space-like and time-like form factors compared analysis

Egle TOMASI-GUSTAFSSON CEA DSM IRFU SPhN and CNRS/IN2P3/ IPNO16-VI-2009 1

Space-Like and Time-LikeForm Factors

Compared analysisEgle Tomasi-Gustafsson

SPhN-Saclay and IPN-Orsay

Varenna, June 16, 2009 2009


PLAN•Introduction:Form factors in one photon exchange approximation

….Model Independent Statements

q2>0

e-

e+ p

p

•Experimental Situation– Space-Like– Time-like

•Future Panda/FAIR and JLab 12 GeV:– Determination of proton form factors– Transition to QCD: Asymptotics– Reaction mechanism (1 or 2 exchange)

•Conclusions


Hadron Electromagnetic Form factorsHadron Electromagnetic Form factors

– Characterize the internal structure of a particle

( point-like)

– In a P- and T-invariant theory, the EM structure of a particle of spin S is defined by 2S+1 form factors.

– Elastic form factors bring information on the nucleon ground state

– Neutron and proton form factors are different

– Playground for theory and experiment

– at low q2 probe the size of the nucleus,

– at high q2 test QCD scaling


The proton vertex is parametrized in terms of FFs: Pauli and Dirac F1,F2

Electromagnetic InteractionElectromagnetic Interaction

q2<0

e-e-

p p)2q(2F

M2qi

)2q(1F

or in terms of Sachs FFs:GE=F1-F2, GM=F1+F2, =-q2/4M2

The electron vertex is known,

The interaction is carried by a virtual photon of mass q2

What about high order

radiative corrections?


AnalyticityAnalyticity

__

q2<0

e-e-

p p

q2>0

e-

e+ p

p

q2q2=4mp2

FFs are complexFFs are real Unp

hysi

cal r

egio

n

GE=GM

Space-like

Time-likeGE(0)=1

GM(0)=p

Asymptotics- QCD- analyticity

p+p ↔ e++e-e+p e+p

p+p

↔ e

++

e- +


The Rosenbluth separation

)2(2)2(2

)1(1 QMGQEG

Mottd

ddd

2M4

2Q,1

2e2)tan1(21

2MG2

EGR

Holds for 1exchange only

Linearity of the reduced cross section

PRL 94, 142301 (2005)

tan2e dependence

Q2 f

ixed


Crossing SymmetryCrossing Symmetry

Scattering and annihilation channels:

- Described by the same amplitude :

- function of two kinematical variables, s and t

p2 → – p2

k2 → – k2

- which scan different kinematical regions


Time-like observables: | GE| 2 and | GM| 2 .

As in SL region:- Dependence on q2 contained in FFs- Even dependence on cos2(1 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, E.T-G., Nucl. Phys. A761,120 (2005).


Experimental Status (space-like)

q2<0

e-e-

p p


The nucleon form factors

VDM : IJLF. Iachello..PLB 43, 191 (1973)

Extended VDM (G.-K. 92): E.L.Lomon PRC 66, 045501 2002)

HohlerNPB 114, 505 (1976)

BostedPRC 51, 409 (1995)

Electric Magneticne

utro

npr

oton

E. T.-G., F. Lacroix, Ch. Duterte, G.I. Gakh, EPJA 24, 419 (2005)

To update…new

data!


The simultaneous measurement of Pt and Pl reduces the systematic errors !

Polarization Method (exp)

A.I. Akhiezer, M.P. Rekalo


Statistics and Preliminary Results from GEp(III)

New equipment workedbeautifully: BigCal and FPP

8.54 GeV2 point: 1.63 billion triggers collected

Analyzing power at 5.4 GeV/c close to Dubna value

6.8 GeV2 point: 160 million triggers

5.2 GeV2 point: a test of the spin transport at 180o

μpGEp/GMp=1.056-0.1427Q2

C. Perdrisat, V. Punjabi


STATUS on EM Form factors

Space-like region

1)"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) contradiction between polarized and unpolarized measurements

4) non vanishing electric neutron FF, GEn.


Two-photon exchange

Different results with different experimental methods !!

- Both methods based on the same formalism

- Experiments repeated

New mechanism?

•1-2 ~ =e2/4=1/137

•1970’s: Gunion, Lev…


Experimental Status (time-like)

q2>0

e-

e+ p

p


Time-Like Region

E. T-G., F. Lacroix, C. Duterte, G.I. Gakh, EPJA 24, 419 (2005)

VDM : IJLF. Iachello..PLB43 191 (1973)

Extended VDM (G.-K. 92): E.L.Lomon PRC66 045501(2002)

‘QCD inspired’

proton

neutron


STATUS on EM Form factors Time-like region

1)No individual determination of |GE| and |GM|2)Assume GE=GM (valid only at threshold) 3)TL nucleon FFs are twice larger than SL FF

QCD =0.3 GeV

A(p) = 56.3 GeV4 A(n) = 77.15 GeV4

)]/(ln[ 2222

ss

AGM

VMD or pQCD inspired parametrizations (for p and n):


Models in T.L. Region (polarization)

VDM : IJL

Ext. VDM

‘QCD inspired’

R

Ay Axx Ayy

Axz

Azz

E. T-G., F. Lacroix, C. Duterte, G.I. Gakh, EPJA 24, 419(2005)


Space-like and Time-like E.T-G, Phys. Part. Nucl. Lett. 4, 281 (2007)

=0.5=0.2

=0.8

FE=G2Ered

FE=tot

FM=tot

GeV2----- 8 GeV2


Space-like and Time-like

=0.2=0.5

=0.8

E.T-G, Phys. Part. Nucl. Lett. 4, 281 (2007)

10%

10%

FE=G2Ered


Radiative Return (ISR)

.s

m,

x

sin

xx

x),x,s(W

,s

m

s

Ex),m)(ppee(),x,s(W

s

m

cosddm

)ppee(d

e

2

22

122

2

2

2

2

e+ +e- p + p +

B. Aubert ( BABAR Collaboration) Phys Rev. D73, 012005 (2006)


Results (ISR)

GE = GM ?

B. Aubert [Babar Collaboration, PRD 73, 012005 (2006)


Form Factors with

p+p e++ e-

1) Knowledge of proton form factors up to large q2

2) Transition to QCD: Asymptotics3) Reaction mechanism (1 or 2 photon exchange)


D. Marchand, IPN Orsay24

3 body reactions: “easy” to eliminate kinematical constraints

PID

2 charged body reactions (π+π-, μ+μ-, K+K-)

Most important background is π+ π- : 610~

ee

Are we able to discriminate e+e- from π+ π- ?

YES !YES !High statistics GEANT4 simulations Worse case : few Worse case : few 00//0000 pollution / cos pollution / cosCMCM bin (0.1) bin (0.1) < 1% on the total cross section up to 16 GeV2

Physical Background


Individual determination of GE and GM up to large Q2

Expected Results(I)

R=GE/GM

BaBAR

PS170 PANDA sim

L = 2x1032 cm-2.s-1, 107 s (~100 days)


Proton: F2 /F1 and pQCD

Brodsky and Farrar (75):Q2F2/F1 constant

Belitsky, Ji and Yuan (03):

Q2F2/F1 → ln2(Q2/2)→

C. Perdrisat


-Asymptotic region

-Test of analytical properties

Expected Results (II)


Phragmèn-Lindelöf theorem

Asymptotic properties for analytical functions

E. T-G. and G. Gakh, Eur. Phys. J. A 26, 265 (2005)

=0.05, 0.1

If f(z) a as z along a straight line, and f(z) b as zalong another straight line, and f(z) is regular and bounded in the angle between, then a=b and f(z) a

uniformly in the angle.


Phragmèn-Lindelöf theorem

E. T-G. and M. P. Rekalo, Phys. Lett. B 504, 291 (2001)

Applies to NN and NNInteraction (Pomeranchuk theorem)t=0 : not a QCD regime!

Connection with QCD asymptotics?


Conclusions•Hadron form factors: a bridge between perturbativeand non perturbative QCD•Progress in experiment and theory

•Next future (> 2014)– 12 GeV beams at JLab: increase Q2 to 15 GeV2. Two experiment in preparation

- Fair@GSI, antiprotons up to 15 GeV/cPrecise determination of |GE| and |GM|

Cross section measurement up to q2 to ~20 GeV2.

Towards a unified description of form factors, for a better comprehension of the hadron structure


GEp/GMp with 12 GeV at JLab

31

Two new experiments approved to run after the 12 GeV upgrade (to be completed end of 2013).

Whether they should run depends again on Dubna calibration to 7.5 GeV/c (12.5 GeV2).


Two-Photon exchange•1-2 interference is of the order of =e2/4p=1/137

(in usual calculations of radiative corrections, one photon is ‘hard’ and one is ‘soft’)

•The 2 amplitude is expected to be mostly imaginary.•The 1-2 interference is more important in time-like region, as the Born amplitude is complex

•In the 70’s it was shown [J. Gunion and L. Stodolsky, V. Franco, F.M.

Lev, V.N. Boitsov, L. Kondratyuk and V.B. Kopeliovich, R. Blankenbecker…]

that, at large momentum transfer, due to the sharp decrease

of the FFs, if the momentum is shared between the two

photons, the 2- contribution can become very large.


Two Photon exchange


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:


Mpp=1.877-1.9Mpp=1.877-1.9

A=0.01A=0.01±±0.020.02

Mpp=2.4-3Mpp=2.4-3

E. T.-G., E.A. Kuraev, S. Bakmaev, S. Pacetti, Phys. Lett. B (2008)


Simulations

Approximations:•Neglect contributions to GE,GM•Consider only real part

Main effect: odd cos- distribution

20.0/3 MGF

02.0/3 MGF

0/3 MGF

05.0/3 MGF

q2=5.4,8.2,13.8 GeV2


2 0.02

2 0.05 2 0.2

1

q2=5.4 GeV2

N=a0+a2cossin2+a1 cos2, a2~2


Two photon exchange•The calculation of the box amplitude requires

thedescription of intermediate nucleon excitation

and of their FFs at any Q2

•Different calculations give quantitatively different results

Theory not enough constrained!

Model independent statements


1{g

1-2 interference

{ 21 {

M. P. Rekalo, E. T.-G. and D. Prout, Phys. Rev. C60, 042202 (1999)


Unpolarized cross section

•Induces four new terms•Odd function of •Does not contribute at =90°

Two Photon Exchange:


•Properties of the TPE amplitudes with respect to the transformation: cos = - cos i.e., -

(equivalent to non-linearity in Rosenbluth fit)

•Based on these properties one can remove or single out TPE contribution

Symmetry relationsSymmetry relations

E. T.-G., G. Gakh, NPA (2007)


•Differential cross section at complementary angles:

Symmetry relations

The DIFFERENCE enhances the 2contribution:

The SUM cancels the 2contribution:


Is there any experimental evidence of

two photon exchange?

(real

part)

NO


From the data:

deviation from linearity

<< 1%!

Parametrization of 2-contribution for e+p

E. T.-G., G. Gakh, Phys. Rev. C 72, 015209 (2005)

)(1

1),( 2)(2 QfQF a

2222

22

]1[ a

Dγ(a)

/m[GeV]Q

GC)(Qf


Linear fit to e+4He scattering


2γ-Gamma Models and Data

47

The inclusion of hard 2γ exchange: Chen et al (2003) with GPDs, Blunden et al (2003) in hadronic model

04/22/23

Expt. Jlab 04-019 measuredRatio PL/PT for Q2=2.49 GeV2

at 3 values of ε

PRELIMINARY

C. Perdrisat,L. Pentchev

NO ε-dependence at 0.01 level

NO evidence of 2 contribution

Bystriskyi et al., LSFPR C75, 015207 (2007)


Asymptotics

space-like and time-like form factors compared analysis

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