1. 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
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2. 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

3. 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
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4. 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, (2005)
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5. 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, (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
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6. Proton Charge Radius Extractions: 2010-2013
4/24/2017
Proton Charge Radius Extractions:
Two new charge/magnetic radii extracted from electron scattering
J. Bernauer, et al., PRL 105 (2010)
X. Zhan, et al., PLB 705 (2011) 59
Lamb shift from muonic hydrogen
R. Pohl, et al. Nature 466, (2010)
A. Antognini, et al., Science 339 (2013) 417
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7. 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
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8. 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

9. 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
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10. Charge and Magnetic Radii
4/24/2017
Charge and Magnetic Radii
E Phase-I (recoil polarization)
~1% extraction of GEp/GMp, 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
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11. 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
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12. 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 E (2012)
1-2% on ratio down to GeV2
JA, W. Melnitchouk, J. Tjon, PRC 76, (2007)
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13. Impact of TPE Apply low-Q2 TPE expansion, valid up to Q2=0.1 GeV2
4/24/2017
Impact of TPE
JA , PRL 107, ; J.Bernauer, et al., PRL 107,
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, (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
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14. Uncertainty in low Q2 TPE calculations?
Blunden, Melnitchouk, Tjon, hadronic calculation [PRC 72, (2005)]
Borisyuk & Kobushkin: Low-Q2 expansion, valid up to 0.1 GeV2 [PRC 75, (2007)]
B&K: Dispersion analysis (proton only)
[PRC 78, (2008)]
B&K: proton + D [arXiv: ]
B&K proton only: (same as Blunden)
Full TPE calculations
JA, arXiv:

15. Additional Corrections? [JA, arXiv:1210.2677]
4/24/2017
Additional Corrections? [JA, arXiv: ]
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.
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16. 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
GeV2: CC slope  +100%/GeV2
GeV2: slope  -8%/GeV2
Higher e: up to ~15%/GeV2
Could impact extraction of RM
Need more detailed calculation
EMA
e = 0.02

17. 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)
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18. 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

19. Proton Radius E00-008 Phase-I (recoil polarization) RE RM
4/24/2017
Proton Radius
E Phase-I (recoil polarization)
~1% extraction of GEp/GMp, 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 )
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

20. 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

21. “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

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

23. 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

24. 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.
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25. “MUSE” - MUon Scattering Experiment [PSI]
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 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)

26. 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

27. 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.

28. 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

29. 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: (9) fm
Ruckstuhl et al. μC X rays: 2.483(2) fm
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30. 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

31. Fin…

32. 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

33. 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
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34. 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

35. 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 to 0.01 GeV2)
Probably lower precision than global extractions, but free from the common model dependences
Muonic 2H, 3He, 4He
Test

36. 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

37. 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

38. 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

39. 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)
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40. 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, (2010)
Test

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

42. 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,
J. Arrington - Extracting the proton charge and magnetization radii
September 9, 2011
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