1. Proton elastic form factors and (various) radii
5/18/2018
Proton elastic form factors and (various) radii
John Arrington
Argonne National Laboratory
Graphic by Joshua Rubin, ANL
Baryons 16, May 16-20, Florida State University
Test

2. Outline
Explain that the elastic form factors are important observables, encoded information spatial distribution of nucleons
New techniques (Polarization)  precision & problems; where do we stand?
New technique (muonic atoms)  precision & problems; where do we stand?
Other radii: e- vs mu-, charge vs. magnetic, up vs. down, quark vs. gluon

3. Nucleon Electromagnetic Form Factors
5/18/2018
Nucleon Electromagnetic Form Factors
Fundamental properties of the proton and neutron
Contain information on charge, magnetization distributions
Non-relativistic limit: Form factors are Fourier transform of charge/magnetization densities
Connect to distribution, dynamics of quarks in hadrons
Experimental program reinvented in late ‘90s, early 2000
Considered by many to be well understood by mid/late 80s
Polarization techniques  dramatic advances in Q2 range, precision
Significant new insight into proton structure
Some unexpected problems: two-photon exchange
Many applications of these new data/techniques
Precise knowledge of FFs needed by other experiments
Neutrino scattering – cross sections, axial form factor
Parity-violating electron scattering – strangeness contributions
Proton knockout – nuclear structure, color transparency, proton in-medium structure
Test

4. New techniques: Polarization and A(e,e’N)
5/18/2018
New techniques: Polarization and A(e,e’N)
Mid ’90s brought measurements using improved techniques
High luminosity, highly polarized electron beams
Polarized targets (1H, 2H, 3He) or recoil polarimeters
Large, efficient neutron detectors for 2H, 3He(e,e’n)
Unpol: tGM2+eGE2
Pol: GE/GM
Polarized 3He target
BLAST at MIT-Bates
Focal plane polarimeter – Jefferson Lab
Test

5. Quark Orbital Angular Momentum
Many calculations reproduce the observed falloff in GE/GM
Descriptions differ in details, but many are directly or indirectly related to quark angular momentum
S. Boffi, et al.
F. Cardarelli, et al.
P. Chung, F. Coester
F. Gross, P. Agbakpe
G.A. Miller, M. Frank
C. Perdrisat, V. Punjabi, and M. Vanderhaeghen, PPNP 59 (2007)

6. Insight from New Measurements
5/18/2018
Insight from New Measurements
New information on proton structure
GE(Q2) ≠ GM(Q2)  different charge, magnetization distributions
Connection to GPDs: spin-space-momentum correlations
Model-dependent extraction of charge, magnetization distribution of proton:
J. Kelly, Phys. Rev. C 66, (2002)
A.Belitsky, X.Ji, F.Yuan, PRD69: (2004)
G.Miller, PRC 68: (2003)
x=0.1
x=0.4
x=0.7
1 fm
Rich substructure when you combine momentum and spatial, spin and spatial distributions.
Test

7. Two Photon Exchange Proton form factor measurements
5/18/2018
Two Photon Exchange
Proton form factor measurements
Comparison of precise Rosenbluth and Polarization measurements of GEp/GMp show clear discrepancy at high Q I.A.Qattan, et al., PRL 94 (2005)
Two-photon exchange corrections believed to explain the discrepancy
Minimal impact on polarization data
P.A.M.Guichon and M.Vanderhaeghen, PRL 91, (2003)
Active program to confirm, calculate, and understand TPE
P. G. Blunden et al, PRC 72 (2005)
A.V. Afanasev et al, PRD 72 (2005)
D. Borisyuk, A. Kobushkin, PRC 78 (2008) C. Carlson, M. Vanderhaeghen,
Ann. Rev. Nucl. Part. Sci. 57 (2007) 171
JA, P. Blunden, W. Melnitchouk, PPNP 66 (2011) 782
+ several completed or ongoing experiments
M.K.Jones, et al., PRL 84, 1398 (2000)
O.Gayou, et al., PRL 88, (2003)
I.A.Qattan, et al., PRL 94, (2005)
Test

8. Two Photon Exchange?
Limits set for non-linear (non-Born) contributions: V. Tvaskis, et al., PRC 73 (2006) Limits set for q-dependent (non-Born) PT contributions: M. Meziane, PRL 106 (2011) Evidence (3s) for TPE in existing e+/e- comparisons (TPE changes sign with lepton charge): JA, PRC 69 (2004) Many model-dependent TPE calculations - generally good qualitative agreement with observed discrepancy: [Afanasev, et al.; Blunden, et al.; Borisyuk and Kobushkin; Chen, et al.; etc……]
Rosenbluth without TPE corrections
Polarization
Rosenbluth with TPE corr. (Blunden, et al.)
Polarization
JA, W. Melnitchouk, J. Tjon, PRC 76, (2007)

9. Three new e+/e- experiments
Two Photon Exchange?
IF TPE corrections fully explain the discrepancy, THEN they are constrained well enough that they do not limit our extractions of the form factor
Limits set for non-linear (non-Born) contributions: V. Tvaskis, et al., PRC 73 (2006) Limits set for q-dependent (non-Born) PT contributions: M. Meziane, PRL 106 (2011) Evidence (3s) for TPE in existing e+/e- comparisons (TPE changes sign with lepton charge): JA, PRC 69 (2004) Many model-dependent TPE calculations - generally good qualitative agreement with observed discrepancy: [Afanasev, et al.; Blunden, et al.; Borisyuk and Kobushkin; Chen, et al.; etc……]
Rosenbluth without TPE corrections
Polarization
Three new e+/e- experiments
BINP Novosibirsk – internal target
Jlab/CLAS – mixed e+/e- beam
DESY (OLYMPUS) - internal target
Rosenbluth with TPE corr. (Blunden, et al.)
Polarization
JA, W. Melnitchouk, J. Tjon, PRC 76, (2007)

10. Snapshot of new e+/e- comparisons
Results in from JLab(CLAS) and Novosibirsk(VEPP-3) experiments
If Olympus also agrees with calculations, very strong overall case for TPE as culprit
Hadronic calculations appear to be reliable at low Q2, where they should be most reliable, and where many of the extremely high-precision data are taken
Other improvements to radiative corrections still being investigated
e.g.., Gramolin and Nikolenko, PRC 93 (2016) [arXiv: ]
JLab: D. Adikaram, et al., PRL 114 (2015)
D. Rimal, et al., arXiv:
VEPP-3: I.A.Rachek, et al., PRL 114 (2015)
Good agreement with hadronic TPE
Point proton (~Q2=0 limit) has opposite sign from data at Q2 = GeV2
OLYMPUS: up to Q2~2 GeV2, ~1% uncertainties [talk by J. Bernauer]

11. Down in momentum scales…
5/18/2018
Down in momentum scales…
High-Q2 Measurements (1999+)
Quark structure, orbital angular momentum
Charge/magnetization densities in Infinite-Momentum Frame
Lower-Q2 Data
Precise comparison of charge, magnetic form factors
Flavor dependence
Proton charge, magnetization radii
Graphic by Josh Rubin, Argonne National Lab
Test

12. The charge radii of the proton
5/18/2018
The charge radii of the proton
Proton elastic electromagnetic form factors
Contain information on charge, magnetization distributions
Non-relativistic limit:
GE,M(Q2) = Fourier transform of charge/magnetization densities
GE(Q2) = <r2> Q2 / <r4> Q4 / ….
<r2> typically defined based on this expansion
dGE(Q2)/dQ2 = - <r2>/6 + <r4> Q2 / ….
Electron scattering can measure GE(Q2) and extract slope
Polarization techniques  improve charge, magnetic separation at low Q2
Lamb shift in hydrogen also sensitive to charge radius
Muonic Hydrogen  dramatic increase in precision of proton radius extraction
Test

13. Finite-size effects in atomic physics
5/18/2018
Finite-size effects in atomic physics
Finite radius  level shifts
Measurement of levels/transitions  measure nuclear size:
- Lamb shift: sensitive to rE(r)
Leading size correction ~ <rE2>
Smaller “shape” corrections ~ <rE3>
- Hyperfine splitting:
Sensitive to both rE(r) and rM(r)
- Field (volume) shift between two nuclei E r p
V ~ - 1/r s
Finite size correction: time spent inside the nucleus
Muonic hydrogen: larger muon mass decreases radius factor ~200, fraction of time spent inside proton by factor of 2003; 10 million times more sensitive to radius
Test

14. Proton Charge Radius Extractions
5/18/2018
Proton Charge Radius Extractions
Lamb shift from muonic hydrogen
R. Pohl, et al. Nature 466, (2010); A. Antognini, et al., Science 339 (2013) 417
Two recent extractions associated with new electron scattering data
J. Bernauer, et al., PRL 105 (2010) ; X. Zhan, et al., PLB 705 (2011) 59
Muonic Hydrogen: Radius 4% below previous best value
Proton is 13% smaller than previously believed
Proton is 13% denser than previous believed
Directly related to strength of QCD in non-perturbative region (which would be really important if we actually knew how to extract “strength of QCD” in non-perturbative region)
Test

15. Where do we stand? Error in the muonic hydrogen measurement
5/18/2018
Where do we stand?
Error in the muonic hydrogen measurement
Additional tests performed; no evidence or indication of problems
Error in the QED corrections for the Lamb shift in hydrogen or muonic hydrogen
Corrections double checked, some very small changes and additional uncertainties
Ideas about unusual structure or unexpected corrections, but not generally accepted
Error in atomic hydrogen (Rydberg constant)
Still leaves inconsistency between Lamb shift and form factor extractions
Pushes some ‘tension’ into other variables
Error in extraction from electron scattering
Still leaves inconsistency with muonic and electronic Lamb shift measurements
No error: New physics? [V. Barger, et al.; W. Marciano; G. Miller, et al.; etc…..]
Violation of e-m universality
New particles which couple preferentially to muons
Heavy photon/Dark photon
Could also resolve g-2 problem, but modifies electronic and muonic hydrogen
Very light (1-10 MeV) scalar Higgs
Issues with neutron-Nuclei scattering
Many, many more….
Test

16. Work following 2010 muonic hydrogen result
Analysis of muonic deuterium, 3He, 4He underway
Impact of nuclear structure, especially for dispersive corrections, introduce another source of significant model dependence
New Lamb shift measurements in electronic hydrogen
Check Rydberg constant, measure several level transitions
Re-examination of electron scattering extractions
New electron (and muon) scattering measurements

17. Impact of TPE TPE does not go to zero at Q2=0
5/18/2018
Impact of TPE
JA , PRL 107, ; J.Bernauer, et al., PRL 107,
TPE does not go to zero at Q2=0
Even if it did, the radius depends on the slope approaching zero
Comparison of Q2=0 limit to low-Q2 TPE expansion, valid to Q2=0.1 GeV2
Borisyuk/Kobushkin, PRC 75, (2007)
<rE2>1/2 = 0.879(8)  (8) fm [Dr= fm (-0.3%)]
<rM2>1/2 = 0.777(17)  (17) fm [Dr= fm (+3.0%)]
(uncertainties do not include any TPE contribution)
Excellent agreement between TPE calculations for Q2 ≤ GeV2
JA, JPG 40 (2013) ; G. Lee, JA, R. Hill, PRD 92 (2015)
Appear to be pretty well under control; important to include in extraction
Test

18. Issues in extracting the radius
5/18/2018
Issues in extracting the radius
Need enough Q2 range for good lever arm to measure slope
Too few parameters bias fit
Too many blow up uncertainty
Need fit function with just enough but not too much flexibility to match data in your Q2 range. How much is that?
Linear fit to a dipole form factor always underestimates radius
Dipole
Linear fit
Two approaches: flexible enough to allow any “reasonable” behavior (at cost of precision on radius), or less flexible fit to provide better fit precision, with estimate of potential mod
Assume dipole form, ten 0.5% GE measurements from Q2 = 0 to Q2max , polynomial fits
Linear fit uncertainty best up to Q2  0.02, where fit & “truncation error” both large (~2%)
Quadratic fit works well up to Q2  0.1 before “truncation error” dominates (~1.2%)
Cubic fit works well up to Q2  0.3 before truncation error dominates (~1.1%)
See also: E. Kraus, K.E. Mesick, A. White, R. Gilman, S. Strauch, PRC 90 (2014)
Test

19. 5/18/2018
Bounded z-expansion
Make use of analyticity; transforming from Q2  z yields bounded (order unity) coefficients
Coefficient bounds limit overfitting
Can use many coefficients to avoid underfitting
Hill & Paz, PRD 62 (2010)
Lee, JA, Hill, PRD 92 (2015)
Aimed for conservative extraction (is consistency with 0.84 fm possible)?
RE = 0.895(35) from Mainz data
RE = 0.916(24) from other world’s data
 RE = (15) fm
Potential issues:
Some dependence on Q2 cutoff
Magnetic radii disagree (~3 sigma)
z-expansion, bounded coefficients
z-expansion, unbounded coefficients
Test

20. 5/18/2018
Low-Q2 fits
Goal: limit Q2 range until single parameter fit is sufficient (remove model dependence)
Hortbatsch&Hessels, PRC93 (2016)
Mainz data, Q2<0.1 GeV2
Compared 2 fits with curvature
R=0.84 (dipole)
R=0.89 (z-expansion)
Concluded that e- scattering data cannot resolve Lamb shift difference [difference = model dependence error]
Higinbotham, et al., PRC (in press)
Earlier data, Q2<0.04 GeV2
Statistical test to select order of fit
Linear fit, R ~ 0.84 fm
Conclude muonic hydrogen result is correct [neglect model dependence]
2% change in RMS radius  4% change in slope. For G_E=0.9, that’s a change in G_E of ~0.004, or 0.5% on G_E.
Test

21. 5/18/2018
Low-Q2 fits
Goal: limit Q2 range until single parameter fit is sufficient (remove model dependence)
Hortbatsch&Hessels, PRC93 (2016)
Mainz data, Q2<0.1 GeV2
Compared 2 fits with curvature
R=0.84 (dipole)
R=0.89 (z-expansion)
Concluded that e- scattering data cannot resolve Lamb shift difference [difference = model dependence error]
Higinbotham, etal., PRC (in press)
Earlier data, Q2<0.04 GeV2
Statistical test to select order of fit
Linear fit, R ~ 0.84 fm
Conclude muonic hydrogen result is correct [neglect model dependence]
2% change in RMS radius  4% change in slope. For G_E=0.9, that’s a change in G_E of ~0.004, or 0.5% on G_E.
Test

22. Where do we go from here?
Muonic measurements on 2H, 3He, 4He; New electronic Lamb shift measurements
New low-energy measurements at Mainz
Measurements at lower Q2 using Initial State Radiation (ISI)
New small-angle measurements (Hall B at JLab)
Map out low-Q2 behavior of GE
Forward angle, nearly independent of GM
Low Q2 measurements of e±, m± scattering cross sections (PSI)
Compare Two-photon exchange for leptons and muons
Make direct e-m comparison
Phase II of JLab polarization measurement (Hall A at JLab)
Provide important constraints on low-Q2 behavior of GM

23. Data taken 2013, under analysis
New data from Mainz
Proton measurements at even lower energy using Initial State Radiation
‘beam’ energies to ~50 MeV
Q2 ~ 10-4 to 10-2 GeV2
Reduce extrapolation
Data taken 2013, under analysis

24. “PRAD” - Proton RADius in Hall B at Jefferson Lab
5/18/2018
“PRAD” - Proton RADius in Hall B at Jefferson Lab
Early (pre-CLAS) Hall B experiment
[1st run in 4 hours]
– 1-3 GeV electrons, large calorimeter
Covers q = 0.7o to 4o
minimize TPE, GM contribution
Q2 = 10-4 to 10-1 GeV2
– Windowless target; no endcap scattering
– Normalize e-p to e-e scattering
Technical challenges, technical advantages
Test

25. MUSE@PSI e/p/m beams “m” vs “e” radii e- π- μ- 0.115-0.210 MeV/c
5/18/2018
R. Gilman, et al., arXiv:
GEM chambers
channel sci-fi array
target sci-fi array
spectrometer chambers
spectrometer Cerenkov
spectrometer trigger scintillators
target
beam Cerenkov
e/p/m beams
MeV/c
(Detector details out of date) e- μ- π-
“m” vs “e” radii
Muon Electron
Beams of electrons, pions, and muons:
Q2 = 10-3 to 10-1 GeV2
Compare e- and e+ (extract/cancel TPE)
Compare m- and m+ (muon TPE)
e – m comparison insensitive to model dependence
0.8409(4)
0.8758(77)
???
0.8770(60)
Spectroscopy
Scattering
Test

26. The various radii of the proton #2
5/18/2018
The various radii of the proton #2
Currently, ~3s disagreement on RM
RM < RE (0.1 fm) from Mainz data
RM ≈ RE worlds data
JLab E08-007b (polarized target)
Less sensitive to TPE
Extract R=GE/GM down to Q2 ≈ 0.02
GM with 1-2% precision
Improve RM (RE) extractions
Continue linear approach to Q2=0 ?
RM approx. 3% smaller then RE
No region where magnetization, charge are simply sum of quark contributions
Charge vs. magnetic radii
Test

27. The various radii of the proton #3
5/18/2018
The various radii of the proton #3
Flavor decomposition at low Q2: including phenomenological TPE (neglect strangeness)  Rd < Ru < Rcharge I.A.Qattan, JA, A. Alsaad, PRC 91 (2015)
“Quark net-charge radius”: u-ubar, d-dbar
Add parity-violating scattering to extract up, down, and strange quarks
“Valence quark” radius smaller than charge radius - both up and down quarks
down-quark vs. up-quark radii
Test

28. The various radii of the proton #4
Bag model:
Bag radius provides as single size scale for both quarks and gluons/sea
Constituent quark model:
Gluons and sea quarks “bound” inside massive quarks
Sea parton distribution similar to valence quark distribution
Flux tube picture:
Shown in quenched LQCD
Gluons localized in center
Bag
Bag
Rglue  Rquark
Rglue ≥ Rquark
Rglue < Rquark
charge vs. gluon radii

29. Summary
Polarization techniques led to dramatic increase in Q2 range of form factor measurements
Quark dynamics: Orbital angular momentum, potential impact of diquark structure of nucleon, “imaging” of the nucleon, etc…
Paralleled progress in theory, interpretation
Significant improvement in precision at low Q2
Understanding of two-photon exchange
Polarization techniques and extremely precise cross section data
Proton radius puzzle still under active investigation
Many implications of these new results
Precise knowledge of FFs needed by other experiments
Strangeness contributions to nucleon structure
Advances in other programs, relying on same techniques
Medium modification of nucleon structure