px(le) Pz(le) Dxx Dyy Dzz Dxz
Again very difficult experiments
Only Model independent ways (without positron beams)M P Rekalo and E T-G Nucl Phys A740 (2004) 271
M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
Time-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
much easier
Time-like observables | GE| 2 and | GM| 2
As in SL region- Dependence on q2 contained in FFs- Even dependence on cos2q (1g exchange)- No dependence on sign of FFs- Enhancement of magnetic term
but TL form factors are complex
A Zichichi S M Berman N Cabibbo R Gatto Il Nuovo Cimento XXIV 170 (1962)B Bilenkii C Giunti V Wataghin Z Phys C 59 475 (1993)G Gakh ET-G Nucl Phys A761120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
Unpolarized cross section
bull Induces four new termsbull Odd function of q bull Does not contribute at q =90deg
Two Photon Exchange
MP Rekalo and E T-G EPJA 22 331 (2004)GI Gakh and E T-G NPA761 120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullProperties of the TPE amplitudes with respect to the transformation cos q = - cos q ie q - q
(equivalent to non-linearity in Rosenbluth fit)
bullBased on these properties one can remove or single out TPE contribution
Symmetry relations
E T-G G Gakh NPA (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullDifferential cross section at complementary angles
Symmetry relations (annihilation)
The DIFFERENCE enhances the 2g contribution
The SUM cancels the 2g contribution
Egle Tomasi-Gustafsson Gatchina July 10 2012
What do data say
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Return (ISR)
s
m
x
sin
xxx
)xs(W
s
m
s
Ex)m)(ppee()xs(W
sm
cosddm)ppee(d
eq
-
q
-a
q
-sqq
gs g--
222
122
2
2
2
2
e+ +e- p + p + g
B Aubert ( BABAR Collaboration) Phys Rev D73 012005 (2006)
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
Two-Photon exchange
bull 1g-2g interference is of the order of a=e24p=1137 (in usual calculations of radiative corrections one photon is lsquohardrsquo and one is lsquosoftrsquo)
bull ldquoInvent a mechanismrdquo to enhance this contributionbull In the 70rsquos it was shown [J Gunion and L Stodolsky V Franco FM Lev VN Boitsov L Kondratyuk and VB Kopeliovich R Blankenbecker and J Gunion] that at large momentum transfer due to the sharp decrease of the FFs if the momentum is shared between the two photons the 2g- contribution can become very large
bull The 2g amplitude is expected to be mostly imaginarybull In this case the 1g-2g interference is more important in time-like region as the Born amplitude is complex
Egle Tomasi-Gustafsson Gatchina July 10 2012
Qualitative estimation of 2g exchange
From quark counting rules Fd ~ t-5 and FN~t-2 At t = 4 GeV2
For d 3He 4He 2g effect should appear at ~1 GeV2for protons ~ 10 GeV2
q2 q2
For ed elastic scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
Two-Photon exchange in ed-scatterng
bull Discrepancy between the results fromndash Hall A [LC Alexa et al PRL 82 1374 (1999)] ndash Hall C [D Abbott et al PRL 82 1379
(1999)]
bull Model-independent parametrization of the 2g- contribution
bull Applied to ed-elastic scattering data
M P Rekalo E T-G and D Prout Phys Rev C60 042202 (1999)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Crossing Symmetry
Scattering and annihilation channels
- Described by the same amplitude
- function of two kinematical variables
p2 rarr ndash p1
k2 rarr ndash k2
- which scan different kinematical regions
Egle Tomasi-Gustafsson Gatchina July 10 2012
1g
1g-2g interference
2g1g
M P Rekalo E T-G and D Prout Phys Rev C (1999)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The 1g-2g interference destroys the linearity
of the Rosenbluth plot
What about data
Egle Tomasi-Gustafsson Gatchina July 10 2012
1g-2g interference
M P Rekalo E T-G and D Prout Phys Rev C60 042202 (1999)
CA DA
Egle Tomasi-Gustafsson Gatchina July 10 2012
From the data deviation from linearity ltlt 1
Parametrization of 2g-contribution for e+p
E T-G G Gakh Phys Rev C 72 015209 (2005)
)(11)( 2)(2 QfQF a
-
222222
]1[ a
Dγ(a)
m[GeV]QGC
)(Qf
e+4He scattering
Spin 0 particle F(q2) in Born approximation
2g exchange F1(sq2)F2(sq2)=F(q2) +f(sq2)
F(q2)~a0 F1(sq2)~a
Egle Tomasi-Gustafsson Gatchina July 10 2012
GI Gakh and E T-G NuclPhys A838 (2010) 50-60
Linear fit to e+4He elastic scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
GI Gakh and E T-G NuclPhys A838 (2010) 50-60
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull One-photon exchange - Two form factors (real in SL complex in TL) - Functions of one variable (t)
16 amplitudes in the general caseP- and T-invariance of EM interaction
helicity conservation
Interaction of 4 spin frac12 fermions
bullTwo-photon exchange
- Three (complex) amplitudes - Functions of two variables (st)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Space-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
Possible but difficult
Egle Tomasi-Gustafsson Gatchina July 10 2012
Determination of EM form factors in presence of 2g exchange
-electron and positron beams
- longitudinally polarized - in identical kinematical
conditions
M P Rekalo E T-G EPJA (2004) Nucl Phys A (2003)
Model independent considerations foreplusmn N scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
Model independent considerations foreplusmn N scattering
Determination of EM form factors in presence of 2g exchange- electron and positron beams
- longitudinally polarized - in identical kinematical conditions
Generalization of the polarization method (A Akhiezer and MP Rekalo)
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
bull Ay unpolarized leptons transversally polarized target or Py outgoing nucleon polarization with unpolarized leptons unpolarized target
bull Depolarization tensor (Dab) dependence of the
b-component of the final nucleon polarization on the a-component of the nucleon target with longitudinally polarized leptons
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Very difficult experimentsThree T-odd polarization observableshellipExpected small of the order of a triple spin correlations buthellip Model independent way
This ratio contains the lsquoTRUE lsquoform factors
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellipor five T-even polarization observableshellip among dsdW Px(le) Pz(le) Dxx Dyy Dzz Dxz
Again very difficult experiments
Only Model independent ways (without positron beams)M P Rekalo and E T-G Nucl Phys A740 (2004) 271
M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
Time-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
much easier
Time-like observables | GE| 2 and | GM| 2
As in SL region- Dependence on q2 contained in FFs- Even dependence on cos2q (1g exchange)- No dependence on sign of FFs- Enhancement of magnetic term
but TL form factors are complex
A Zichichi S M Berman N Cabibbo R Gatto Il Nuovo Cimento XXIV 170 (1962)B Bilenkii C Giunti V Wataghin Z Phys C 59 475 (1993)G Gakh ET-G Nucl Phys A761120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
Unpolarized cross section
bull Induces four new termsbull Odd function of q bull Does not contribute at q =90deg
Two Photon Exchange
MP Rekalo and E T-G EPJA 22 331 (2004)GI Gakh and E T-G NPA761 120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullProperties of the TPE amplitudes with respect to the transformation cos q = - cos q ie q - q
(equivalent to non-linearity in Rosenbluth fit)
bullBased on these properties one can remove or single out TPE contribution
Symmetry relations
E T-G G Gakh NPA (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullDifferential cross section at complementary angles
Symmetry relations (annihilation)
The DIFFERENCE enhances the 2g contribution
The SUM cancels the 2g contribution
Egle Tomasi-Gustafsson Gatchina July 10 2012
What do data say
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Return (ISR)
s
m
x
sin
xxx
)xs(W
s
m
s
Ex)m)(ppee()xs(W
sm
cosddm)ppee(d
eq
-
q
-a
q
-sqq
gs g--
222
122
2
2
2
2
e+ +e- p + p + g
B Aubert ( BABAR Collaboration) Phys Rev D73 012005 (2006)
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
Qualitative estimation of 2g exchange
From quark counting rules Fd ~ t-5 and FN~t-2 At t = 4 GeV2
For d 3He 4He 2g effect should appear at ~1 GeV2for protons ~ 10 GeV2
q2 q2
For ed elastic scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
Two-Photon exchange in ed-scatterng
bull Discrepancy between the results fromndash Hall A [LC Alexa et al PRL 82 1374 (1999)] ndash Hall C [D Abbott et al PRL 82 1379
(1999)]
bull Model-independent parametrization of the 2g- contribution
bull Applied to ed-elastic scattering data
M P Rekalo E T-G and D Prout Phys Rev C60 042202 (1999)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Crossing Symmetry
Scattering and annihilation channels
- Described by the same amplitude
- function of two kinematical variables
p2 rarr ndash p1
k2 rarr ndash k2
- which scan different kinematical regions
Egle Tomasi-Gustafsson Gatchina July 10 2012
1g
1g-2g interference
2g1g
M P Rekalo E T-G and D Prout Phys Rev C (1999)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The 1g-2g interference destroys the linearity
of the Rosenbluth plot
What about data
Egle Tomasi-Gustafsson Gatchina July 10 2012
1g-2g interference
M P Rekalo E T-G and D Prout Phys Rev C60 042202 (1999)
CA DA
Egle Tomasi-Gustafsson Gatchina July 10 2012
From the data deviation from linearity ltlt 1
Parametrization of 2g-contribution for e+p
E T-G G Gakh Phys Rev C 72 015209 (2005)
)(11)( 2)(2 QfQF a
-
222222
]1[ a
Dγ(a)
m[GeV]QGC
)(Qf
e+4He scattering
Spin 0 particle F(q2) in Born approximation
2g exchange F1(sq2)F2(sq2)=F(q2) +f(sq2)
F(q2)~a0 F1(sq2)~a
Egle Tomasi-Gustafsson Gatchina July 10 2012
GI Gakh and E T-G NuclPhys A838 (2010) 50-60
Linear fit to e+4He elastic scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
GI Gakh and E T-G NuclPhys A838 (2010) 50-60
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull One-photon exchange - Two form factors (real in SL complex in TL) - Functions of one variable (t)
16 amplitudes in the general caseP- and T-invariance of EM interaction
helicity conservation
Interaction of 4 spin frac12 fermions
bullTwo-photon exchange
- Three (complex) amplitudes - Functions of two variables (st)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Space-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
Possible but difficult
Egle Tomasi-Gustafsson Gatchina July 10 2012
Determination of EM form factors in presence of 2g exchange
-electron and positron beams
- longitudinally polarized - in identical kinematical
conditions
M P Rekalo E T-G EPJA (2004) Nucl Phys A (2003)
Model independent considerations foreplusmn N scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
Model independent considerations foreplusmn N scattering
Determination of EM form factors in presence of 2g exchange- electron and positron beams
- longitudinally polarized - in identical kinematical conditions
Generalization of the polarization method (A Akhiezer and MP Rekalo)
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
bull Ay unpolarized leptons transversally polarized target or Py outgoing nucleon polarization with unpolarized leptons unpolarized target
bull Depolarization tensor (Dab) dependence of the
b-component of the final nucleon polarization on the a-component of the nucleon target with longitudinally polarized leptons
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Very difficult experimentsThree T-odd polarization observableshellipExpected small of the order of a triple spin correlations buthellip Model independent way
This ratio contains the lsquoTRUE lsquoform factors
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellipor five T-even polarization observableshellip among dsdW Px(le) Pz(le) Dxx Dyy Dzz Dxz
Again very difficult experiments
Only Model independent ways (without positron beams)M P Rekalo and E T-G Nucl Phys A740 (2004) 271
M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
Time-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
much easier
Time-like observables | GE| 2 and | GM| 2
As in SL region- Dependence on q2 contained in FFs- Even dependence on cos2q (1g exchange)- No dependence on sign of FFs- Enhancement of magnetic term
but TL form factors are complex
A Zichichi S M Berman N Cabibbo R Gatto Il Nuovo Cimento XXIV 170 (1962)B Bilenkii C Giunti V Wataghin Z Phys C 59 475 (1993)G Gakh ET-G Nucl Phys A761120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
Unpolarized cross section
bull Induces four new termsbull Odd function of q bull Does not contribute at q =90deg
Two Photon Exchange
MP Rekalo and E T-G EPJA 22 331 (2004)GI Gakh and E T-G NPA761 120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullProperties of the TPE amplitudes with respect to the transformation cos q = - cos q ie q - q
(equivalent to non-linearity in Rosenbluth fit)
bullBased on these properties one can remove or single out TPE contribution
Symmetry relations
E T-G G Gakh NPA (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullDifferential cross section at complementary angles
Symmetry relations (annihilation)
The DIFFERENCE enhances the 2g contribution
The SUM cancels the 2g contribution
Egle Tomasi-Gustafsson Gatchina July 10 2012
What do data say
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Return (ISR)
s
m
x
sin
xxx
)xs(W
s
m
s
Ex)m)(ppee()xs(W
sm
cosddm)ppee(d
eq
-
q
-a
q
-sqq
gs g--
222
122
2
2
2
2
e+ +e- p + p + g
B Aubert ( BABAR Collaboration) Phys Rev D73 012005 (2006)
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
Two-Photon exchange in ed-scatterng
bull Discrepancy between the results fromndash Hall A [LC Alexa et al PRL 82 1374 (1999)] ndash Hall C [D Abbott et al PRL 82 1379
(1999)]
bull Model-independent parametrization of the 2g- contribution
bull Applied to ed-elastic scattering data
M P Rekalo E T-G and D Prout Phys Rev C60 042202 (1999)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Crossing Symmetry
Scattering and annihilation channels
- Described by the same amplitude
- function of two kinematical variables
p2 rarr ndash p1
k2 rarr ndash k2
- which scan different kinematical regions
Egle Tomasi-Gustafsson Gatchina July 10 2012
1g
1g-2g interference
2g1g
M P Rekalo E T-G and D Prout Phys Rev C (1999)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The 1g-2g interference destroys the linearity
of the Rosenbluth plot
What about data
Egle Tomasi-Gustafsson Gatchina July 10 2012
1g-2g interference
M P Rekalo E T-G and D Prout Phys Rev C60 042202 (1999)
CA DA
Egle Tomasi-Gustafsson Gatchina July 10 2012
From the data deviation from linearity ltlt 1
Parametrization of 2g-contribution for e+p
E T-G G Gakh Phys Rev C 72 015209 (2005)
)(11)( 2)(2 QfQF a
-
222222
]1[ a
Dγ(a)
m[GeV]QGC
)(Qf
e+4He scattering
Spin 0 particle F(q2) in Born approximation
2g exchange F1(sq2)F2(sq2)=F(q2) +f(sq2)
F(q2)~a0 F1(sq2)~a
Egle Tomasi-Gustafsson Gatchina July 10 2012
GI Gakh and E T-G NuclPhys A838 (2010) 50-60
Linear fit to e+4He elastic scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
GI Gakh and E T-G NuclPhys A838 (2010) 50-60
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull One-photon exchange - Two form factors (real in SL complex in TL) - Functions of one variable (t)
16 amplitudes in the general caseP- and T-invariance of EM interaction
helicity conservation
Interaction of 4 spin frac12 fermions
bullTwo-photon exchange
- Three (complex) amplitudes - Functions of two variables (st)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Space-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
Possible but difficult
Egle Tomasi-Gustafsson Gatchina July 10 2012
Determination of EM form factors in presence of 2g exchange
-electron and positron beams
- longitudinally polarized - in identical kinematical
conditions
M P Rekalo E T-G EPJA (2004) Nucl Phys A (2003)
Model independent considerations foreplusmn N scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
Model independent considerations foreplusmn N scattering
Determination of EM form factors in presence of 2g exchange- electron and positron beams
- longitudinally polarized - in identical kinematical conditions
Generalization of the polarization method (A Akhiezer and MP Rekalo)
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
bull Ay unpolarized leptons transversally polarized target or Py outgoing nucleon polarization with unpolarized leptons unpolarized target
bull Depolarization tensor (Dab) dependence of the
b-component of the final nucleon polarization on the a-component of the nucleon target with longitudinally polarized leptons
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Very difficult experimentsThree T-odd polarization observableshellipExpected small of the order of a triple spin correlations buthellip Model independent way
This ratio contains the lsquoTRUE lsquoform factors
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellipor five T-even polarization observableshellip among dsdW Px(le) Pz(le) Dxx Dyy Dzz Dxz
Again very difficult experiments
Only Model independent ways (without positron beams)M P Rekalo and E T-G Nucl Phys A740 (2004) 271
M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
Time-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
much easier
Time-like observables | GE| 2 and | GM| 2
As in SL region- Dependence on q2 contained in FFs- Even dependence on cos2q (1g exchange)- No dependence on sign of FFs- Enhancement of magnetic term
but TL form factors are complex
A Zichichi S M Berman N Cabibbo R Gatto Il Nuovo Cimento XXIV 170 (1962)B Bilenkii C Giunti V Wataghin Z Phys C 59 475 (1993)G Gakh ET-G Nucl Phys A761120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
Unpolarized cross section
bull Induces four new termsbull Odd function of q bull Does not contribute at q =90deg
Two Photon Exchange
MP Rekalo and E T-G EPJA 22 331 (2004)GI Gakh and E T-G NPA761 120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullProperties of the TPE amplitudes with respect to the transformation cos q = - cos q ie q - q
(equivalent to non-linearity in Rosenbluth fit)
bullBased on these properties one can remove or single out TPE contribution
Symmetry relations
E T-G G Gakh NPA (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullDifferential cross section at complementary angles
Symmetry relations (annihilation)
The DIFFERENCE enhances the 2g contribution
The SUM cancels the 2g contribution
Egle Tomasi-Gustafsson Gatchina July 10 2012
What do data say
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Return (ISR)
s
m
x
sin
xxx
)xs(W
s
m
s
Ex)m)(ppee()xs(W
sm
cosddm)ppee(d
eq
-
q
-a
q
-sqq
gs g--
222
122
2
2
2
2
e+ +e- p + p + g
B Aubert ( BABAR Collaboration) Phys Rev D73 012005 (2006)
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
Crossing Symmetry
Scattering and annihilation channels
- Described by the same amplitude
- function of two kinematical variables
p2 rarr ndash p1
k2 rarr ndash k2
- which scan different kinematical regions
Egle Tomasi-Gustafsson Gatchina July 10 2012
1g
1g-2g interference
2g1g
M P Rekalo E T-G and D Prout Phys Rev C (1999)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The 1g-2g interference destroys the linearity
of the Rosenbluth plot
What about data
Egle Tomasi-Gustafsson Gatchina July 10 2012
1g-2g interference
M P Rekalo E T-G and D Prout Phys Rev C60 042202 (1999)
CA DA
Egle Tomasi-Gustafsson Gatchina July 10 2012
From the data deviation from linearity ltlt 1
Parametrization of 2g-contribution for e+p
E T-G G Gakh Phys Rev C 72 015209 (2005)
)(11)( 2)(2 QfQF a
-
222222
]1[ a
Dγ(a)
m[GeV]QGC
)(Qf
e+4He scattering
Spin 0 particle F(q2) in Born approximation
2g exchange F1(sq2)F2(sq2)=F(q2) +f(sq2)
F(q2)~a0 F1(sq2)~a
Egle Tomasi-Gustafsson Gatchina July 10 2012
GI Gakh and E T-G NuclPhys A838 (2010) 50-60
Linear fit to e+4He elastic scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
GI Gakh and E T-G NuclPhys A838 (2010) 50-60
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull One-photon exchange - Two form factors (real in SL complex in TL) - Functions of one variable (t)
16 amplitudes in the general caseP- and T-invariance of EM interaction
helicity conservation
Interaction of 4 spin frac12 fermions
bullTwo-photon exchange
- Three (complex) amplitudes - Functions of two variables (st)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Space-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
Possible but difficult
Egle Tomasi-Gustafsson Gatchina July 10 2012
Determination of EM form factors in presence of 2g exchange
-electron and positron beams
- longitudinally polarized - in identical kinematical
conditions
M P Rekalo E T-G EPJA (2004) Nucl Phys A (2003)
Model independent considerations foreplusmn N scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
Model independent considerations foreplusmn N scattering
Determination of EM form factors in presence of 2g exchange- electron and positron beams
- longitudinally polarized - in identical kinematical conditions
Generalization of the polarization method (A Akhiezer and MP Rekalo)
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
bull Ay unpolarized leptons transversally polarized target or Py outgoing nucleon polarization with unpolarized leptons unpolarized target
bull Depolarization tensor (Dab) dependence of the
b-component of the final nucleon polarization on the a-component of the nucleon target with longitudinally polarized leptons
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Very difficult experimentsThree T-odd polarization observableshellipExpected small of the order of a triple spin correlations buthellip Model independent way
This ratio contains the lsquoTRUE lsquoform factors
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellipor five T-even polarization observableshellip among dsdW Px(le) Pz(le) Dxx Dyy Dzz Dxz
Again very difficult experiments
Only Model independent ways (without positron beams)M P Rekalo and E T-G Nucl Phys A740 (2004) 271
M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
Time-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
much easier
Time-like observables | GE| 2 and | GM| 2
As in SL region- Dependence on q2 contained in FFs- Even dependence on cos2q (1g exchange)- No dependence on sign of FFs- Enhancement of magnetic term
but TL form factors are complex
A Zichichi S M Berman N Cabibbo R Gatto Il Nuovo Cimento XXIV 170 (1962)B Bilenkii C Giunti V Wataghin Z Phys C 59 475 (1993)G Gakh ET-G Nucl Phys A761120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
Unpolarized cross section
bull Induces four new termsbull Odd function of q bull Does not contribute at q =90deg
Two Photon Exchange
MP Rekalo and E T-G EPJA 22 331 (2004)GI Gakh and E T-G NPA761 120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullProperties of the TPE amplitudes with respect to the transformation cos q = - cos q ie q - q
(equivalent to non-linearity in Rosenbluth fit)
bullBased on these properties one can remove or single out TPE contribution
Symmetry relations
E T-G G Gakh NPA (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullDifferential cross section at complementary angles
Symmetry relations (annihilation)
The DIFFERENCE enhances the 2g contribution
The SUM cancels the 2g contribution
Egle Tomasi-Gustafsson Gatchina July 10 2012
What do data say
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Return (ISR)
s
m
x
sin
xxx
)xs(W
s
m
s
Ex)m)(ppee()xs(W
sm
cosddm)ppee(d
eq
-
q
-a
q
-sqq
gs g--
222
122
2
2
2
2
e+ +e- p + p + g
B Aubert ( BABAR Collaboration) Phys Rev D73 012005 (2006)
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
1g
1g-2g interference
2g1g
M P Rekalo E T-G and D Prout Phys Rev C (1999)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The 1g-2g interference destroys the linearity
of the Rosenbluth plot
What about data
Egle Tomasi-Gustafsson Gatchina July 10 2012
1g-2g interference
M P Rekalo E T-G and D Prout Phys Rev C60 042202 (1999)
CA DA
Egle Tomasi-Gustafsson Gatchina July 10 2012
From the data deviation from linearity ltlt 1
Parametrization of 2g-contribution for e+p
E T-G G Gakh Phys Rev C 72 015209 (2005)
)(11)( 2)(2 QfQF a
-
222222
]1[ a
Dγ(a)
m[GeV]QGC
)(Qf
e+4He scattering
Spin 0 particle F(q2) in Born approximation
2g exchange F1(sq2)F2(sq2)=F(q2) +f(sq2)
F(q2)~a0 F1(sq2)~a
Egle Tomasi-Gustafsson Gatchina July 10 2012
GI Gakh and E T-G NuclPhys A838 (2010) 50-60
Linear fit to e+4He elastic scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
GI Gakh and E T-G NuclPhys A838 (2010) 50-60
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull One-photon exchange - Two form factors (real in SL complex in TL) - Functions of one variable (t)
16 amplitudes in the general caseP- and T-invariance of EM interaction
helicity conservation
Interaction of 4 spin frac12 fermions
bullTwo-photon exchange
- Three (complex) amplitudes - Functions of two variables (st)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Space-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
Possible but difficult
Egle Tomasi-Gustafsson Gatchina July 10 2012
Determination of EM form factors in presence of 2g exchange
-electron and positron beams
- longitudinally polarized - in identical kinematical
conditions
M P Rekalo E T-G EPJA (2004) Nucl Phys A (2003)
Model independent considerations foreplusmn N scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
Model independent considerations foreplusmn N scattering
Determination of EM form factors in presence of 2g exchange- electron and positron beams
- longitudinally polarized - in identical kinematical conditions
Generalization of the polarization method (A Akhiezer and MP Rekalo)
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
bull Ay unpolarized leptons transversally polarized target or Py outgoing nucleon polarization with unpolarized leptons unpolarized target
bull Depolarization tensor (Dab) dependence of the
b-component of the final nucleon polarization on the a-component of the nucleon target with longitudinally polarized leptons
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Very difficult experimentsThree T-odd polarization observableshellipExpected small of the order of a triple spin correlations buthellip Model independent way
This ratio contains the lsquoTRUE lsquoform factors
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellipor five T-even polarization observableshellip among dsdW Px(le) Pz(le) Dxx Dyy Dzz Dxz
Again very difficult experiments
Only Model independent ways (without positron beams)M P Rekalo and E T-G Nucl Phys A740 (2004) 271
M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
Time-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
much easier
Time-like observables | GE| 2 and | GM| 2
As in SL region- Dependence on q2 contained in FFs- Even dependence on cos2q (1g exchange)- No dependence on sign of FFs- Enhancement of magnetic term
but TL form factors are complex
A Zichichi S M Berman N Cabibbo R Gatto Il Nuovo Cimento XXIV 170 (1962)B Bilenkii C Giunti V Wataghin Z Phys C 59 475 (1993)G Gakh ET-G Nucl Phys A761120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
Unpolarized cross section
bull Induces four new termsbull Odd function of q bull Does not contribute at q =90deg
Two Photon Exchange
MP Rekalo and E T-G EPJA 22 331 (2004)GI Gakh and E T-G NPA761 120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullProperties of the TPE amplitudes with respect to the transformation cos q = - cos q ie q - q
(equivalent to non-linearity in Rosenbluth fit)
bullBased on these properties one can remove or single out TPE contribution
Symmetry relations
E T-G G Gakh NPA (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullDifferential cross section at complementary angles
Symmetry relations (annihilation)
The DIFFERENCE enhances the 2g contribution
The SUM cancels the 2g contribution
Egle Tomasi-Gustafsson Gatchina July 10 2012
What do data say
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Return (ISR)
s
m
x
sin
xxx
)xs(W
s
m
s
Ex)m)(ppee()xs(W
sm
cosddm)ppee(d
eq
-
q
-a
q
-sqq
gs g--
222
122
2
2
2
2
e+ +e- p + p + g
B Aubert ( BABAR Collaboration) Phys Rev D73 012005 (2006)
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
The 1g-2g interference destroys the linearity
of the Rosenbluth plot
What about data
Egle Tomasi-Gustafsson Gatchina July 10 2012
1g-2g interference
M P Rekalo E T-G and D Prout Phys Rev C60 042202 (1999)
CA DA
Egle Tomasi-Gustafsson Gatchina July 10 2012
From the data deviation from linearity ltlt 1
Parametrization of 2g-contribution for e+p
E T-G G Gakh Phys Rev C 72 015209 (2005)
)(11)( 2)(2 QfQF a
-
222222
]1[ a
Dγ(a)
m[GeV]QGC
)(Qf
e+4He scattering
Spin 0 particle F(q2) in Born approximation
2g exchange F1(sq2)F2(sq2)=F(q2) +f(sq2)
F(q2)~a0 F1(sq2)~a
Egle Tomasi-Gustafsson Gatchina July 10 2012
GI Gakh and E T-G NuclPhys A838 (2010) 50-60
Linear fit to e+4He elastic scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
GI Gakh and E T-G NuclPhys A838 (2010) 50-60
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull One-photon exchange - Two form factors (real in SL complex in TL) - Functions of one variable (t)
16 amplitudes in the general caseP- and T-invariance of EM interaction
helicity conservation
Interaction of 4 spin frac12 fermions
bullTwo-photon exchange
- Three (complex) amplitudes - Functions of two variables (st)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Space-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
Possible but difficult
Egle Tomasi-Gustafsson Gatchina July 10 2012
Determination of EM form factors in presence of 2g exchange
-electron and positron beams
- longitudinally polarized - in identical kinematical
conditions
M P Rekalo E T-G EPJA (2004) Nucl Phys A (2003)
Model independent considerations foreplusmn N scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
Model independent considerations foreplusmn N scattering
Determination of EM form factors in presence of 2g exchange- electron and positron beams
- longitudinally polarized - in identical kinematical conditions
Generalization of the polarization method (A Akhiezer and MP Rekalo)
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
bull Ay unpolarized leptons transversally polarized target or Py outgoing nucleon polarization with unpolarized leptons unpolarized target
bull Depolarization tensor (Dab) dependence of the
b-component of the final nucleon polarization on the a-component of the nucleon target with longitudinally polarized leptons
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Very difficult experimentsThree T-odd polarization observableshellipExpected small of the order of a triple spin correlations buthellip Model independent way
This ratio contains the lsquoTRUE lsquoform factors
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellipor five T-even polarization observableshellip among dsdW Px(le) Pz(le) Dxx Dyy Dzz Dxz
Again very difficult experiments
Only Model independent ways (without positron beams)M P Rekalo and E T-G Nucl Phys A740 (2004) 271
M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
Time-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
much easier
Time-like observables | GE| 2 and | GM| 2
As in SL region- Dependence on q2 contained in FFs- Even dependence on cos2q (1g exchange)- No dependence on sign of FFs- Enhancement of magnetic term
but TL form factors are complex
A Zichichi S M Berman N Cabibbo R Gatto Il Nuovo Cimento XXIV 170 (1962)B Bilenkii C Giunti V Wataghin Z Phys C 59 475 (1993)G Gakh ET-G Nucl Phys A761120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
Unpolarized cross section
bull Induces four new termsbull Odd function of q bull Does not contribute at q =90deg
Two Photon Exchange
MP Rekalo and E T-G EPJA 22 331 (2004)GI Gakh and E T-G NPA761 120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullProperties of the TPE amplitudes with respect to the transformation cos q = - cos q ie q - q
(equivalent to non-linearity in Rosenbluth fit)
bullBased on these properties one can remove or single out TPE contribution
Symmetry relations
E T-G G Gakh NPA (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullDifferential cross section at complementary angles
Symmetry relations (annihilation)
The DIFFERENCE enhances the 2g contribution
The SUM cancels the 2g contribution
Egle Tomasi-Gustafsson Gatchina July 10 2012
What do data say
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Return (ISR)
s
m
x
sin
xxx
)xs(W
s
m
s
Ex)m)(ppee()xs(W
sm
cosddm)ppee(d
eq
-
q
-a
q
-sqq
gs g--
222
122
2
2
2
2
e+ +e- p + p + g
B Aubert ( BABAR Collaboration) Phys Rev D73 012005 (2006)
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
1g-2g interference
M P Rekalo E T-G and D Prout Phys Rev C60 042202 (1999)
CA DA
Egle Tomasi-Gustafsson Gatchina July 10 2012
From the data deviation from linearity ltlt 1
Parametrization of 2g-contribution for e+p
E T-G G Gakh Phys Rev C 72 015209 (2005)
)(11)( 2)(2 QfQF a
-
222222
]1[ a
Dγ(a)
m[GeV]QGC
)(Qf
e+4He scattering
Spin 0 particle F(q2) in Born approximation
2g exchange F1(sq2)F2(sq2)=F(q2) +f(sq2)
F(q2)~a0 F1(sq2)~a
Egle Tomasi-Gustafsson Gatchina July 10 2012
GI Gakh and E T-G NuclPhys A838 (2010) 50-60
Linear fit to e+4He elastic scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
GI Gakh and E T-G NuclPhys A838 (2010) 50-60
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull One-photon exchange - Two form factors (real in SL complex in TL) - Functions of one variable (t)
16 amplitudes in the general caseP- and T-invariance of EM interaction
helicity conservation
Interaction of 4 spin frac12 fermions
bullTwo-photon exchange
- Three (complex) amplitudes - Functions of two variables (st)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Space-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
Possible but difficult
Egle Tomasi-Gustafsson Gatchina July 10 2012
Determination of EM form factors in presence of 2g exchange
-electron and positron beams
- longitudinally polarized - in identical kinematical
conditions
M P Rekalo E T-G EPJA (2004) Nucl Phys A (2003)
Model independent considerations foreplusmn N scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
Model independent considerations foreplusmn N scattering
Determination of EM form factors in presence of 2g exchange- electron and positron beams
- longitudinally polarized - in identical kinematical conditions
Generalization of the polarization method (A Akhiezer and MP Rekalo)
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
bull Ay unpolarized leptons transversally polarized target or Py outgoing nucleon polarization with unpolarized leptons unpolarized target
bull Depolarization tensor (Dab) dependence of the
b-component of the final nucleon polarization on the a-component of the nucleon target with longitudinally polarized leptons
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Very difficult experimentsThree T-odd polarization observableshellipExpected small of the order of a triple spin correlations buthellip Model independent way
This ratio contains the lsquoTRUE lsquoform factors
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellipor five T-even polarization observableshellip among dsdW Px(le) Pz(le) Dxx Dyy Dzz Dxz
Again very difficult experiments
Only Model independent ways (without positron beams)M P Rekalo and E T-G Nucl Phys A740 (2004) 271
M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
Time-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
much easier
Time-like observables | GE| 2 and | GM| 2
As in SL region- Dependence on q2 contained in FFs- Even dependence on cos2q (1g exchange)- No dependence on sign of FFs- Enhancement of magnetic term
but TL form factors are complex
A Zichichi S M Berman N Cabibbo R Gatto Il Nuovo Cimento XXIV 170 (1962)B Bilenkii C Giunti V Wataghin Z Phys C 59 475 (1993)G Gakh ET-G Nucl Phys A761120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
Unpolarized cross section
bull Induces four new termsbull Odd function of q bull Does not contribute at q =90deg
Two Photon Exchange
MP Rekalo and E T-G EPJA 22 331 (2004)GI Gakh and E T-G NPA761 120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullProperties of the TPE amplitudes with respect to the transformation cos q = - cos q ie q - q
(equivalent to non-linearity in Rosenbluth fit)
bullBased on these properties one can remove or single out TPE contribution
Symmetry relations
E T-G G Gakh NPA (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullDifferential cross section at complementary angles
Symmetry relations (annihilation)
The DIFFERENCE enhances the 2g contribution
The SUM cancels the 2g contribution
Egle Tomasi-Gustafsson Gatchina July 10 2012
What do data say
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Return (ISR)
s
m
x
sin
xxx
)xs(W
s
m
s
Ex)m)(ppee()xs(W
sm
cosddm)ppee(d
eq
-
q
-a
q
-sqq
gs g--
222
122
2
2
2
2
e+ +e- p + p + g
B Aubert ( BABAR Collaboration) Phys Rev D73 012005 (2006)
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
From the data deviation from linearity ltlt 1
Parametrization of 2g-contribution for e+p
E T-G G Gakh Phys Rev C 72 015209 (2005)
)(11)( 2)(2 QfQF a
-
222222
]1[ a
Dγ(a)
m[GeV]QGC
)(Qf
e+4He scattering
Spin 0 particle F(q2) in Born approximation
2g exchange F1(sq2)F2(sq2)=F(q2) +f(sq2)
F(q2)~a0 F1(sq2)~a
Egle Tomasi-Gustafsson Gatchina July 10 2012
GI Gakh and E T-G NuclPhys A838 (2010) 50-60
Linear fit to e+4He elastic scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
GI Gakh and E T-G NuclPhys A838 (2010) 50-60
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull One-photon exchange - Two form factors (real in SL complex in TL) - Functions of one variable (t)
16 amplitudes in the general caseP- and T-invariance of EM interaction
helicity conservation
Interaction of 4 spin frac12 fermions
bullTwo-photon exchange
- Three (complex) amplitudes - Functions of two variables (st)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Space-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
Possible but difficult
Egle Tomasi-Gustafsson Gatchina July 10 2012
Determination of EM form factors in presence of 2g exchange
-electron and positron beams
- longitudinally polarized - in identical kinematical
conditions
M P Rekalo E T-G EPJA (2004) Nucl Phys A (2003)
Model independent considerations foreplusmn N scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
Model independent considerations foreplusmn N scattering
Determination of EM form factors in presence of 2g exchange- electron and positron beams
- longitudinally polarized - in identical kinematical conditions
Generalization of the polarization method (A Akhiezer and MP Rekalo)
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
bull Ay unpolarized leptons transversally polarized target or Py outgoing nucleon polarization with unpolarized leptons unpolarized target
bull Depolarization tensor (Dab) dependence of the
b-component of the final nucleon polarization on the a-component of the nucleon target with longitudinally polarized leptons
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Very difficult experimentsThree T-odd polarization observableshellipExpected small of the order of a triple spin correlations buthellip Model independent way
This ratio contains the lsquoTRUE lsquoform factors
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellipor five T-even polarization observableshellip among dsdW Px(le) Pz(le) Dxx Dyy Dzz Dxz
Again very difficult experiments
Only Model independent ways (without positron beams)M P Rekalo and E T-G Nucl Phys A740 (2004) 271
M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
Time-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
much easier
Time-like observables | GE| 2 and | GM| 2
As in SL region- Dependence on q2 contained in FFs- Even dependence on cos2q (1g exchange)- No dependence on sign of FFs- Enhancement of magnetic term
but TL form factors are complex
A Zichichi S M Berman N Cabibbo R Gatto Il Nuovo Cimento XXIV 170 (1962)B Bilenkii C Giunti V Wataghin Z Phys C 59 475 (1993)G Gakh ET-G Nucl Phys A761120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
Unpolarized cross section
bull Induces four new termsbull Odd function of q bull Does not contribute at q =90deg
Two Photon Exchange
MP Rekalo and E T-G EPJA 22 331 (2004)GI Gakh and E T-G NPA761 120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullProperties of the TPE amplitudes with respect to the transformation cos q = - cos q ie q - q
(equivalent to non-linearity in Rosenbluth fit)
bullBased on these properties one can remove or single out TPE contribution
Symmetry relations
E T-G G Gakh NPA (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullDifferential cross section at complementary angles
Symmetry relations (annihilation)
The DIFFERENCE enhances the 2g contribution
The SUM cancels the 2g contribution
Egle Tomasi-Gustafsson Gatchina July 10 2012
What do data say
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Return (ISR)
s
m
x
sin
xxx
)xs(W
s
m
s
Ex)m)(ppee()xs(W
sm
cosddm)ppee(d
eq
-
q
-a
q
-sqq
gs g--
222
122
2
2
2
2
e+ +e- p + p + g
B Aubert ( BABAR Collaboration) Phys Rev D73 012005 (2006)
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
e+4He scattering
Spin 0 particle F(q2) in Born approximation
2g exchange F1(sq2)F2(sq2)=F(q2) +f(sq2)
F(q2)~a0 F1(sq2)~a
Egle Tomasi-Gustafsson Gatchina July 10 2012
GI Gakh and E T-G NuclPhys A838 (2010) 50-60
Linear fit to e+4He elastic scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
GI Gakh and E T-G NuclPhys A838 (2010) 50-60
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull One-photon exchange - Two form factors (real in SL complex in TL) - Functions of one variable (t)
16 amplitudes in the general caseP- and T-invariance of EM interaction
helicity conservation
Interaction of 4 spin frac12 fermions
bullTwo-photon exchange
- Three (complex) amplitudes - Functions of two variables (st)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Space-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
Possible but difficult
Egle Tomasi-Gustafsson Gatchina July 10 2012
Determination of EM form factors in presence of 2g exchange
-electron and positron beams
- longitudinally polarized - in identical kinematical
conditions
M P Rekalo E T-G EPJA (2004) Nucl Phys A (2003)
Model independent considerations foreplusmn N scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
Model independent considerations foreplusmn N scattering
Determination of EM form factors in presence of 2g exchange- electron and positron beams
- longitudinally polarized - in identical kinematical conditions
Generalization of the polarization method (A Akhiezer and MP Rekalo)
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
bull Ay unpolarized leptons transversally polarized target or Py outgoing nucleon polarization with unpolarized leptons unpolarized target
bull Depolarization tensor (Dab) dependence of the
b-component of the final nucleon polarization on the a-component of the nucleon target with longitudinally polarized leptons
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Very difficult experimentsThree T-odd polarization observableshellipExpected small of the order of a triple spin correlations buthellip Model independent way
This ratio contains the lsquoTRUE lsquoform factors
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellipor five T-even polarization observableshellip among dsdW Px(le) Pz(le) Dxx Dyy Dzz Dxz
Again very difficult experiments
Only Model independent ways (without positron beams)M P Rekalo and E T-G Nucl Phys A740 (2004) 271
M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
Time-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
much easier
Time-like observables | GE| 2 and | GM| 2
As in SL region- Dependence on q2 contained in FFs- Even dependence on cos2q (1g exchange)- No dependence on sign of FFs- Enhancement of magnetic term
but TL form factors are complex
A Zichichi S M Berman N Cabibbo R Gatto Il Nuovo Cimento XXIV 170 (1962)B Bilenkii C Giunti V Wataghin Z Phys C 59 475 (1993)G Gakh ET-G Nucl Phys A761120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
Unpolarized cross section
bull Induces four new termsbull Odd function of q bull Does not contribute at q =90deg
Two Photon Exchange
MP Rekalo and E T-G EPJA 22 331 (2004)GI Gakh and E T-G NPA761 120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullProperties of the TPE amplitudes with respect to the transformation cos q = - cos q ie q - q
(equivalent to non-linearity in Rosenbluth fit)
bullBased on these properties one can remove or single out TPE contribution
Symmetry relations
E T-G G Gakh NPA (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullDifferential cross section at complementary angles
Symmetry relations (annihilation)
The DIFFERENCE enhances the 2g contribution
The SUM cancels the 2g contribution
Egle Tomasi-Gustafsson Gatchina July 10 2012
What do data say
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Return (ISR)
s
m
x
sin
xxx
)xs(W
s
m
s
Ex)m)(ppee()xs(W
sm
cosddm)ppee(d
eq
-
q
-a
q
-sqq
gs g--
222
122
2
2
2
2
e+ +e- p + p + g
B Aubert ( BABAR Collaboration) Phys Rev D73 012005 (2006)
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Linear fit to e+4He elastic scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
GI Gakh and E T-G NuclPhys A838 (2010) 50-60
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull One-photon exchange - Two form factors (real in SL complex in TL) - Functions of one variable (t)
16 amplitudes in the general caseP- and T-invariance of EM interaction
helicity conservation
Interaction of 4 spin frac12 fermions
bullTwo-photon exchange
- Three (complex) amplitudes - Functions of two variables (st)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Space-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
Possible but difficult
Egle Tomasi-Gustafsson Gatchina July 10 2012
Determination of EM form factors in presence of 2g exchange
-electron and positron beams
- longitudinally polarized - in identical kinematical
conditions
M P Rekalo E T-G EPJA (2004) Nucl Phys A (2003)
Model independent considerations foreplusmn N scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
Model independent considerations foreplusmn N scattering
Determination of EM form factors in presence of 2g exchange- electron and positron beams
- longitudinally polarized - in identical kinematical conditions
Generalization of the polarization method (A Akhiezer and MP Rekalo)
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
bull Ay unpolarized leptons transversally polarized target or Py outgoing nucleon polarization with unpolarized leptons unpolarized target
bull Depolarization tensor (Dab) dependence of the
b-component of the final nucleon polarization on the a-component of the nucleon target with longitudinally polarized leptons
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Very difficult experimentsThree T-odd polarization observableshellipExpected small of the order of a triple spin correlations buthellip Model independent way
This ratio contains the lsquoTRUE lsquoform factors
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellipor five T-even polarization observableshellip among dsdW Px(le) Pz(le) Dxx Dyy Dzz Dxz
Again very difficult experiments
Only Model independent ways (without positron beams)M P Rekalo and E T-G Nucl Phys A740 (2004) 271
M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
Time-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
much easier
Time-like observables | GE| 2 and | GM| 2
As in SL region- Dependence on q2 contained in FFs- Even dependence on cos2q (1g exchange)- No dependence on sign of FFs- Enhancement of magnetic term
but TL form factors are complex
A Zichichi S M Berman N Cabibbo R Gatto Il Nuovo Cimento XXIV 170 (1962)B Bilenkii C Giunti V Wataghin Z Phys C 59 475 (1993)G Gakh ET-G Nucl Phys A761120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
Unpolarized cross section
bull Induces four new termsbull Odd function of q bull Does not contribute at q =90deg
Two Photon Exchange
MP Rekalo and E T-G EPJA 22 331 (2004)GI Gakh and E T-G NPA761 120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullProperties of the TPE amplitudes with respect to the transformation cos q = - cos q ie q - q
(equivalent to non-linearity in Rosenbluth fit)
bullBased on these properties one can remove or single out TPE contribution
Symmetry relations
E T-G G Gakh NPA (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullDifferential cross section at complementary angles
Symmetry relations (annihilation)
The DIFFERENCE enhances the 2g contribution
The SUM cancels the 2g contribution
Egle Tomasi-Gustafsson Gatchina July 10 2012
What do data say
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Return (ISR)
s
m
x
sin
xxx
)xs(W
s
m
s
Ex)m)(ppee()xs(W
sm
cosddm)ppee(d
eq
-
q
-a
q
-sqq
gs g--
222
122
2
2
2
2
e+ +e- p + p + g
B Aubert ( BABAR Collaboration) Phys Rev D73 012005 (2006)
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull One-photon exchange - Two form factors (real in SL complex in TL) - Functions of one variable (t)
16 amplitudes in the general caseP- and T-invariance of EM interaction
helicity conservation
Interaction of 4 spin frac12 fermions
bullTwo-photon exchange
- Three (complex) amplitudes - Functions of two variables (st)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Space-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
Possible but difficult
Egle Tomasi-Gustafsson Gatchina July 10 2012
Determination of EM form factors in presence of 2g exchange
-electron and positron beams
- longitudinally polarized - in identical kinematical
conditions
M P Rekalo E T-G EPJA (2004) Nucl Phys A (2003)
Model independent considerations foreplusmn N scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
Model independent considerations foreplusmn N scattering
Determination of EM form factors in presence of 2g exchange- electron and positron beams
- longitudinally polarized - in identical kinematical conditions
Generalization of the polarization method (A Akhiezer and MP Rekalo)
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
bull Ay unpolarized leptons transversally polarized target or Py outgoing nucleon polarization with unpolarized leptons unpolarized target
bull Depolarization tensor (Dab) dependence of the
b-component of the final nucleon polarization on the a-component of the nucleon target with longitudinally polarized leptons
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Very difficult experimentsThree T-odd polarization observableshellipExpected small of the order of a triple spin correlations buthellip Model independent way
This ratio contains the lsquoTRUE lsquoform factors
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellipor five T-even polarization observableshellip among dsdW Px(le) Pz(le) Dxx Dyy Dzz Dxz
Again very difficult experiments
Only Model independent ways (without positron beams)M P Rekalo and E T-G Nucl Phys A740 (2004) 271
M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
Time-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
much easier
Time-like observables | GE| 2 and | GM| 2
As in SL region- Dependence on q2 contained in FFs- Even dependence on cos2q (1g exchange)- No dependence on sign of FFs- Enhancement of magnetic term
but TL form factors are complex
A Zichichi S M Berman N Cabibbo R Gatto Il Nuovo Cimento XXIV 170 (1962)B Bilenkii C Giunti V Wataghin Z Phys C 59 475 (1993)G Gakh ET-G Nucl Phys A761120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
Unpolarized cross section
bull Induces four new termsbull Odd function of q bull Does not contribute at q =90deg
Two Photon Exchange
MP Rekalo and E T-G EPJA 22 331 (2004)GI Gakh and E T-G NPA761 120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullProperties of the TPE amplitudes with respect to the transformation cos q = - cos q ie q - q
(equivalent to non-linearity in Rosenbluth fit)
bullBased on these properties one can remove or single out TPE contribution
Symmetry relations
E T-G G Gakh NPA (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullDifferential cross section at complementary angles
Symmetry relations (annihilation)
The DIFFERENCE enhances the 2g contribution
The SUM cancels the 2g contribution
Egle Tomasi-Gustafsson Gatchina July 10 2012
What do data say
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Return (ISR)
s
m
x
sin
xxx
)xs(W
s
m
s
Ex)m)(ppee()xs(W
sm
cosddm)ppee(d
eq
-
q
-a
q
-sqq
gs g--
222
122
2
2
2
2
e+ +e- p + p + g
B Aubert ( BABAR Collaboration) Phys Rev D73 012005 (2006)
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
Space-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
Possible but difficult
Egle Tomasi-Gustafsson Gatchina July 10 2012
Determination of EM form factors in presence of 2g exchange
-electron and positron beams
- longitudinally polarized - in identical kinematical
conditions
M P Rekalo E T-G EPJA (2004) Nucl Phys A (2003)
Model independent considerations foreplusmn N scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
Model independent considerations foreplusmn N scattering
Determination of EM form factors in presence of 2g exchange- electron and positron beams
- longitudinally polarized - in identical kinematical conditions
Generalization of the polarization method (A Akhiezer and MP Rekalo)
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
bull Ay unpolarized leptons transversally polarized target or Py outgoing nucleon polarization with unpolarized leptons unpolarized target
bull Depolarization tensor (Dab) dependence of the
b-component of the final nucleon polarization on the a-component of the nucleon target with longitudinally polarized leptons
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Very difficult experimentsThree T-odd polarization observableshellipExpected small of the order of a triple spin correlations buthellip Model independent way
This ratio contains the lsquoTRUE lsquoform factors
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellipor five T-even polarization observableshellip among dsdW Px(le) Pz(le) Dxx Dyy Dzz Dxz
Again very difficult experiments
Only Model independent ways (without positron beams)M P Rekalo and E T-G Nucl Phys A740 (2004) 271
M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
Time-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
much easier
Time-like observables | GE| 2 and | GM| 2
As in SL region- Dependence on q2 contained in FFs- Even dependence on cos2q (1g exchange)- No dependence on sign of FFs- Enhancement of magnetic term
but TL form factors are complex
A Zichichi S M Berman N Cabibbo R Gatto Il Nuovo Cimento XXIV 170 (1962)B Bilenkii C Giunti V Wataghin Z Phys C 59 475 (1993)G Gakh ET-G Nucl Phys A761120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
Unpolarized cross section
bull Induces four new termsbull Odd function of q bull Does not contribute at q =90deg
Two Photon Exchange
MP Rekalo and E T-G EPJA 22 331 (2004)GI Gakh and E T-G NPA761 120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullProperties of the TPE amplitudes with respect to the transformation cos q = - cos q ie q - q
(equivalent to non-linearity in Rosenbluth fit)
bullBased on these properties one can remove or single out TPE contribution
Symmetry relations
E T-G G Gakh NPA (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullDifferential cross section at complementary angles
Symmetry relations (annihilation)
The DIFFERENCE enhances the 2g contribution
The SUM cancels the 2g contribution
Egle Tomasi-Gustafsson Gatchina July 10 2012
What do data say
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Return (ISR)
s
m
x
sin
xxx
)xs(W
s
m
s
Ex)m)(ppee()xs(W
sm
cosddm)ppee(d
eq
-
q
-a
q
-sqq
gs g--
222
122
2
2
2
2
e+ +e- p + p + g
B Aubert ( BABAR Collaboration) Phys Rev D73 012005 (2006)
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
Determination of EM form factors in presence of 2g exchange
-electron and positron beams
- longitudinally polarized - in identical kinematical
conditions
M P Rekalo E T-G EPJA (2004) Nucl Phys A (2003)
Model independent considerations foreplusmn N scattering
Egle Tomasi-Gustafsson Gatchina July 10 2012
Model independent considerations foreplusmn N scattering
Determination of EM form factors in presence of 2g exchange- electron and positron beams
- longitudinally polarized - in identical kinematical conditions
Generalization of the polarization method (A Akhiezer and MP Rekalo)
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
bull Ay unpolarized leptons transversally polarized target or Py outgoing nucleon polarization with unpolarized leptons unpolarized target
bull Depolarization tensor (Dab) dependence of the
b-component of the final nucleon polarization on the a-component of the nucleon target with longitudinally polarized leptons
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Very difficult experimentsThree T-odd polarization observableshellipExpected small of the order of a triple spin correlations buthellip Model independent way
This ratio contains the lsquoTRUE lsquoform factors
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellipor five T-even polarization observableshellip among dsdW Px(le) Pz(le) Dxx Dyy Dzz Dxz
Again very difficult experiments
Only Model independent ways (without positron beams)M P Rekalo and E T-G Nucl Phys A740 (2004) 271
M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
Time-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
much easier
Time-like observables | GE| 2 and | GM| 2
As in SL region- Dependence on q2 contained in FFs- Even dependence on cos2q (1g exchange)- No dependence on sign of FFs- Enhancement of magnetic term
but TL form factors are complex
A Zichichi S M Berman N Cabibbo R Gatto Il Nuovo Cimento XXIV 170 (1962)B Bilenkii C Giunti V Wataghin Z Phys C 59 475 (1993)G Gakh ET-G Nucl Phys A761120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
Unpolarized cross section
bull Induces four new termsbull Odd function of q bull Does not contribute at q =90deg
Two Photon Exchange
MP Rekalo and E T-G EPJA 22 331 (2004)GI Gakh and E T-G NPA761 120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullProperties of the TPE amplitudes with respect to the transformation cos q = - cos q ie q - q
(equivalent to non-linearity in Rosenbluth fit)
bullBased on these properties one can remove or single out TPE contribution
Symmetry relations
E T-G G Gakh NPA (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullDifferential cross section at complementary angles
Symmetry relations (annihilation)
The DIFFERENCE enhances the 2g contribution
The SUM cancels the 2g contribution
Egle Tomasi-Gustafsson Gatchina July 10 2012
What do data say
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Return (ISR)
s
m
x
sin
xxx
)xs(W
s
m
s
Ex)m)(ppee()xs(W
sm
cosddm)ppee(d
eq
-
q
-a
q
-sqq
gs g--
222
122
2
2
2
2
e+ +e- p + p + g
B Aubert ( BABAR Collaboration) Phys Rev D73 012005 (2006)
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
Model independent considerations foreplusmn N scattering
Determination of EM form factors in presence of 2g exchange- electron and positron beams
- longitudinally polarized - in identical kinematical conditions
Generalization of the polarization method (A Akhiezer and MP Rekalo)
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
bull Ay unpolarized leptons transversally polarized target or Py outgoing nucleon polarization with unpolarized leptons unpolarized target
bull Depolarization tensor (Dab) dependence of the
b-component of the final nucleon polarization on the a-component of the nucleon target with longitudinally polarized leptons
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Very difficult experimentsThree T-odd polarization observableshellipExpected small of the order of a triple spin correlations buthellip Model independent way
This ratio contains the lsquoTRUE lsquoform factors
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellipor five T-even polarization observableshellip among dsdW Px(le) Pz(le) Dxx Dyy Dzz Dxz
Again very difficult experiments
Only Model independent ways (without positron beams)M P Rekalo and E T-G Nucl Phys A740 (2004) 271
M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
Time-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
much easier
Time-like observables | GE| 2 and | GM| 2
As in SL region- Dependence on q2 contained in FFs- Even dependence on cos2q (1g exchange)- No dependence on sign of FFs- Enhancement of magnetic term
but TL form factors are complex
A Zichichi S M Berman N Cabibbo R Gatto Il Nuovo Cimento XXIV 170 (1962)B Bilenkii C Giunti V Wataghin Z Phys C 59 475 (1993)G Gakh ET-G Nucl Phys A761120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
Unpolarized cross section
bull Induces four new termsbull Odd function of q bull Does not contribute at q =90deg
Two Photon Exchange
MP Rekalo and E T-G EPJA 22 331 (2004)GI Gakh and E T-G NPA761 120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullProperties of the TPE amplitudes with respect to the transformation cos q = - cos q ie q - q
(equivalent to non-linearity in Rosenbluth fit)
bullBased on these properties one can remove or single out TPE contribution
Symmetry relations
E T-G G Gakh NPA (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullDifferential cross section at complementary angles
Symmetry relations (annihilation)
The DIFFERENCE enhances the 2g contribution
The SUM cancels the 2g contribution
Egle Tomasi-Gustafsson Gatchina July 10 2012
What do data say
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Return (ISR)
s
m
x
sin
xxx
)xs(W
s
m
s
Ex)m)(ppee()xs(W
sm
cosddm)ppee(d
eq
-
q
-a
q
-sqq
gs g--
222
122
2
2
2
2
e+ +e- p + p + g
B Aubert ( BABAR Collaboration) Phys Rev D73 012005 (2006)
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
bull Ay unpolarized leptons transversally polarized target or Py outgoing nucleon polarization with unpolarized leptons unpolarized target
bull Depolarization tensor (Dab) dependence of the
b-component of the final nucleon polarization on the a-component of the nucleon target with longitudinally polarized leptons
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Very difficult experimentsThree T-odd polarization observableshellipExpected small of the order of a triple spin correlations buthellip Model independent way
This ratio contains the lsquoTRUE lsquoform factors
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellipor five T-even polarization observableshellip among dsdW Px(le) Pz(le) Dxx Dyy Dzz Dxz
Again very difficult experiments
Only Model independent ways (without positron beams)M P Rekalo and E T-G Nucl Phys A740 (2004) 271
M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
Time-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
much easier
Time-like observables | GE| 2 and | GM| 2
As in SL region- Dependence on q2 contained in FFs- Even dependence on cos2q (1g exchange)- No dependence on sign of FFs- Enhancement of magnetic term
but TL form factors are complex
A Zichichi S M Berman N Cabibbo R Gatto Il Nuovo Cimento XXIV 170 (1962)B Bilenkii C Giunti V Wataghin Z Phys C 59 475 (1993)G Gakh ET-G Nucl Phys A761120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
Unpolarized cross section
bull Induces four new termsbull Odd function of q bull Does not contribute at q =90deg
Two Photon Exchange
MP Rekalo and E T-G EPJA 22 331 (2004)GI Gakh and E T-G NPA761 120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullProperties of the TPE amplitudes with respect to the transformation cos q = - cos q ie q - q
(equivalent to non-linearity in Rosenbluth fit)
bullBased on these properties one can remove or single out TPE contribution
Symmetry relations
E T-G G Gakh NPA (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullDifferential cross section at complementary angles
Symmetry relations (annihilation)
The DIFFERENCE enhances the 2g contribution
The SUM cancels the 2g contribution
Egle Tomasi-Gustafsson Gatchina July 10 2012
What do data say
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Return (ISR)
s
m
x
sin
xxx
)xs(W
s
m
s
Ex)m)(ppee()xs(W
sm
cosddm)ppee(d
eq
-
q
-a
q
-sqq
gs g--
222
122
2
2
2
2
e+ +e- p + p + g
B Aubert ( BABAR Collaboration) Phys Rev D73 012005 (2006)
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellip
M P Rekalo and E T-G Nucl Phys A740 (2004) 271 M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Very difficult experimentsThree T-odd polarization observableshellipExpected small of the order of a triple spin correlations buthellip Model independent way
This ratio contains the lsquoTRUE lsquoform factors
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellipor five T-even polarization observableshellip among dsdW Px(le) Pz(le) Dxx Dyy Dzz Dxz
Again very difficult experiments
Only Model independent ways (without positron beams)M P Rekalo and E T-G Nucl Phys A740 (2004) 271
M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
Time-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
much easier
Time-like observables | GE| 2 and | GM| 2
As in SL region- Dependence on q2 contained in FFs- Even dependence on cos2q (1g exchange)- No dependence on sign of FFs- Enhancement of magnetic term
but TL form factors are complex
A Zichichi S M Berman N Cabibbo R Gatto Il Nuovo Cimento XXIV 170 (1962)B Bilenkii C Giunti V Wataghin Z Phys C 59 475 (1993)G Gakh ET-G Nucl Phys A761120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
Unpolarized cross section
bull Induces four new termsbull Odd function of q bull Does not contribute at q =90deg
Two Photon Exchange
MP Rekalo and E T-G EPJA 22 331 (2004)GI Gakh and E T-G NPA761 120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullProperties of the TPE amplitudes with respect to the transformation cos q = - cos q ie q - q
(equivalent to non-linearity in Rosenbluth fit)
bullBased on these properties one can remove or single out TPE contribution
Symmetry relations
E T-G G Gakh NPA (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullDifferential cross section at complementary angles
Symmetry relations (annihilation)
The DIFFERENCE enhances the 2g contribution
The SUM cancels the 2g contribution
Egle Tomasi-Gustafsson Gatchina July 10 2012
What do data say
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Return (ISR)
s
m
x
sin
xxx
)xs(W
s
m
s
Ex)m)(ppee()xs(W
sm
cosddm)ppee(d
eq
-
q
-a
q
-sqq
gs g--
222
122
2
2
2
2
e+ +e- p + p + g
B Aubert ( BABAR Collaboration) Phys Rev D73 012005 (2006)
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Very difficult experimentsThree T-odd polarization observableshellipExpected small of the order of a triple spin correlations buthellip Model independent way
This ratio contains the lsquoTRUE lsquoform factors
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellipor five T-even polarization observableshellip among dsdW Px(le) Pz(le) Dxx Dyy Dzz Dxz
Again very difficult experiments
Only Model independent ways (without positron beams)M P Rekalo and E T-G Nucl Phys A740 (2004) 271
M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
Time-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
much easier
Time-like observables | GE| 2 and | GM| 2
As in SL region- Dependence on q2 contained in FFs- Even dependence on cos2q (1g exchange)- No dependence on sign of FFs- Enhancement of magnetic term
but TL form factors are complex
A Zichichi S M Berman N Cabibbo R Gatto Il Nuovo Cimento XXIV 170 (1962)B Bilenkii C Giunti V Wataghin Z Phys C 59 475 (1993)G Gakh ET-G Nucl Phys A761120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
Unpolarized cross section
bull Induces four new termsbull Odd function of q bull Does not contribute at q =90deg
Two Photon Exchange
MP Rekalo and E T-G EPJA 22 331 (2004)GI Gakh and E T-G NPA761 120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullProperties of the TPE amplitudes with respect to the transformation cos q = - cos q ie q - q
(equivalent to non-linearity in Rosenbluth fit)
bullBased on these properties one can remove or single out TPE contribution
Symmetry relations
E T-G G Gakh NPA (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullDifferential cross section at complementary angles
Symmetry relations (annihilation)
The DIFFERENCE enhances the 2g contribution
The SUM cancels the 2g contribution
Egle Tomasi-Gustafsson Gatchina July 10 2012
What do data say
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Return (ISR)
s
m
x
sin
xxx
)xs(W
s
m
s
Ex)m)(ppee()xs(W
sm
cosddm)ppee(d
eq
-
q
-a
q
-sqq
gs g--
222
122
2
2
2
2
e+ +e- p + p + g
B Aubert ( BABAR Collaboration) Phys Rev D73 012005 (2006)
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
If no positron beamhellip
Either three T-odd polarization observableshellipor five T-even polarization observableshellip among dsdW Px(le) Pz(le) Dxx Dyy Dzz Dxz
Again very difficult experiments
Only Model independent ways (without positron beams)M P Rekalo and E T-G Nucl Phys A740 (2004) 271
M P Rekalo and E T-G Nucl Phys A742 (2004) 322
Egle Tomasi-Gustafsson Gatchina July 10 2012
Time-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
much easier
Time-like observables | GE| 2 and | GM| 2
As in SL region- Dependence on q2 contained in FFs- Even dependence on cos2q (1g exchange)- No dependence on sign of FFs- Enhancement of magnetic term
but TL form factors are complex
A Zichichi S M Berman N Cabibbo R Gatto Il Nuovo Cimento XXIV 170 (1962)B Bilenkii C Giunti V Wataghin Z Phys C 59 475 (1993)G Gakh ET-G Nucl Phys A761120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
Unpolarized cross section
bull Induces four new termsbull Odd function of q bull Does not contribute at q =90deg
Two Photon Exchange
MP Rekalo and E T-G EPJA 22 331 (2004)GI Gakh and E T-G NPA761 120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullProperties of the TPE amplitudes with respect to the transformation cos q = - cos q ie q - q
(equivalent to non-linearity in Rosenbluth fit)
bullBased on these properties one can remove or single out TPE contribution
Symmetry relations
E T-G G Gakh NPA (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullDifferential cross section at complementary angles
Symmetry relations (annihilation)
The DIFFERENCE enhances the 2g contribution
The SUM cancels the 2g contribution
Egle Tomasi-Gustafsson Gatchina July 10 2012
What do data say
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Return (ISR)
s
m
x
sin
xxx
)xs(W
s
m
s
Ex)m)(ppee()xs(W
sm
cosddm)ppee(d
eq
-
q
-a
q
-sqq
gs g--
222
122
2
2
2
2
e+ +e- p + p + g
B Aubert ( BABAR Collaboration) Phys Rev D73 012005 (2006)
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
Time-like region
Is it still possible to extract the laquo real raquo FFs in presence of 2g exchange
much easier
Time-like observables | GE| 2 and | GM| 2
As in SL region- Dependence on q2 contained in FFs- Even dependence on cos2q (1g exchange)- No dependence on sign of FFs- Enhancement of magnetic term
but TL form factors are complex
A Zichichi S M Berman N Cabibbo R Gatto Il Nuovo Cimento XXIV 170 (1962)B Bilenkii C Giunti V Wataghin Z Phys C 59 475 (1993)G Gakh ET-G Nucl Phys A761120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
Unpolarized cross section
bull Induces four new termsbull Odd function of q bull Does not contribute at q =90deg
Two Photon Exchange
MP Rekalo and E T-G EPJA 22 331 (2004)GI Gakh and E T-G NPA761 120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullProperties of the TPE amplitudes with respect to the transformation cos q = - cos q ie q - q
(equivalent to non-linearity in Rosenbluth fit)
bullBased on these properties one can remove or single out TPE contribution
Symmetry relations
E T-G G Gakh NPA (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullDifferential cross section at complementary angles
Symmetry relations (annihilation)
The DIFFERENCE enhances the 2g contribution
The SUM cancels the 2g contribution
Egle Tomasi-Gustafsson Gatchina July 10 2012
What do data say
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Return (ISR)
s
m
x
sin
xxx
)xs(W
s
m
s
Ex)m)(ppee()xs(W
sm
cosddm)ppee(d
eq
-
q
-a
q
-sqq
gs g--
222
122
2
2
2
2
e+ +e- p + p + g
B Aubert ( BABAR Collaboration) Phys Rev D73 012005 (2006)
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Time-like observables | GE| 2 and | GM| 2
As in SL region- Dependence on q2 contained in FFs- Even dependence on cos2q (1g exchange)- No dependence on sign of FFs- Enhancement of magnetic term
but TL form factors are complex
A Zichichi S M Berman N Cabibbo R Gatto Il Nuovo Cimento XXIV 170 (1962)B Bilenkii C Giunti V Wataghin Z Phys C 59 475 (1993)G Gakh ET-G Nucl Phys A761120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
Unpolarized cross section
bull Induces four new termsbull Odd function of q bull Does not contribute at q =90deg
Two Photon Exchange
MP Rekalo and E T-G EPJA 22 331 (2004)GI Gakh and E T-G NPA761 120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullProperties of the TPE amplitudes with respect to the transformation cos q = - cos q ie q - q
(equivalent to non-linearity in Rosenbluth fit)
bullBased on these properties one can remove or single out TPE contribution
Symmetry relations
E T-G G Gakh NPA (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullDifferential cross section at complementary angles
Symmetry relations (annihilation)
The DIFFERENCE enhances the 2g contribution
The SUM cancels the 2g contribution
Egle Tomasi-Gustafsson Gatchina July 10 2012
What do data say
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Return (ISR)
s
m
x
sin
xxx
)xs(W
s
m
s
Ex)m)(ppee()xs(W
sm
cosddm)ppee(d
eq
-
q
-a
q
-sqq
gs g--
222
122
2
2
2
2
e+ +e- p + p + g
B Aubert ( BABAR Collaboration) Phys Rev D73 012005 (2006)
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
Unpolarized cross section
bull Induces four new termsbull Odd function of q bull Does not contribute at q =90deg
Two Photon Exchange
MP Rekalo and E T-G EPJA 22 331 (2004)GI Gakh and E T-G NPA761 120 (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullProperties of the TPE amplitudes with respect to the transformation cos q = - cos q ie q - q
(equivalent to non-linearity in Rosenbluth fit)
bullBased on these properties one can remove or single out TPE contribution
Symmetry relations
E T-G G Gakh NPA (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullDifferential cross section at complementary angles
Symmetry relations (annihilation)
The DIFFERENCE enhances the 2g contribution
The SUM cancels the 2g contribution
Egle Tomasi-Gustafsson Gatchina July 10 2012
What do data say
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Return (ISR)
s
m
x
sin
xxx
)xs(W
s
m
s
Ex)m)(ppee()xs(W
sm
cosddm)ppee(d
eq
-
q
-a
q
-sqq
gs g--
222
122
2
2
2
2
e+ +e- p + p + g
B Aubert ( BABAR Collaboration) Phys Rev D73 012005 (2006)
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullProperties of the TPE amplitudes with respect to the transformation cos q = - cos q ie q - q
(equivalent to non-linearity in Rosenbluth fit)
bullBased on these properties one can remove or single out TPE contribution
Symmetry relations
E T-G G Gakh NPA (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullDifferential cross section at complementary angles
Symmetry relations (annihilation)
The DIFFERENCE enhances the 2g contribution
The SUM cancels the 2g contribution
Egle Tomasi-Gustafsson Gatchina July 10 2012
What do data say
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Return (ISR)
s
m
x
sin
xxx
)xs(W
s
m
s
Ex)m)(ppee()xs(W
sm
cosddm)ppee(d
eq
-
q
-a
q
-sqq
gs g--
222
122
2
2
2
2
e+ +e- p + p + g
B Aubert ( BABAR Collaboration) Phys Rev D73 012005 (2006)
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
bullDifferential cross section at complementary angles
Symmetry relations (annihilation)
The DIFFERENCE enhances the 2g contribution
The SUM cancels the 2g contribution
Egle Tomasi-Gustafsson Gatchina July 10 2012
What do data say
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Return (ISR)
s
m
x
sin
xxx
)xs(W
s
m
s
Ex)m)(ppee()xs(W
sm
cosddm)ppee(d
eq
-
q
-a
q
-sqq
gs g--
222
122
2
2
2
2
e+ +e- p + p + g
B Aubert ( BABAR Collaboration) Phys Rev D73 012005 (2006)
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
What do data say
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Return (ISR)
s
m
x
sin
xxx
)xs(W
s
m
s
Ex)m)(ppee()xs(W
sm
cosddm)ppee(d
eq
-
q
-a
q
-sqq
gs g--
222
122
2
2
2
2
e+ +e- p + p + g
B Aubert ( BABAR Collaboration) Phys Rev D73 012005 (2006)
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Return (ISR)
s
m
x
sin
xxx
)xs(W
s
m
s
Ex)m)(ppee()xs(W
sm
cosddm)ppee(d
eq
-
q
-a
q
-sqq
gs g--
222
122
2
2
2
2
e+ +e- p + p + g
B Aubert ( BABAR Collaboration) Phys Rev D73 012005 (2006)
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
1877divide1950
Angular distribution
Eve
nts
02
vs c
os q
2400divide30002200divide24002100divide2200
2025divide21001950divide2025
2g-exchange
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
Angular Asymmetry
Mpp=1877-19
A=001plusmn002
Mpp=24-3
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
Structure Function method
e+ +e- p + p + g
DE=005
E T-G EA Kuraev S Bakmaev S Pacetti Phys Lett B (2008)
EA Kuraev V Meledin Nucl Phys B
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
Cross section at 900 Angular asymmetry
The form of the differential cross section
is equivalent to
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
Fitting the angular distributions
E T-G and M P Rekalo Phys Lett B 504 291 (2001)
1 g exchange
Linear Fit in cos2q
2 g exchange Quadratic Fit in x=cosq
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 0
Fitting the angular distributions
ForwardBackward
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 002
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 005
Fitting the angular distributions
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
q2=54 GeV2
2g 020
Fitting the angular distributionshellip
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
Which alternative for Gep
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Polarization experiments - JlabAI Akhiezer and MP Rekalo 1967
GEp collaboration1) standard dipole function
for the nucleon magnetic FFs GMp and GMn
2) linear deviation from the dipole function for the electric proton FF Gep
3) QCD scaling not reached3) Zero crossing of Gep4) contradiction between
polarized and unpolarized measurements
AJR Puckett et al PRL (2010)
PRC85 (2012) 045203
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
WHY these points are aligned
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
Rosenbluth separation
=05=02
=08
Contribution of the electric term
hellipto be compared to the absolute value of the error on s and to the size and dependence of RC
ET-G Phys Part Nucl Lett 4 281 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
Reduced cross section and RCData from L Andivahis et al Phys Rev D50 5491 (1994)
Q2=175 GeV2
Q2=5 GeV2
Q2=325 GeV2
Q2=4 GeV2
Q2=25 GeV2
Q2=7 GeV2
Q2=6 GeV2
Radiative Corrected data
Raw data without RC
Slope from P M
E T-G G Gakh Phys Rev C (2005)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
Radiative Corrections (ep)
RC to the cross section- large (may reach 40)- and Q2 dependent- calculated at first order
May change the slope of sR
(and even the sign )Q2=5 GeV2
Q2=375 GeV2
Q2=175 GeV2
Andivahis et al PRD50 5491 (1994)2MG2
EGR s
CF Perdrisat Progr Part Nucl Phys 59694 (2007)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
Experimental correlationsel=smeas RC
Q2 gt 2 GeV2Q2 lt 2 GeV2
RC()only published values
Correlation (ltRCbull)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
Scattered electron energy
All orders of PT needed beyond Mo amp Tsai approximation
Initial state emission
final state emission
Quasi-elastic scattering
3
Y0
Not so smallShift to LOWER Q2
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Polarization ratio (-dependence)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull DATA No evidence of -dependence at 1 level
bull MODELS large correction (opposite sign) at small ε
bullTheory corrections to the Born approximation at Q2= 25 GeV2 Y Bystritskiy EA Kuraev and ET-G PhysRevC75 015207 (2007) P Blunden et al Phys Rev C72034612 (2005) (mainly GM) A Afanasev et al Phys Rev D72013008 (2005) (mainly GE) NKivel and MVanderhaeghen Phys Rev Lett103092004 (2009) (high Q2)
bull SF method -independent corrections
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
SummaryOur Suggestion for search of 2g effectsbull Search for model independent statements (MP Rekalo G Gakh)
bull Exact calculation in frame of QED (p~m)bull Prove that QED box is upper limit of QCD box diagrambull Study analytical properties of the Compton amplitudebull Compare to experimental dataOur Conclusions for elastic ep scatteringbull Two photon contribution is negligible (real part) (EA Kuraev)bull Radiative corrections are huge take into account higher order effects (Structure Functions method) ) (Yu Bystricky)
Look for Multiple Photon Exchange in e-A scatteringbull Small angle e or p or pbar - Heavy ion scatteringEA Kuraev M Shatnev ET-G PRC80 (2009) 018201
2g effects are expected to be larger in TL region (complex nature)
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
The Pauli and Dirac Form Factors
Normalization
F1p(0)=1 F2p(0)= κp
GEp(0)=1 GMp(0)=μp=279
The electromagnetic current in terms of the Pauli and Dirac FFs
Related to the Sachs FFs
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Systematics
Egle Tomasi-Gustafsson Gatchina July 10 2012
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Differential cross section (SF)
Egle Tomasi-Gustafsson Gatchina July 10 2012
bull The structure function of the lepton
Energy fractions of the leptons
Partition function
Odd term
K-factor
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Charge Asymmetry
Egle Tomasi-Gustafsson Gatchina July 10 2012
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
K-factor (hard)
1 of the order of one2 from the even part of the cross section
cos q
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Radiative correction factor
Egle Tomasi-Gustafsson Gatchina July 10 2012
s=10 GeV2
cos q
NcorrNraw(1d)
d
Integrated in all phase space for gProton structureless
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Imaginary part of the 2g amplitude
electronproton
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
QED versus QCD
Q2=005 GeV2
Q2=12 GeV2
Q2=2 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
Interference of 1g 2g exchange
bullExplicit calculation for structureless proton ndash The contribution is small for unpolarized
and polarized ep scatteringndash Does not contain the enhancement factor
L ndash The relevant contribution to K is ~ 1
bull em (elastic) scattering is upper limit for epEAKuraev V Bytev Yu Bystricky ET-G Phys Rev D74 013003 (1076)
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
Simulations
Approximationsbull Neglect contributions to GEGMbull Consider only real part
Main effect odd cosq-distribution
2003 MGF
0203 MGF
03 MGF
0503 MGF
q2=5482138 GeV2
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
002q2=54 GeV2
q2= 82 GeV2
q2=138 GeV2
005 0201g 2g
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-
Egle Tomasi-Gustafsson Gatchina July 10 2012
N=a0+a2cosq sinq +a1 cos2q a2~2g
- Model dependent and model independent considerations on two
- Slide 2
- Two-Photon exchange
- Qualitative estimation of 2g exchange
- Two-Photon exchange in ed-scatterng
- Crossing Symmetry
- 1g-2g interference
- The 1g-2g interference destroys the linearity of the Rosenblu
- 1g-2g interference (2)
- Slide 10
- e+4He scattering
- Linear fit to e+4He elastic scattering
- Slide 13
- Slide 14
- Slide 15
- Model independent considerations for eplusmn N scattering
- If no positron beamhellip
- If no positron beamhellip (2)
- If no positron beamhellip (3)
- If no positron beamhellip (4)
- Slide 21
- Time-like observables | GE| 2 and | GM| 2
- Unpolarized cross section
- Symmetry relations
- Symmetry relations (annihilation)
- What do data say
- Radiative Return (ISR)
- Angular distribution
- Angular Asymmetry
- Structure Function method
- Fitting the angular distributions
- Fitting the angular distributions (2)
- Fitting the angular distributions (3)
- Fitting the angular distributions (4)
- Fitting the angular distributions (5)
- Fitting the angular distributionshellip
- Which alternative for Gep
- Slide 38
- Slide 39
- Rosenbluth separation
- Reduced cross section and RC
- Radiative Corrections (ep)
- Experimental correlation
- Scattered electron energy
- Polarization ratio (e-dependence)
- Summary
- The Pauli and Dirac Form Factors
- Systematics
- Differential cross section (SF)
- Charge Asymmetry
- K-factor (hard)
- Radiative correction factor
- QED versus QCD
- QED versus QCD (2)
- Interference of 1 2 exchange
- Simulations
- Slide 57
- Slide 58
-