Update on the proton radius puzzle: 4/24/2017 Update on the proton radius puzzle: What electron (and muon) scattering can tell us about the proton radius John Arrington, Argonne National Laboratory 2013 JLab Users Meeting, May 29-31, Jefferson Lab Test

Electron scattering Powerful and versatile tool, long history of probing proton structure High energy scattering resolves small scale structure: quark and gluons Low energy scattering reveals large scale structure: Charge radius Graphic by Joshua Rubin, Argonne National Laboratory

New techniques: Polarization and A(e,e’N) 4/24/2017 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

Polarization vs. Rosenbluth: GE/GM 4/24/2017 Polarization vs. Rosenbluth: GE/GM mpGEp/GMp from Rosenbluth measurements New data: Recoil polarization and p(e,p) “Super-Rosenbluth” Slope from recoil polarization JLab Hall A: M. Jones, et al.; O. Gayou, et al. I. A. Qattan, et al, PRL 94, 142301 (2005) Test

4/24/2017 Two Photon Exchange Golden mode: positron-proton vs. electron-proton elastic scattering Existing data show evidence for TPE contributions that could explain the discrepancy Signal for non-zero TPE is only at 3s level JA, PRC 69, 032201 (2004) IF TPE fully explains discrepancy, then they are constrained well enough that they do not limit our extractions of the high-Q2 form factors Three new e+/e- experiments run: BINP Novosibirsk – internal target JLab Hall B – LH2 target, CLAS (2012) DESY (OLYMPUS) - internal target Test

Proton Charge Radius Extractions: 2010-2013 4/24/2017 Proton Charge Radius Extractions: 2010-2013 Two new charge/magnetic radii extracted from electron scattering J. Bernauer, et al., PRL 105 (2010) 242001 X. Zhan, et al., PLB 705 (2011) 59 Lamb shift from muonic hydrogen R. Pohl, et al. Nature 466, 213-217 (2010) A. Antognini, et al., Science 339 (2013) 417 Test

Finite-size effects in atomic physics 4/24/2017 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 Test

Proton Charge Radius Muon Electron 0.8409(4) 0.8758(77) ??? 0.8770(60) 4/24/2017 Proton Charge Radius Muon Electron 0.8409(4) 0.8758(77) ??? 0.8770(60) Further test and improve electron scattering results Spectroscopy Scattering Test

Challenges in extracting the proton radius 4/24/2017 Challenges in extracting the proton radius Radius defined as slope of GE(Q2) at Q2=0 Need to understand any small changes that occur as the beam energy and scattering angles change Need to apply correction for small angle-independent part ( GM2 ) Need to control extrapolation to Q2=0 Need to correct for Coulomb effects/two-photon exchange Some proposed explanations (that can be tested) Structure in GE that modified extrapolation Difference in TPE contributions for muon, electron cases Test

Charge and Magnetic Radii 4/24/2017 Charge and Magnetic Radii E00-008 Phase-I (recoil polarization) ~1% extraction of GEp/GMp, 0.3-0.8 GeV2 Smaller TPE corrections than in s Global fit with TPE: RE = 0.875(10) fm Precise ratios help fix normalizations when combining multiple data sets RE X. Zhan, et al., PLB 705, 59 (2011) RM Test

Linear fit to a dipole form factor always underestimates radius 4/24/2017 Fitting issues Need Q2 lever-arm to get slope Need to limit Q2 to avoid data that’s insensitive to the radius Need to have fit function with enough flexibility to match data in your Q2 range Linear fit to a dipole form factor always underestimates radius Dipole Linear fit Linear fit works well up to Q2  0.02, but fit function mismatch error dominates (~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%) Based on assumption of dipole form, ten 1% measurements from Q2 = 0 to Q2max Test

Fitting issues: Magnetic radius 4/24/2017 Fitting issues: Magnetic radius Cross section sensitivity to GM decreases at low Q2 Sensitive to q-dependent effects Extrapolation more difficult Fits can be dominated by precise high-Q2 extractions Better low-Q2 GM data important: Phase-II of E08-007 (2012) 1-2% on ratio down to 0.015 GeV2 JA, W. Melnitchouk, J. Tjon, PRC 76, 035205 (2007) Test

Impact of TPE Apply low-Q2 TPE expansion, valid up to Q2=0.1 GeV2 4/24/2017 Impact of TPE JA , PRL 107, 119101; J.Bernauer, et al., PRL 107, 119102 Apply low-Q2 TPE expansion, valid up to Q2=0.1 GeV2 Small change, but still larger than total quoted uncertainty Main impact is on GM Borisyuk/Kobushkin, PRC 75, 028203 (2007) RADII: <rM2>1/2 goes from 0.777(17) to 0.803(17) fm [+3.0%, ~1.5 sigma] <rE2>1/2 goes from 0.879(8) to 0.876(8) fm [-0.3%, <0.5 sigma] Helps resolve discrepancy in magnetic radius, minimal impact on charge radius Note: quoted uncertainties do not include any contribution related to TPE A1 collab. argues that these are extremely large, TPE very poorly understood Test

Uncertainty in low Q2 TPE calculations? Blunden, Melnitchouk, Tjon, hadronic calculation [PRC 72, 034612 (2005)] Borisyuk & Kobushkin: Low-Q2 expansion, valid up to 0.1 GeV2 [PRC 75, 038202 (2007)] B&K: Dispersion analysis (proton only) [PRC 78, 025208 (2008)] B&K: proton + D [arXiv:1206.0155] B&K proton only: (same as Blunden) Full TPE calculations JA, arXiv:1210.2677

Additional Corrections? [JA, arXiv:1210.2677] 4/24/2017 Additional Corrections? [JA, arXiv:1210.2677] 2nd Born Effective Momentum Approximation Coulomb potential boosts energy at scattering vertex Flux factor enhancement Used in QE scattering (Coulomb field of nucleus) Key parameter: average e-p separation at the scattering ~1.6 MeV at surface of proton Decreases as 1/R outside proton Assume scattering occurs at R = 1/q Limits correction below Q20.06 GeV2 where scattering away from proton EMA EMA not more precise, but potentially includes more information. Note Q^2-depndence, a lot like hard TPE. Test

Additional Corrections? EMA Very little effect at high e ; no impact on charge radius Large Q2 dependence at low e Proton radius: slope  -600%/GeV2 0-0.02 GeV2: CC slope  +100%/GeV2 0.05-0.2 GeV2: slope  -8%/GeV2 Higher e: up to ~15%/GeV2 Could impact extraction of RM Need more detailed calculation EMA e = 0.02

Proton magnetic radius 4/24/2017 Proton magnetic radius Updated TPE yields DRM=0.026 fm 0.777(17)  0.803(17) If more parameters required for RM, could further increase radius Mainz/JLab difference goes from 3.4s to ~2s or less, further reduced if include TPE uncertainty RE value almost unchanged Sick (2003) Bernauer, et al. (2010) Zhan, et al., (2010) Antognini, et al., (2013) Test

Future low-Q2 form factor measurements Phase II of JLab polarization measurement (Hall A at JLab) Provide important constraints on low-Q2 behavior of GM Updated measurements at Mainz Measurements at lower Q2 using Initial State Radiation (ISI) Measure electron—deuteron scattering Very low Q2 cross section 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

Proton Radius E00-008 Phase-I (recoil polarization) RE RM 4/24/2017 Proton Radius E00-008 Phase-I (recoil polarization) ~1% extraction of GEp/GMp, 0.3-0.8 GeV2 Global fit with TPE: RE = 0.875(10) fm Smaller TPE corrections than in s Precise ratios help fix normalizations when combining multiple data sets RE X. Zhan, et al., PLB 705, 59 (2011) RM Phase-II (polarized target - 2012) Extract R=GE/GM down to Q2 = 0.015 Extract GM to 1-2% at very low Q2 Improve RM (and RE) extractions Improve calc. of hyperfine splitting Continue linear approach to Q2=0 ? RM approx. 3% smaller then RE No region where magnetization, charge are simply sum of quarks Test

Both plan to begin data taking in 2013 New data from Mainz Proton measurements at even lower energy using Initial State Radiation Reduce extrapolation Improved GM sensitivity Deuteron measurements Compare deuteron radius to muonic spectroscopy Both plan to begin data taking in 2013

“PRAD” - Proton RADius in Hall B at Jefferson Lab 4/24/2017 “PRAD” - Proton RADius in Hall B at Jefferson Lab First experiment in Hall B – High energy beam, small scattering angle Large calorimeter covers q = 0.7o to 4o – Windowless gas target No endcap scattering – Normalize e-p to e-e scattering Technical challenges, technical advantages Test

Separation of Elastic from Moller Events Overlap of Ee' spectra of radiated events Calorimeter detects good part of hard radiated photons

Extraction of Proton Charge Radius Linear fit yields dR=0.006 fm [0.7%] statistical uncertainty Systematics comparable to high-Q2 statistics Forward angle: negligible GM contribution, TPE corrections Very low Q2 values (no extrapolation), all measured simultaneously

4/24/2017 PRAD++ ?? Plan is to use inner calorimeter only (better position resolution) Refurbishing full calorimeter gives more Q2 coverage at each energy Better lever arm at 1.1 GeV More overlap, systematics checks More work, more manpower Additional data at higher energy Total rates in calorimeter go down Rates for data (fixed Q2 range) go up Larger Q2 coverage in less time, but pushed to smaller angle If systematics for data at smallest angles are a larger-than- expected issue, these data provide additional overlap/tests. Test

“MUSE” - MUon Scattering Experiment [PSI] R. Gilman, et al., arXiv:1303.2160 GEM chambers channel sci-fi array target sci-fi array spectrometer chambers spectrometer Cerenkov spectrometer trigger scintillators target beam Cerenkov e/p/m beams 0.115-0.210 MeV/c e- μ- π-- Note: Detector details not up to date Beams of electrons, pions, and muons: Very low Q2 (reduced extrapolation) Compare e- and e+ (opposite Coulomb/TPE correction) Compare m- and m+ (compare electron/muon corrections)

MUSE Radius Extractions Left: independent absolute extraction Right: extraction with only relative uncertainties TPE extraction in l+/l- comparison e-m comparison: 5s value for R(e)-R(m) if discrepancy persists

e-μ Universality Ellsworth et al., form factors from elastic μp Several experiments compared e-p, μ-p interactions. No convincing differences, once the μp data are renormalized up about 10%. In light of the proton ``radius’’ puzzle, the experiments are not as good as one would like.

e-μ Universality Ellsworth et al., form factors from elastic μp Several experiments compared e-p, μ-p interactions. No convincing differences, once the μp data are renormalized up about 10%. In light of the proton ``radius’’ puzzle, the experiments are not as good as one would like. no difference Kostoulas et al. parameterization of μp vs. ep elastic differences

4/24/2017 e-μ Universality Ellsworth et al., form factors from elastic μp Several experiments compared e-p, μ-p interactions. No convincing differences, once the μp data are renormalized up about 10%. In light of the proton ``radius’’ puzzle, the experiments are not as good as one would like. Entenberg et al. DIS: σμp/σep ≈ 1.0±0.04±0.09 Consistent extractions of 12C radius from e-C scattering and μC atoms Offermann et al. e-C: 2.478(9) fm Ruckstuhl et al. μC X rays: 2.483(2) fm Test

Final check: e-μ universality, physics beyond SM Muon Electron 0.8409(4) 0.8758(77) ??? 0.8770(60) MUSE: Start data taking in 2015 or 2016 Muon interaction different from electron??? Spectroscopy Scattering

Fin…

What happens when this program is finished? Will yield improved understanding of our precision techniques Might find experimental correction that is larger than we thought Still leaves difference between electron and muon spectroscopy Test and improve our calculations of electromagnetic interactions Might show that some correction was larger than expected Could highlight interesting physics or unusually large correction Direct test of “electron-muon universality” Most exciting and intriguing possibility Ideas for “new physics” explanations being actively investigated

Impact of low Q2 form factor measurements 4/24/2017 Impact of low Q2 form factor measurements Zemach moment: Comes from integral of [1-GE(Q2)GM(Q2)/mp] / Q2 1/Q2 term suppresses high Q2 [1-GE(Q2)GM(Q2) /mp] suppresses lowest Q2 As GE, GM become small, [1-GE(Q2)GM(Q2) /mp]  1, and the form factor uncertainty has almost no impact on Zemach moment Phase I (complete) Phase II (2012) Significant contribution to integral above Q2=1 GeV2 and below Q2=0.01 GeV2 Negligible contribution to uncertainty above Q2=1 GeV2 Test

Proton Charge Radius Muon Electron 0.8409(4) 0.8758(77) ??? 0.8770(60) 4/24/2017 Proton Charge Radius 3 years later, still have a mystery Muon Electron 0.8409(4) 0.8758(77) ??? 0.8770(60) Further test and improve electron scattering results Fill in the muon scattering case Spectroscopy Scattering Test

Where do we stand Error in the muonic hydrogen measurement 4/24/2017 Where do we stand Error in the muonic hydrogen measurement Not much evidence or indication Error in Rydberg constant Still leaves inconsistency between Lamb shift and form factor measurements Error in the QED corrections for the Lamb shift in hydrogen or muonic hydrogen Everything has been checked, some very small changes Higher order terms from charge distribution could change results but not resolve discrepancy DeRujula resolves discrepancy with toy model of form factor, requires ~10% change in normalization of cross section data (dramatic dropoff from GE(0)=1 to lowest Q2 measurements) No error: New physics? [V. Barger, et al., W. Marciano] 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 Future plans Proposal for very low Q2 measurements at JLab (Q2 from 0.0001 to 0.01 GeV2) Probably lower precision than global extractions, but free from the common model dependences Muonic 2H, 3He, 4He Test

JLab E08-007: Low Q2 Proton Form Factor 4/24/2017 JLab E08-007: Low Q2 Proton Form Factor Phase-I (polarization transfer) Phase-II (polarized target: Feb-may 2012) Extract R down to Q20.01 (important for GM extraction) Good overlap with Phase-I, using different technique Lost to problems with target magnet (Q2>0.2), septum magnet (Q2>0.1) Linear approach to Q2=0? If so, no region where magnetization, charge are simply sum of quarks Test

Fitting issues: Magnetic radius 4/24/2017 Fitting issues: Magnetic radius Cross section sensitivity to GM decreases at low Q2 Extrapolation to Q2=0 is more difficult for magnetic radius GM more sensitive to angle-dependent effects at low Q2 Precise data at higher Q2 have more statistical power than the low Q2 data J.Bernauer, PhD Thesis Test

Averaging of fits? No visible effect in <RE>2 4/24/2017 Averaging of fits? Weighted average: 0.777 “By eye” average of high-N fits Limited precision on GM at low Q2 means that more parameters are needed to reproduce low Q2 data  Low Npar fits may be less reliable Statistics-weighted average of fits with different #/parameters  Emphasizes small Npar Expect fits with more parameters to be more reliable Increase <rM>2 by ~0.020 Increase “statistical” uncertainty No visible effect in <RE>2 Test

Evaluating uncertainties: JLab global analysis Fit directly to cross sections and polarization ratios Limit fit to low Q2 data Two-photon exchange corrections applied to cross sections Estimate model uncertainty by varying fit function, cutoffs Different parameterizations (continued fraction, inverse polynomial) Vary number of parameters (2-5 each for GE and GM ) Vary Q2 cutoff (0.3, 0.4, 0.5, 1.0) Mainz does similar tests Always fit full Q2 range (up to ~1 GeV2) More data allows for fit functions with 8-11 parameters for GE and GM P. G. Blunden, W. Melnitchouk, J. Tjon, PRC 72 (2005) 034612 Go to ”Insert (View) | Header and Footer" to add your organization, sponsor, meeting name here; then, click "Apply to All"

Low Q2 data: Mainz ~1400 high-precision cross sections: 4/24/2017 Low Q2 data: Mainz ~1400 high-precision cross sections: ~ 0.2% statistics < 0.5% systematics Wide range in q Q2 up to 1 GeV2 GE, GM obtained from global fit Q2 [GeV2] J. Bernauer, et al., PRL 105, 242001 (2010) Test

Comparison to Muonic Hydrogen MAINZ: <RE2>1/2 = 0.879(80) <RM2>1/2 = 0.777(170) Muonic Hydrogen: <RE2>1/2 = 0.8409(4) RMS charge (magnetization) radius related to the slope of GE (GM) at Q2=0: GE(Q2) ~ 1 – 1/6 Q2<R2> + …

Two-photon exchange corrections 4/24/2017 Two-photon exchange corrections QED: straightforward to calculate QED+QCD: depends on proton internal structure m m Mainz analysis took Q2=0 limit of “2nd Born approximation” (structureless proton) Applied 50% uncertainty in fit (no uncertainty for radius extraction) 2nd Born approximation (Coulomb correction) has significant Q2 dependence at low Q2 At these Q2 values, 2nd Born, full hadronic TPE, and low Q2 expansion of TPE are all in good agreement Q2=0 Q2=0.03 Q2=0.1 Q2=0.3 Q2=1 JA (Comment), PRL 107, 119101 J. Arrington - Extracting the proton charge and magnetization radii September 9, 2011 Test