nucleon elastic form factors: an experimentalist’s perspective
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Nucleon Elastic Form Factors: An Experimentalist’s Perspective. Outline: The Fib and the Questions EM FF Strangeness. Glen Warren Battelle & Jefferson Lab Division of Nuclear Physics October 31, 2003. First, I’m going to fib. - PowerPoint PPT PresentationTRANSCRIPT
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Nucleon Elastic Form Factors: An Experimentalist’s Perspective
Outline:• The Fib and the
Questions• EM FF
•Strangeness
Glen WarrenBattelle
& Jefferson Lab
Division of Nuclear PhysicsOctober 31, 2003
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First, I’m going to fib• This mini-symposium is titled “Progress in Nucleon
Form Factors”.
• To recognize the “progress” we must know from where we came.
• I will first present the classic introduction to nucleon form factors. It would have raised few eyebrows even as little as 5 years ago.
• Listen, learn if you need to, but do not think this is the whole truth.
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Form Factors
Structure of particles described by form factors.
Form factors hide our ignorance of how the composite particle is constructed.
ER,PRE’, k’
E , k
Electron
q q2 = -Q2
G(Q2)
M
Target
Time
or Z
Elastic Scattering:Q2 = 2Mn
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Interpretation of Form Factors
In non-relativistic limit, form factors are Fourier transforms of distributions:
3expE ch rG q iq r d r
Spin 1/2 particles have two elastic electromagnetic form factors:
GE : electric form factor F1 : Dirac form factorGM : magnetic form factor F2 : Pauli form factor
GE = F1 - F2 and GM = F1 + F2
OR
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pQCD• For elastic scattering in
one photon exchange, quarks must exchange two gluons to distribute momentum to remain a nucleon– F1 ~ 1/Q4
• F2 requires an additional spin flip:– F2 ~ F1/Q2 ~ 1/Q6
• Expect in pQCD regime:– Q2 F2/F1 ~ constant
– or GE/GM ~ constant
• At low Q2, forced to use effective theories.
• At high Q2, use pQCD, which relies on quark helicity conservation.
• pQCD predicts asymptotic behavior for F1 and F2 following “counting rules.”
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Seeds of Doubt ...Interpretation of form factors as distributions requires:• non-relativisitic limit,
– data exists well into the relativistic region.
• or, if relativistic, there is no energy transferred (Breit frame)– a “physical” property for an unphysical reference frame?
• To think that the form factors are intimately connected to charge and magnetic distributions is simplistic and may lead to physical misinterpretation of the experimental results.
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Dipole Form Factor
Mn n DG G
GEp, GMp and GMn roughly follow the Dipole Form Factor.
The 0.71 is determined from a fit to the world’s data.
An Exponential distribution has dipole form factor:
221 / 0.71DG Q
For Example:
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“World” Data up to 1997
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GMn ResultsTwo Modern Methods:
1) Ratio of Cross sectionsmeasure
Difficulty is absolute neutron detection efficiency
2) Beam-Target Asymmetries
whereDifficulty is nuclear corrections
( ( , ))( ( , ))D eD e pe
ne
2
21Mn
Mn
Aa
GG
2 1MnaG
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GMn Future
Hall B has taken data using ratio of cross sections method: a talk on this experiment will be presented in this session.
Error bars are for uniform bins in Q2. Could increase bin size to reduce errors at large Q2.
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GEn ResultsTwo Modern Methods:
1) Polarization Observables
2) Extraction from deuteron quadrupole form factor FC2.
3
( , )
( , )( , )
e e n p
e e n ppD e
D
eHe
n p
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GEn Future
One experiment (MAMI) is completed and in analysis
Polarization measurements planned in:• Hall A: polarized 3He up to Q2=3.4• BLAST: precision measurements up to Q2=0.9
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GEp ResultsRecoil Polarimetry
Measure ratio of polarization transferred to proton
( ) tan2 2
Ep T e
Mp L
G P E EG P m
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GEp Future• Super Rosenbluth separation experiment is completed and in analysis.
• Another recoil polarimetry experiment at high Q2 in Hall C.
• Precision polarized target experiment with BLAST.
• Rosenbluth measurement from data taken in Hall C of JLab.
Talks on each of these experiments will be presented today.
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Physics Models
• pQCD - high Q2: Q2 dependence
– GM = F1+F2, GE = F1-F2; F1~ Q-4, F2~Q-6 .• Hybrids - combine Vector Meson Dominance at low
Q2 and pQCD at high Q2.• Lattice QCD Calculations.• Relativistic Quark Models vary on:
– address relativity– dynamics
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Models
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Q F2/F1
• Recall from pQCD expect F2/F1 ~ 1/Q2
• Explanations:– OAM breaks helicity
conservation (Ralston).– Higher twist contributions lead
to log terms in F2/F1 (Brodsky).– Need OAM for spin-flip of
massless quark which leads to log terms in F2/F1 (Belitsky).
– Relativistic model leads to terms in lower spinor components (eqv. To OAM) (Miller).
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Rosenbluth vs. PolarimetryWhat explains the difference between these two experimental results?
• Rosenbluth Separation– Data shown to be consistent– Very difficult measurements in
high Q2
– Leading explanation: 2 exchange which is dependent.
• Shown to explain half the difference when include elastic contributions only.
• Polarimetry:– probably less susceptible to
radiation issues since directly measure GE/GM.
– Experimental technique is robust.
WARNING: Be careful mixing cross section and polarimetry results because they may be measuring different quantities.
Much of second part of this symposium is devoted to this issue.
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Strangeness• EM current
• Neutral current
• We can define a analogous to . Assuming isospin invariance, we can define strange form factors
21 2
FFN J N U i q UM
52
1 2NC
ZZ Z
AFN J N U i q UM
F G
,ZE MG ,
,p nE MG
2, ,, ,1 4sin p n
E M Es
MM WZ
E E MG G G G
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Strange Experiments• Consider PV e-p scattering, the asymmetry is
• Need three different measurements to separate GZ’s, and must consider different targets, radiative corrections, ...– SAMPLE I,II, III: H, D at backward angles for Q2 = 0.1, 0.038– HAPPEX I,II,III: H, 4He at forward angles for Q2 = 0.48, 0.10– PVA4: H at forward angles for Q2 = 0.23, 0.10– G0: H,D at forward and backward angles for Q2 = 0.1-1.0
• Each of these takes a different experimental approach
21 4sin ( , )PV Wp pZ Z e
E E M MAp
MA G G GG f G G
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Summary• Tremendous advance in experimental results in last
several years for EM form factors. – Convergence in GEn and GMn
– Models doing a respectable job
• GEp/GMp controversy continues– 2 radiative corrections?– Implications for “delicate” Rosenbluth separations?– importance of orbital angular momentum in relativistic models
• Extremely healthy experimental and theoretical progress in neutral current results.
• In a few more years, we will have more data to continue to whet our appetites.
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Asymptotic DependencepQCD predicts the asymptotic
dependence of F1 and F2
– 1/Q2 per gluon line– 1/Q2 per helicity flip
• F1 ~ 1/Q4
– two gluon exchange,
• F2 ~ 1/Q6
– two gluon exchange– helicity flip
as Q2 • GE and GM ~ 1/Q4
• GE/GM ~ 1
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GEp Analysis• Brash et al. reanalyzed cross section data to extract
GMp assuming GEp/GMp fall-off.– New parameterization with slightly larger GMp
– GMp results more consistent than published data
• J. Arrington examined cross section experiments– no one experiment has significant impact on result.– GMp results more consistent when assume constant GEp/GMp.– normalization errors cannot cross section result.– Cross section measurements are consistent with each other.