1. Proton Electromagnetic Form Factors at Low Q2 & the Proton Size Puzzle
Xiaohui Zhan
Argonne National Lab
Jlab Pizza Seminar
Apr. 20th 2011

2. Outline Introduction New measurements at low Q2
Electron scattering & nucleon Sachs form factors
World measurements
Form factor theory review
New measurements at low Q2
Low momentum region & pion cloud
Mainz cross section results
Polarization Jefferson Lab E08-007
Puzzle on the proton charge radius
Muonic hydrogen Lamb shift measurement
ep scattering global analysis
Summary

3. Introduction
Proton and neutron are basic building blocks of visible matter.
Most fundamental bound state of quarks and gluons---strong force (QCD).
Structure of the nucleon is a defining problem of hadronic physics, being a primary interest for decades.
NP 1943: proton anomalous magnetic moment.
NP 1961: First proton form factor measurement.
NP 1990: Quark-level structure of the proton.
NP 2004: Strong force theory– QCD.
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4. Electron Elastic Scattering Formalism
Very powerful tool in probing the structure of nucleon and nuclei.
Dirac & Pauli form factors describes the difference between scattering from a structureless particle and an extended spin-1/2 object:
F1: helicity conserving
F2: helicity flipping
single photon exchange
(Born approximation)
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5. Sachs Form Factors
Linear combination of F1 and F2, Fourier transform of the charge (magnetization) densities in the Breit frame at non relativistic limit.
Electric:
Magnetic:
Early experiments found ~ dipole form GD (Q2 < 2 GeV2), naively corresponds to an exponential shape in space.
Normalized to static properties at Q2=0 Limit
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6. Form Factor Measurements – Unpolarized
Rosenbluth separation:
Difficulties:
σ is not sensitive to GE at large Q2 and to GM at small Q2,
Limited by accuracy of cross section measurement at different settings.
Radiative correction 10-30%, 2γ exchange (ε-dependent).
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7. Form Factor Measurements – Recoil Polarimetry
Direct measurement of form factor ratios by measuring the ratio of the transferred polarization Pt and Pl .
Advantages:
Only one measurement is needed for each Q2.
Much better precision than a cross section measurement.
Complementary to XS measurements.
Famous discrepancy between Rosenbluth and polarized measurement, mostly explained by 2-γ exchange.
J. Arrington, W. Melnitchouk, J. A. Tjon, Phys. Rev. C 76, , 2007
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8. Form Factor Measurement – Beam Target Asymmetry
Polarized cross section:
Beam helicity h=±1:
Super ratio of the asymmetries:
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9. Theory Review - I
pQCD:
Theory of strong interaction, well tested in high-energy region
Hadron helicity conservation for Q2 > Ϛ2pQCD >> Λ2QCD
Dimensional counting rules gives (Brodsky and Farrar):
Data seems to be in better agreement with QF2/F1, asymptotic region not reached yet? (GEp III up to Q2 ~ 8.5 GeV2)
Vector coupling between quark gluon, quark helicity conservation, neglect quark orbital angular momentum
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10. Theory Review - II VMD (Vector Meson Dominance):
Early VMD fits predicted a linear decrease of the proton FF ratio (Iachello et. al), amplitude in terms of parameters and fit to the data.
Dispersion analyses: performed separately for nucleon isoscalar and isovector FFs
Recent analysis: constraints from meson nucleon scattering, unitarity and pQCD, including 2π, ρπ, continua.
Extended GK model: basic VMD + quark dynamics via pQCD + ρ width + ρ’, ω, ω’
Fits to nucleon EMFFs for space-like momentum transfer with the explicit pQCD continuum.
M. A. Belushkin et. al, Phys. Rev. C (2007)
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11. Theory Review - III CQM/LFCQM:
Ground state of a quantum-mechanical 3-quark system, SU(6) spin-flavor WFs & antisymmetric color WF.
Relativistic treatment needed for FFs calculation. Three forms of dynamics:
Instant form
Point form
Light-front form
Shortcomings: break all symmetry properties of the QCD Lagrangian. Included the pionic degrees of freedom for improvement.
Thomas, Adv. Nucl. Phys. 13, 1 (1984)
Miller, Phys. Rev. C 66, (R) (2002)
Comparison between data (Punjabi et al. & Gayou et al.) and various CQM calculations: dotted: front form calculation of Chung and Coester.
thick solid: front form of Frank et al.
dot-dashed: front form of Cardarelli et al.
dashed: point form of Boffi et al.
thin solid: covariant spectator model of Gross and Agbakpe.
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12. Theory review - IV Dressed-quark:
Defined by the solution of a Poincare covariant Faddeev equation in which dressed-quark provide the elementary degree of freedom.
Nucleon-photon vertex only has one free parameter: diquark charge radius.
For both the proton and neutron, the form factor ratio possesses a zero.
Below data for Q2<3 GeV2, likely attributed to the omission of the pion cloud contributions.
I. C. Cloёt, G. Eichmann, B. El-Bennich, T. Klӓhn, C. D. Roberts, Few-Body Syst 46:1, (2009)

13. Theory review - V Lattice QCD
Starts from first principles with quark masses and coupling constants as independent inputs.
Extrapolation down to the physical quark masses are required.
Results from Nicosia-MIT group for isovector (p-n) form factor.
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14. Interpretation of the Sachs Form Factors
In NR limit, FFs are Fourier transforms of the nucleon charge (magnetization) densities in the Breit frame, but ruined as Q increases.
Model dependent corrections need to be applied to extract the rest frame densities.
Kelly, Phys. Rev. C 66, (2002)
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15. Scale of the photon probe—why low Q2?
High Q2 sensitive to the fine details of the structure, and the importance of relativity and quark orbital angular momentum.
Low Q2 probes the long-scale properties—pion cloud picture.
Low Q2 investigation motivated by previous world data which shows hints of narrow structures in all four nucleon form factors.
Many implications in nuclear physics: proton size, strangeness form factors, hydrogen hyperfine splitting, DVCS…
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16. World high precision polarization data before 2008.
J. Friedrich and Th. Walcher, Eur. Phys. J. A 17, 607 (2003)
World high precision polarization data before 2008.

17. Mainz Cross Section Measurement (A1)
Bernauer et al. Phys. Rev. Lett. 105, , 2010
High precision xs survey at Q2 = – 1 GeV2 (~1400 points).
Direct fits by various parameterizations to extract the form factors.
Normalization factors determined by fits, no TPE applied.
Hint of structures at Q2~m2π~0.2GeV2, indication of pion cloud?

18. High precision proton form factor ratio measurement at Jlab (E08-007)
Electron injected into the accelerator from polarized gun.
Two Linac contains 20 cryomodules : 5MeV/m. Beam energy up to 6 GeV
Deliver to 3 experimental halls independently, up to 180mA in a single hall.
Beam polarization up to 85%, with helicity flipping at 30 Hz. A C B
Completed in 2008 in Hall A
High precision survey at Q2 = GeV2
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19. Experimental Setup LHRS Ee: 1.192GeV Pb: ~83% BigBite
Non-focusing Dipole
Big acceptance.
Δp: MeV
ΔΩ: 96msr
PS + Scint. + SH

20. Analysis
Spin-orbit coupling between proton and the carbon nuclei induced azimuthal asymmetries in the second scattering
Focal Plane Polarimeter (FPP)
Carbon doors S
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21. Analysis
Detector frame > target frame

22. Results & Discussions
Strongly deviates from unity, systematically lower than previous polarization measurements.
Slowly decrease as Q2, no sign of “narrow structure”. Led to LEDEX reanalysis, agree with new data.
(G. Ron, X. Zhan, J. Arrington, et al. to be submitted)
Most models don’t match, however, indicates the importance of the pion-cloud contribution.
Lowest point still significantly below 1, slope change at lower Q2, change of knowledge of the long-range scale structure.
X. Zhan et al. eprint: nucl-ex, arXiv: , 2011, submitted to Phys. Rev. Lett.
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23. Global fit & Extraction of Form Factors
Combined fit to non-Mainz world xs (TPE corrected) and polarization data.
16 parameters for GE & GM, 32 floating normalization factors for xs data sets.
Updated global fit with new ratio results indicate ~2% (1%) decrease(increase) in GE(GM) , precision greatly improved.
Ratio results consistent with Mainz extractions, but systematically lower GM…
(J. Arrington, W. Melnitchouk, J. A. Tjon, Phys. Rev. C 76, , 2007)

24. Proton Size Puzzle
Leading QED corrections
Proton RMS radius can be obtained from the form factor slopes at Q2=0
Atomic measurements through hydrogen lamb shift: energy split between 2S1/2-2P1/2, effect from the interaction between electron and the vacuum on 2S1/2 state.
Recent muonic-hydrogen lamb shift measurement revealed a much more precise and smaller proton charge radius (67) fm. (P. Pohl et al, Nature, 466, 213,2010)
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25. Extraction from ep scattering
Fit issues & strategy
Sensitive to low Q2 data
Different Q2 cutoff (0.3,0.5,1.0)
Difficulties: functional behavior unknown, model independent?
Different parameterizations
Choice of number of parameters
Tests with MC
Treatment of xs normalization uncertainties, estimate of exp. error.
Cross reference between data sets
Search for Δχ2=1 range
CODATA mainly inferred from hydrogen lamb shift measurements.
Results from ep interaction system suggests the discrepancy relates to the difference between the electron and muon probes.
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26. Magnetic radius Real discrepancy between data sets?
Mainz: 0.777±0.017 fm
Non-Mainz (this work): 0.850±0.025 fm
Real discrepancy between data sets?
Inconsistent treatment of TPE?
Coulomb distortion ~ 0.5%
Full TPE ~ 2%
Different normalization? Potential change if combine data sets?

27. Recent speculations - I
Consistency check of definitions
Role of Darwin-Foldy term in atomic physics:
The atomic physics convention: proportional to the slope of a subtracted Sachs form factor GE, same as what we measure!
U. D. Jentschura, Eur. Phys. J. D (2010)
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28. Recent speculations - I
Role of Darwin-Foldy correction in nuclear charge radius:
Result in a nonvanishing nuclear size correction for the atomic binding energy even for a point-like nucleus.
On the same page!
J. L. Friar, J. Martorell, D. W. L. Sprung, Phys. Rev. A 56, 4579 (1997)
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29. Recent speculations - II
Role of the 3rd Zemach moment
I. C. Cloёt and G. A. Miller, Phys. Rev. C 83, (R), 2011
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30. Recent speculations - III
Off-mass-shell effects at the photon-nucleon vertex (increase the 1st term by 0.15meV):
Could be resolved with an effect:
Strength constrained by nuclear physics phenomena: EMC, quasi-elastic scattering, deviations from Coulomb sum rule.
Lepton-nucleus scattering via binding effects of the nucleon, two photon effects, muonic deuterium.
G. A. Miller, A. W. Thomas, J. D. Carroll, J. Rafelski, arXiv: , 2011
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31. Outlook E08-007 phase II scheduled in 2012:
Beam target asymmetry, systematic check…
Ratio down to Q2 ~ GeV2, overlapped with Mainz.
Direct comparison with Bates.
Better constraints on GM.

32. Summary
Nucleon FFs are fundamental quantities describing the nucleon internal structure, and has been a longstanding subject of interest in nuclear and particle physics.
pQCD not applicable at low momentum transfer region, precision FF measurements are needed for all the experimental accessible region to test various models.
Present the new high precision measurements on the proton elastic form factors at low Q2, found the structure is not as simple as previously believed.
New global fit were performed to extract individual form factors, low Q2 data are essential to extract the proton RMS radius.
The proton charge radius given by recent muonic-hydrogen lamb shift measurement shows a severe discrepancy from the one from the ep interaction system, no solid explanation so far…
Further analysis on the ep scattering data underway, and new measurement at JLab in 2012, stay tuned…
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33. Thank you!

34. Back up
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35. Lattice Calculation

36. Analysis diagram

37. BigBite Spectrometer Scintillator Detect scattered electrons.
Only elastic-peak blocks were in the trigger.
Background minimized with tight elastic cut. e’
Pre-shower
Shower

38. Elastic Events Selection
proton dpkin
HRS acceptance cut:
out of plane: +/- 60 mr
in plane: +/-30 mr
momentum: +/ (dp/p0)
reaction vertex cut
FPP cuts:
scattering angle θfpp 5o ~ 30o
reaction vertex (carbon door)
conetest cut
Other cuts:
Coin. Timing cut
Coin. event type (trigger)
single track event
dpkin (proton angle vs. momentum)

39. Spin Transport in HRS

40. Systematic Budget
Spin transport: OPTICS and COSY---major uncertainty (0.7 ~ 1.2 %)
Others negligible: FPP alignment, Al end cap contamination, VDC reconstruction, spectrometer settings, beam energy, charge asymmetry, pion contamination, etc.

41. Analysis summary
World cross section database – two-photon exchange corrected (John)
Updated polarization database.
New Mainz data NOT included.
Normalization factors allow to float in the combined fit.
Focus at the low Q2 for the radius analysis.
Choice of fitting functions for systematic study:
MC used to test the functional forms:
Dipole (MC) --- CF & Poly. (Fit)
CF (MC) -- Poly. (Fit)
Poly.(MC)– CF (Fit)
Give almost identical results on the dipole form
Consistent within error in extracting the other.

42. Cross-validation CF Determine the optimal fit
Randomly separate data sample, fit one, and calculate the χ2 validation set.
Poly.
Black: fit sample
Red: validation sample

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