1. Thomas Jefferson National Accelerator Facility
Nucleon Electromagnetic Form Factors
A Review
General Introduction
Electromagnetic Form Factors
Formalism
Neutron
Proton
Two-Photon Exchange Contributions
Interpretation
Summary
Outlook towards 12 GeV upgrade γ
Kees de Jager
Jefferson Lab
INFN/Roma Sanita
June 30, 2008
Thomas Jefferson National Accelerator Facility

2. Kinematics
Q2 > 0 space-like region, studied through elastic electron scattering
Q2 < 0 time-like region, studied through creation or annihilation
e+ + e- -> N + N or N + N -> e+ + e-
In the isovector channel (T = 1) two pions can contribute, so Q2 < -4mπ2
In the isoscalar channel (T = 0) only an odd number of pions can couple, so Q2 < -9mπ2 _ _

3. Formalism
Dirac (non-spin-flip) F1 and Pauli (spin-flip) F2 Form Factors γ
with E (E’) incoming (outgoing) energy, θ scattering angle, κ anomalous magnetic moment and τ = Q2/4M2
Alternatively, Sachs Form Factors GE and GM can be used
In the Breit (centre-of mass) frame the Sachs FF can be written as the Fourier transforms of the charge and magnetization radial density distributions

4. Modern Era Akhiezer et al., Sov. Phys. JETP 6, 588 (1958) and
Arnold, Carlson and Gross, PR C 23, 363 (1981)
showed that:
accuracy of form-factor measurements can be significantly improved by measuring an interference term GEGM through the beam helicity asymmetry with a polarized target or with recoil polarimetry
Had to wait over 30 years for development of
Polarized beam with
high intensity (~100 µA) and high polarization (>70 %)
(strained or superlattice GaAs, high-power diode/Ti-Sapphire lasers)
Beam polarimeters with 1-3 % absolute accuracy
Polarized targets with a high polarization or
Ejectile polarimeters with large analyzing powers

5. Double Polarization Experiments to Measure GnE
Study the (e,e’n) reaction from a polarized ND3 target
limitations: low current (~80 nA) on target
deuteron polarization (~25 %)
Study the (e,e’n) reaction from a LD2 target and
measure the neutron polarization with a polarimeter limitations: Figure of Merit of polarimeter
Study the (e,e’n) reaction from a polarized 3He target
limitations: current on target (12 µA)
target polarization (50 %)
nuclear medium corrections

6. Neutron Electric Form Factor GEn
Galster:
a parametrization fitted to old (<1971) data set of very limited quality
Schiavilla and Sick analyzed data on deuteron elastic quadrupole form factor
Most recent results (Mainz, JLab) are in excellent agreement, even though all three different techniques were used
For Q2 > 1 GeV2 data hint that GEn has similar Q2-behaviour as GEp

7. Exclusive QE scattering: 3He(e,e′n)
7 Iron/scintillator
sandwich planes
Q2 = 1.3, 1.7, 2.5, 3.5 GeV2 n
Target polarization ~50%
Beam polarization 84%
2 veto planes
Requires: sufficient resolution to identify quasi-elastic events. e e′

8. GEN experiment E02-013 Electron Arm Polarized He-3 target Neutron Arm
Six planes, total 244 bars
Two planes of 192 veto counters
Overall 1.8x5.0 m2 front area
35-40% neutron detection efficiency
ns time resolution
Electron Arm
15 planes, fast Drift Chambers
Shower/preshower calorimeter
Luminosity 1x1037 cm-2/s
Solid angle of 75 msr
Momentum resolution at 1% at 1.5 GeV/c
Polarized He-3 target
Novel hybrid K-Rb cell
Novel scheme for target field
Record high polarization, 50%

9. Data analysis: step 1 - Time-of-Flight
Finally we approaching the data analysis.
First if TOF = raw - black line and after cut of
Angular correlation - red - almost clean!
RED lines present events after
cut on e’-n angular correlation:
accidentals and tails almost gone
Raw events (BLACK lines) have significant accidental level and large tail from slower protons

10. Analysis: step 2 - q⊥ vs W; 1.7 GeV2
perpendicular “q” = q x tan(ϑqh); W2 = M2 + 2M(E-E’) - Q2
Second step is analysis based on W = sqrt ( M^2 + 2 M (E-E’) -Q2)
For elastic scattering all events at W = 0.94 GeV.
For Quasi-Elastic there is a peak which width is growing with Q2.
This slide for Q2 = 1.7 GeV2. Raw data on left. Cuts of angular
And time peaks plus missing mass of two protons -> Right plot.
Right plot has final event sample!
Quasi elastic events dominates after Full Cuts have been applied
max value of
qperp used

11. Analysis: step 2 - q⊥ vs W; 3.5 GeV2
Second step is analysis based on W = sqrt ( M^2 + 2 M (E-E’) -Q2)
For elastic scattering all events at W = 0.94 GeV.
For Quasi-Elastic there is a peak which width is growing with Q2.
This slide for Q2 = 3.5 GeV2. Raw data on left. Cut on TOF - second plot.
Next after all cuts: Right Bottom plot has final event sample!

12. Analysis: step 3 - W distribution
One dimensional spectra are better for quantitative illustration -
Again for both Q2 1.7 and for 3.5
Black curve shows distribution for all events (limited just by acceptance).
Red curve presents events after angular correlation cut
Blue line shows events after ALL CUTS

13. Analysis: step 4 - corrections
Asymmetry then corrected for
Conversions p-n in shielding
Accidental events
A|| contribution and Ap
FSI for 3He(e,e’n) process
Target and beam polarizations
Finally we approaching the RESULTS
Need several corrections.
Comparison p/n yields for three targets with
different ratio of N/Z : 0/1; 1/2; 1/1
Analysis of large detector area
From known GMn and GEp, GMp
In progress by Misak Sarksian
Accurate to 4% (relative) for the target

14. Preliminary results from Hall A GEN E02-013
GEn at 1.7 GeV2 is well above GGalster
GEn at 3.4 GeV2 is closer to GGalster, far below CQM (Miller) and Belitsky’s log scaling, reasonably close to Roberts’ DSE
Final accuracy for 3.4 GeV2 expected to improve by factor 1.5
Next release will be the result at 2.5 GeV2

15. Measuring GnM Old method: quasi-elastic scattering from 2H
large systematic errors due to subtraction of proton contribution
Measure (en)/(ep) ratio
Luminosities cancel
Determine neutron detector efficiency
On-line through e+p->e’+π+(+n) reaction (CLAS)
Off-line with neutron beam (Mainz)
Measure inclusive quasi-elastic scattering off polarized 3He
RT’ directly sensitive to (GMn)2

16. Preliminary CLAS results for GMn
A systematic difference of several % between results
( ) in Q2 range GeV2.
A final analysis and paper from CLAS is coming soon.
Reminder that at least two independent experiments are always needed.
The data set for GMN at low Q2 also significant. Useful to point that there is inconsistency between results of two
Measurements which both used ratio method, and polarized target method just between them

17. Spin Transfer Reaction 1H(e,e’p)
No error contributions from
analyzing power
beam polarimetry

18. JLab Polarization Transfer Data
E PRL 84, 1398 (2000)
Used both HRS in Hall A with FPP
E PRL 88, (2002)
used Pb-glass calorimeter for electron detection to match proton HRS acceptance
Reanalysis of E93-027
(Punjabi, nucl-ex/ )
Using corrected HRS properties
No dependence of polarization transfer on any of the kinematic variables

19. Ongoing extension for GEp
Perdrisat et al. E01-109
Used Hall C HMS (with new FPP) and larger Pb-glass calorimeter
Just completed

20. Super-Rosenbluth (E01-001)
I. Qattan et al. (PRL 94, (2005))
Detect recoil protons in HRS-L to diminish sensitivity to:
Particle momentum
Particle angle
Rate
Use HRS-R as luminosity monitor
Very careful survey
Rosenbluth
Pol Trans
MC simulations

21. Rosenbluth Compared to Polarization Transfer
John Arrington performed detailed reanalysis of SLAC data
Hall C Rosenbluth data (PRC 70, (2004)) in agreement with SLAC data
No reason to doubt quality of either Rosenbluth or polarization transfer data
Investigate possible theoretical sources for discrepancy

22. Two-Photon Exchange 11/18/2018 Proton form factor measurements
Comparison of precise Rosenbluth and polarization measurements of GEp/GMp show clear discrepancy at high Q2
Two-photon exchange corrections believed to explain the discrepancy
P.A.M. Guichon and M. Vanderhaeghen, PRL 91, (2003)
Compatible with e+/e- ?
Yes: previous data limited to low Q2 or small scattering angle
Still lack direct evidence of effect on cross section, except for
Beam normal spin asymmetry, the only observable in elastic e-p where TPE are observed
Chen et al., PRL 93, (2004)
Test

23. Two-Photon Exchange Measurements
11/18/2018
Two-Photon Exchange Measurements
Comparisons of e+-p and e--p scattering [VEPP-III, JLab-Hall B,
ε dependence of polarization transfer and unpolarized σe-p [JLab-Hall C]
More quantitative measure of the discrepancy
Test against models of TPE at both low and high Q2
TPE effects in Born-forbidden observables [JLab-Hall A, Hall C, Mainz]
Target single spin asymmetry, Ay in e-n scattering
Induced polarization, py, in e-p scattering
Vector analyzing power, AN, in e-p scattering
World data
Novosibirsk
JLab – Hall B
Test

24. Two-Photon Exchange Calculations
11/18/2018
Significant progress in theoretical understanding
Hadronic calculations appear sufficient up to 2-3 GeV2
GPD-based calculations used at higher Q2
Experimental program will quantify TPE for several e-p observables
Precise test of calculations
Tests against different observables
Arrington, Melnitchouk, Tjon
[nucl-ex]
Used TPE from Blunden et al. with additional phenomenological corrections
Want calculations well tested for elastic e-p, reliable enough to be used for other reactions
Test

25. Reanalysis of SLAC data on GMp
E. Brash et al. (PRC 65, (2002)) have reanalyzed SLAC data with JLab GEp/GMp results
as constraint, using a similar fit function as Bosted
Reanalysis results in 1.5-3%
increase of GMp data

26. μpGpE/GpM and GnE at low Q2 from
C.B. Crawford et al., PRL98 (2007)
It is very interesting to look at the impact of the GE/GM ratio on the separation of GE and GM. In blue is an extraction of GE and GM from existing unpolarized data, suitably binned. In red, the result of the same extraction when the BLAST GE/GM ratios are taken into account as a constraint. Tremendous accuracy achieved, with clear evidence for a deviation from the “dipole” form.
Impact of BLAST data combined with cross sections on separation of GpE and GpM
Errors factor ~2 smaller
Reduced correlation
Deviation from dipole at low Q2!
E. Geis et al., ArXiv [nucl-ex]
*Ph.D. work of C. Crawford (MIT) and A. Sindile (UNH)

27. New Hall A Polarization Transfer Results for GEp
PRL 99, (2007)
Cross Section from C. Berger et al., Phys. Lett. B35 (1971) 87
Deviation in Ratio is due to Electric Form Factor
Parasitic to G0
40% Polarized Beam
Approx. 12 hours/point

28. Experiment E04-007 One Day of Beam Time per Point! Completed on June 9
Achieved 0.5% precision for most data points
Extensive ongoing program of accurate low-Q2 cross-section measurements at MAMI

29. Charge and Magnetization Radii
Experimental values
<rE2>p1/2= fm
<rM2>p1/2= fm
<rE2>n= fm2
<rM2>n1/2= fm
Even at low Q2-values Coulomb distortion effects have to be taken into account
The three real radii are identical within the experimental accuracy
Foldy term = fm2 canceled by relativistic corrections (Isgur)
implying neutron charge distribution is determined by GEn

30. Nucleon densities and relativity
Q2-evolution of quark mass
intrinsic FF
rest frame density
non-rel :
importance of relativity (with increasing Q2) : Lorentz contraction of spatial distributions in Breit frame
At Q ≈ 0.5 GeV mu/d ≈ 0.3 GeV
limit : k = 2 M (Compton wavelength)
Thus Fourier transform remains valid for r > rmin ≈ 0.3 fm

31. Low Q2 Systematics
All EMFF show minimum (maximum for GEn) at Q ≈ 0.5 GeV

32. Pion Cloud No information extractable
Kelly has performed simultaneous fit to all four EMFF in coordinate space using Laguerre-Gaussian expansion and first-order approximation for Lorentz contraction of local Breit frame
Friedrich and Walcher have performed a similar analysis using a sum of dipole FF for valence quarks but neglecting the Lorentz contraction
Both observe a structure in the proton and neutron densities at ~0.9 fm which they assign to a pion cloud _
Hammer et al. have extracted the pion cloud assigned to the NN2π component which they find to peak at ~ 0.4 fm

33. High-Q2 behaviour of GEp/GMp
Basic pQCD (Bjørken) scaling predicts
F1 ∝ 1/Q4 ; F2 ∝1/Q6
F2/F1 ∝ 1/Q2 (Brodsky & Farrar)
Data clearly do not follow this trend
Schlumpf (1994), Miller (1996) and
Ralston (2002) agree that by
freeing the pT=0 pQCD condition
applying a (Melosh) transformation to a relativistic (light-front) system
an orbital angular momentum component is introduced in the proton wf (giving up helicity conservation) and one obtains
F2/F1 ∝ 1/Q
and equivalently a linear drop off of GE/GM with Q2
Brodsky argues that in pQCD limit non-zero OAM contributes to both F1 and F2

34. High-Q2 Behaviour
Belitsky et al. have included logarithmic corrections in pQCD limit
They warn that the observed scaling could very well be precocious
Clearly GEn does not follow Belitsky scaling

35. Theory Vector Meson Dominance
Photon couples to nucleon exchanging vector meson (ρ, ω, φ)
Adjust high-Q2 behaviour to pQCD scaling
Include 2π-continuum in finite width of ρ
Lomon 3 isoscalar, isovector poles, intrinsic core FF
Bijker 2 isoscalar, 1 isovector pole, intrinsic core FF
Hammer 4 isoscalar, 3 isovector poles, no additional FF
Relativistic chiral soliton model
Holzwarth one VM in Lagrangian, boost to Breit frame
Goeke NJL Lagrangian, few parameters

36. Vector-Meson Dominance
charge
magnetization
proton
neutron

37. Theory Relativistic Constituent Quark Models
Variety of q-q potentials (harmonic oscillator, hypercentral, linear)
Non-relativistic treatment of quark dynamics, relativistic EM currents
Miller: extension of cloudy bag model, light-front kinematics
wave function and pion cloud adjusted to static parameters
Cardarelli & Simula
Isgur-Capstick oge potential, light-front kinematics
constituent quark FF in agreement with DIS data
Wagenbrunn & Plessas
point-form spectator approximation
linear confinement potential, Goldstone-boson exchange
Giannini et al.
gluon-gluon interaction in hypercentral model
boost to Breit frame
Metsch et al.
solve Bethe-Salpeter equation, linear confinement potential

38. Relativistic Constituent Quark
charge
magnetization
proton
neutron

39. Lattice QCD calculations
LHPC collaboration
Isovector radius is insensitive to neglect of disconnected diagrams, but has double the pion cloud effect at small pion mass

40. quark transverse charge densities in nucleon
Model-independent Fourier transform on the light front
q+ = q0 + q3 = 0
photon only couples to forward moving quarks
quark charge density operator
unpolarized nucleon
Marc Vanderhaeghen

41. empirical quark transverse densities
Marc Vanderhaeghen
proton ρ0 ρT
neutron

42. GPDs yield 3-dim quark structure of nucleon
Burkardt (2000, 2003)
Belitsky, Ji, Yuan (2004)
Elastic Scattering
transverse quark
distribution in
coordinate space
DIS
longitudinal
quark distribution
in momentum space
DES (GPDs)
fully-correlated
quark distribution in
both coordinate and
momentum space

43. Electromagnetic Form Factors
PROTON
NEUTRON
modified Regge GPD parameterization
1 : Regge slope -> proton Dirac (Pauli) radius
2, 3 : large x behavior of GPD Eu, Ed -> large Q2 behavior of F2p, F2n
3-parameter fit
Guidal, Polyakov, Radyushkin, Vdh (2005)
world data (2006)
also Diehl, Feldmann, Jakob, Kroll (2005)

44. Summary
Very active experimental program on hadron electro-weak form factors thanks to development of polarized beam (> 100 µA, > 75 %) with extremely small helicity-correlated properties, polarized targets and polarimeters with large analyzing powers
Electromagnetic Form Factors
GEp discrepancy between Rosenbluth and polarization transfer not an experimental problem, but highly likely caused by TPE effects, recently data taken up till 8.4 GeV2
GEn precise data up to Q2 = 1.5 GeV2
GMn precise data up to Q2 = 5 GeV2, but inconsistency at ~ 1 GeV2
Further accurate data will continue to become available as benchmark for Lattice QCD calculations
In addition, many exciting new data to be expected with the JLab 12 GeV upgrade

45. Upgrade magnets and power supplies
Add new hall 12 11
6 GeV CEBAF
Upgrade magnets and power supplies
CHL-2
INFO FOR ME, BUT DO NOT SAY UNLESS ASKED!!!!!
Cost range (from Mission Needs Statement) $170M-$250M
This includes $30-50 M that could come from redirection of the present JLab Ops budget, and
~$20M that might come from foreign contributors (if they match what they did for the original project)
About $47M of the total could come from a redirection of present operating funds over the duration of the project."
Enhance equipment in existing halls

46. Extensions with JLab 12 GeV Upgrade
11/18/2018
~7.5 GeV2
Test
BLUE = CDR or PAC30 approved, GREEN = new ideas under development

47. GEP-15: GEp/GMp up to 15 GeV2 approved by PAC32 for 12 GeV program
Perdrisat, Pentchev, Cisbani, Punjabi, Wojtsekhowski
Beam: 75 μA, 85% polarization
Target is 40 cm liquid H2
Electron arm at 37o, covers Q2 = 12.5 to 16 GeV2
Proton arm at 14o, ΔΩ ~ 35 msr
58 days of production time
resulting accuracy:
Layout and Parameters of the proposed experiment
Beam line with +/- 25 milli radian opening to beam dump
40 cm long liquid hydrogen target
Beam of 75 micro Ampere
Scattered electron detected in Lead-glass calorimeter resolution of 3.5%
at 3.5 GeV energy of final electron, position resolution of 5 mm
Proton arm consists of a Magnet, Tracking devices and Trigger calorimeter
approved by PAC32
for 12 GeV program

48. GEP-15: Projected accuracy
Plan for GEP-15
Layout and Parameters of the proposed experiment
Beam line with +/- 25 milli radian opening to beam dump
40 cm long liquid hydrogen target
Beam of 75 micro Ampere
Scattered electron detected in Lead-glass calorimeter resolution of 3.5%
at 3.5 GeV energy of final electron, position resolution of 5 mm
Proton arm consists of a Magnet, Tracking devices and Trigger calorimeter

49. Perspective: GEn up to 7.5 GeV2
The most familiar for me is GEN, I had similar experiment a year ago. In E we double
Range of Q2 from 1.5 to 3.4 GeV2. The ideas how to go ahead now exist.
With larger magnet and better tracking device we will be able to reach 7 GeV2 with reasonable
accuracy for neutron F2/F1.
Beam at 6.6 GeV
Resolution δp/p for electron - BNL magnet, GEM
He-3 cell in vacuum, lower background in neutron arm
Hybrid He-3 cell with narrow pumping laser line
Target polarization 70% at 30 µA
GEn at 7.5 GeV2 with uncertainty 30% in 25-day run

50. THANK YOU !

51. Time-Like Region _
Can be probed through e+e- -> NN or inverse reaction
Data quality insufficient to separate charge and magnetization contributions
No scaling observed with dipole form factor
Iachello only model in reasonable agreement with data
Large new accurate data set from BaBar/ CLEO /DAΦNE

52. New Data in Time-Like Region
Asymptotic behaviour for Mpp > 3 GeV/c2
Steep rise at threshold
GMn data only from FENICE and DM2
Clear need for new data

53. Consequences for d(x)
New GEn datum has strong impact on F1d behaviour

54. GPDs : x + ξ x - ξ P + Δ/2 Q2 >> P - Δ/2 t = Δ2 GPD (x, ξ ,t)*
Q2 >>
x + ξ
x - ξ
P - Δ/2
t = Δ2
GPD (x, ξ ,t)
GPDs :
ξ = 0
Fourier transform of GPDs : simultaneous distributions of quarks w.r.t. longitudinal momentum x P and transverse position b

55. GPDs : 3D quark/gluon imaging of nucleon
Fourier transform of GPDs :
simultaneous distributions of quarks w.r.t. longitudinal momentum x P and transverse position b

56. quark transverse charge densities in nucleon (II)
transversely polarized nucleon
transverse spin
e.g. along x-axis :
dipole field pattern

57. Chiral Quark Model
Calculation by Tuebingen group PRD 73, (2006)
Constituent quarks are dressed by mesonic DOF through chirally invariant effective Lagrangian
ChPT at the quark level automatically includes all excited states of the nucleon
Five free parameters, three of which are fitted to the magnetic dipole moments of the nucleons and hyperons, the two remaining ones to the form factors of the valence quarks at Q2 ≥ 0.7 GeV2

58. The Chiral Quark Cloud
Model gives excellent description of all 4 EMFF up to large Q2
Cloud in charge FF peaks at Q2≈ 0.25 GeV2
In magnetic FF mesonic cloud contributes ~15% to dipole moment