Proton Elastic Form Factors and Radii: Precision, Problems, and New Techniques

1. 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

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 • 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

4. 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

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. 1 fm 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, 065203 (2002) A.Belitsky, X.Ji, F.Yuan, PRD69:074014 (2004) G.Miller, PRC 68:022201 (2003) x=0.1 x=0.4 x=0.7

7. Two Photon Exchange • Proton form factor measurements • Comparison of precise Rosenbluth and Polarization measurements of GEp/GMp show clear discrepancy at high Q2I.A.Qattan, et al., PRL 94 (2005) 142301 • Two-photon exchange corrections believed to explain the discrepancy • Minimal impact on polarization data P.A.M.Guichon and M.Vanderhaeghen, PRL 91, 142303 (2003) • Active program to confirm, calculate, and understand TPE P. G. Blunden et al, PRC 72 (2005) 034612 A.V. Afanasev et al, PRD 72 (2005) 013008 D. Borisyuk, A. Kobushkin, PRC 78 (2008) 025208C. 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, 092301 (2003) I.A.Qattan, et al., PRL 94, 142301 (2005)

8. Rosenbluth without TPE corrections Polarization Two Photon Exchange? Limits set for non-linear (non-Born) contributions: V. Tvaskis, et al., PRC 73 (2006) 025206 Limits set for q-dependent (non-Born) PT contributions: M. Meziane, PRL 106 (2011) 132501 Evidence (3s) for TPE in existing e+/e- comparisons (TPE changes sign with lepton charge): JA, PRC 69 (2004) 032201 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 with TPE corr. (Blunden, et al.) Polarization JA, W. Melnitchouk, J. Tjon, PRC 76, 035205 (2007)

9. Rosenbluth without TPE corrections Polarization Two Photon Exchange? IF TPE corrections fully explain the discrepancy, THENthey 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) 025206 Limits set for q-dependent (non-Born) PT contributions: M. Meziane, PRL 106 (2011) 132501 Evidence (3s) for TPE in existing e+/e- comparisons (TPE changes sign with lepton charge): JA, PRC 69 (2004) 032201 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……] 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, 035205 (2007)

10. Snapshot of new e+/e- comparisons JLab: D. Adikaram, et al., PRL 114 (2015) 062003 D. Rimal, et al., arXiv:1603.00315 VEPP-3: I.A.Rachek, et al., PRL 114 (2015) 062005 Good agreement with hadronic TPE Point proton (~Q2=0 limit) has opposite sign from data at Q2 = 1-1.5 GeV2 OLYMPUS: up to Q2~2 GeV2, ~1% uncertainties [talk by J. Bernauer] • 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) 055201 [arXiv:1603.06920]

11. 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

12. 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) = 1 - <r2> Q2 / 6 + <r4> Q4 / 120 + …. • <r2> typically defined based on this expansion • dGE(Q2)/dQ2 = - <r2>/6 + <r4> Q2 / 120 + …. • 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

13. Finite-size effects in atomic physics E • 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 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

14. Proton Charge Radius Extractions • Lamb shift from muonic hydrogen • R. Pohl, et al. Nature 466, 213-217 (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) 242001; 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)

15. 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….

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. JA , PRL 107, 119101; J.Bernauer, et al., PRL 107, 119102 Impact of TPE 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, 028203 (2007) <rE2>1/2 = 0.879(8)  0.876(8) fm [Dr=-0.003 fm (-0.3%)] <rM2>1/2 = 0.777(17)  0.803(17) fm [Dr=+0.026 fm (+3.0%)] (uncertainties do not include any TPE contribution) Excellent agreement between TPE calculations for Q2 ≤ 0.2-0.3 GeV2 JA, JPG 40 (2013) 115003; G. Lee, JA, R. Hill, PRD 92 (2015) 013013 Appear to be pretty well under control; important to include in extraction

18. 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 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) 045206

19. 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) 113005 Lee, JA, Hill, PRD 92 (2015) 013013 • 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 = 0.904(15) fm Potential issues: • Some dependence on Q2 cutoff • Magnetic radii disagree (~3 sigma) z-expansion, bounded coefficients z-expansion, unbounded coefficients

20. Low-Q2 fits Goal: limit Q2 range until single parameter fit is sufficient (remove model dependence) Hortbatsch&Hessels, PRC93 (2016) 015204 • 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]

21. Low-Q2 fits Goal: limit Q2 range until single parameter fit is sufficient (remove model dependence) Hortbatsch&Hessels, PRC93 (2016) 015204 • 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]

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) • Map out low-Q2 behavior of GE • 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. 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 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

25. MUSE@PSI R. Gilman, et al., arXiv:1303.2160 e- target sci-fi array π- e/p/m beams 0.115-0.210 MeV/c (Detector details out of date) target channel sci-fi array μ- GEM chambers beam Cerenkov “m” vs “e” radii spectrometer chambers 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 spectrometer Cerenkov Spectroscopy Scattering spectrometer trigger scintillators

26. 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

27. The various radii of the proton #3 • Flavor decomposition at low Q2: including phenomenological TPE (neglect strangeness)  Rd < Ru < RchargeI.A.Qattan, JA, A. Alsaad, PRC 91 (2015) 065203 • “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

28. The various radii of the proton #4 Bag Bag • 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 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