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Update on the proton radius puzzle:
What electron (and muon) scattering can tell us about the
proton radius
John Arrington, Argonne National Laboratory2013 JLab Users Meeting, May 29-31, Jefferson Lab
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) 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)
Polarized 3He target
BLAST at MIT-Bates
Focal plane polarimeter – Jefferson Lab
Unpol:GM2+GE
2
Pol:GE/GM
Polarization vs. Rosenbluth: GE/GM
pGEp/GMp from Rosenbluth measurements
I. A. Qattan, et al, PRL 94, 142301 (2005)JLab Hall A: M. Jones, et al.; O. Gayou, et al.
New data: Recoil polarization and p(e,p) “Super-Rosenbluth” Slope from recoil
polarization
Golden mode: positron-proton vs. electron-proton elastic scattering
Three new e+/e- experiments run:
• BINP Novosibirsk – internal target
• JLab Hall B – LH2 target, CLAS (2012)
• DESY (OLYMPUS) - internal target
Two Photon Exchange
JA, PRC 69, 032201 (2004)
Existing data show evidence for TPE contributions that could explain the discrepancy
Signal for non-zero TPE is only at 3level IF TPE fully explains discrepancy, then they are constrained well enough
that they do not limit our extractions of the high-Q2 form factors
Two new charge/magnetic radii extracted from electron scatteringJ. Bernauer, et al., PRL 105 (2010) 242001X. Zhan, et al., PLB 705 (2011) 59
Lamb shift from muonic hydrogenR. Pohl, et al. Nature 466, 213-217 (2010)A. Antognini, et al., Science 339 (2013) 417
Proton Charge Radius Extractions: 2010-2013
Finite-size effects in atomic physics
rE
s
p
V ~ - 1/r
Finite radius level shifts
Measurement of levels/transitions measure nuclear size:
- Lamb shift: sensitive to E(r)
Leading size correction ~ <rE2>
Smaller “shape” corrections ~ <rE3>
- Hyperfine splitting:
Sensitive to both E(r) and M(r)
- Field (volume) shift between two nuclei:
Finite size correction: time spent inside the nucleus
AA
FS rZe
222 )0(3
2
Proton Charge Radius
0.8409(4) 0.8758(77)
??? 0.8770(60)
Muon Electron
Spectroscopy
Scattering
Further test and improve electron scattering results
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 ( GM
2 )– 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
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 – Global fit with TPE: RE = 0.875(10) fm
– Precise ratios help fix normalizations when combining multiple data sets
X. Zhan, et al., PLB 705, 59 (2011)
RE
RM
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
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
Linear fit to a dipole form factor always underestimates radius
Fitting issues: Magnetic radius
JA, W. Melnitchouk, J. Tjon, PRC 76, 035205 (2007)Cross section sensitivity to GM decreases at low Q2
•Sensitive to -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
Impact of TPE
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
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
JA , PRL 107, 119101; J.Bernauer, et al., PRL 107, 119102
Borisyuk/Kobushkin, PRC 75, 028203 (2007)
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 + [arXiv:1206.0155]
B&K proton only: (same as Blunden)
Full TPE Full TPE calculationscalculations
JA, arXiv:1210.2677
Additional Corrections?
[JA, arXiv:1210.2677] 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 Q20.06
GeV2 where scattering away from proton
EMAEMA
22ndnd Born Born
Additional Corrections?
Very little effect at high ; no impact on charge radius
Large Q2 dependence at low
Proton radius: slope -600%/GeV2
– 0-0.02 GeV2: CC slope +100%/GeV2
– 0.05-0.2 GeV2: slope -8%/GeV2
– Higher : up to ~15%/GeV2
CouldCould impact extraction of Rimpact extraction of RMM
– Need more detailed calculation
EMAEMA
= 0.02= 0.02
EMAEMA
Proton magnetic radius
Sick (2003)
Bernauer, et al. (2010)
Zhan, et al., (2010)
Antognini, et al., (2013)
Updated TPE yields RM=0.026 fm
0.777(17) 0.803(17)
If more parameters required for RM, could further increase radius
Mainz/JLab difference goes from 3.4 to ~2or less, further reduced if include TPE uncertainty
RE value almost unchanged
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 scattering cross sections (PSI)– Map out low-Q2 behavior of GE
– Compare Two-photon exchange for leptons and muons– Make direct e- comparison
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 – Precise ratios help fix normalizations when combining multiple data sets
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
X. Zhan, et al., PLB 705, 59 (2011)
RE
RM
New data from Mainz
1. Proton measurements at even lower energy using Initial State Radiation– Reduce extrapolation– Improved GM sensitivity
2. Deuteron measurements– Compare deuteron radius
to muonic spectroscopy
Both plan to begin data taking in 2013
– High energy beam, small scattering angle Large calorimeter covers = 0.7o to 4o
– Windowless gas target No endcap scattering
– Normalize e-p to e-e scattering
“PRAD” - Proton RADius in Hall B at Jefferson Lab
First experiment in Hall B
Overlap of Ee' spectra of radiated events
Calorimeter detects good part of hard radiated photons
Separation of Elastic from Moller Events
Extraction of Proton Charge Radius
Linear fit yields R=0.006 fm [0.7%] statistical uncertaintySystematics comparable to high-Q2 statistics
• Forward angle: negligible GM contribution, TPE corrections• Very low Q2 values (no extrapolation), all measured simultaneously
• 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
PRAD++ ??
• 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.
e-
μ-
π--
“MUSE” - MUon Scattering Experiment [PSI]
GEM chambers
channel sci-fi array
target sci-fi array
spectrometer chambersspectrometer Cerenkovspectrometer trigger scintillators
target
beam Cerenkov
Beams of electrons, pions, and muons: Very low Q2 (reduced extrapolation) Compare e and e(opposite Coulomb/TPE correction) Compare and (compare electron/muon corrections)
e//beams0.115-0.210 MeV/c
Note: Detector details not up to date
R. Gilman, et al., arXiv:1303.2160
26
MUSE Radius Extractions
Left: independent absolute extractionRight: extraction with only relative uncertainties
TPE extraction in l+/l- comparisone- comparison: 5 value for R(e)-R() if discrepancy persists
e-μ Universality
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.
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.
Ellsworth et al., form factors from elastic μp
no difference
Kostoulas et al. parameterization of μp vs. ep elastic differences
e-μ Universality
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.
Ellsworth et al., form factors from elastic μp
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) fmRuckstuhl et al. μC X rays: 2.483(2) fm
e-μ Universality
0.8409(4) 0.8758(77)
??? 0.8770(60)
Muon Electron
Spectroscopy
Scattering
MUSE: Start data taking in 2015 or 2016
Muon interaction different from electron???
Final check: e-μ universality, physics beyond SM
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 Zemach moment: Comes from integral of [1-GE(Q2)GM(Q2)/p] / Q2
– 1/Q2 term suppresses high Q2
– [1-GE(Q2)GM(Q2) /p] suppresses lowest Q2
– As GE, GM become small, [1-GE(Q2)GM(Q2) /p] 1, and the form factor uncertainty has almost no impact on Zemach moment
Significant contribution to integral above Q2=1 GeV2 and below Q2=0.01 GeV2
Negligible contribution to uncertainty above Q2=1 GeV2
Phase I (complete)
Phase II (2012)
Proton Charge Radius
0.8409(4) 0.8758(77)
??? 0.8770(60)
Muon Electron
Spectroscopy
Scattering
Further test and improve electron scattering results
Fill in the muon scattering case
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- 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
JLab E08-007: Low Q2 Proton Form FactorPhase-I (polarization transfer)Phase-II (polarized target: Feb-may 2012)–Extract R down to Q20.01 (important for GM extraction)
–Good overlap with Phase-I, using different techniqueLost to problems with target magnet (Q2>0.2), septum magnet (Q2>0.1)
–Linear approach to Q2=0?If so, no region wheremagnetization, chargeare simply sum of quarks
Fitting issues: Magnetic radius
J.Bernauer, PhD ThesisCross 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
Averaging of 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
Weighted average: 0.777
“By eye” average of high-N fits
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
11
1
1)(
21
20
2
QbQb
QGCF
...1
1)(
62
41
20
2
QbQbQbQGpoly
P. G. Blunden, W. Melnitchouk, J. Tjon, PRC 72 (2005) 034612
Low Q2 data: Mainz
~1400 high-precision cross sections:
– ~ 0.2% statistics– < 0.5% systematics– Wide range in – Q2 up to 1 GeV2
GE, GM obtained from global fit
J. Bernauer, et al., PRL 105, 242001 (2010)Q2 [GeV2]
Comparison to Muonic Hydrogen
MAINZ: <RE2>1/2 = 0.879(80)
<RM2>1/2 = 0.777(170)
Muonic Hydrogen: <RE
2>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> + …
September 9, 2011
J. Arrington - Extracting the proton charge and magnetization radii
42
Two-photon exchange corrections
Mainz analysis took Q2=0 limit of “2nd Born approximation” (structureless proton)
Applied 50% uncertainty in fit (no uncertainty for radius extraction)
JA (Comment), PRL 107, 119101
QED: straightforward to calculate
QED+QCD: depends on proton internal structure
Q2=0
Q2=0.1
Q2=0.3
Q2=1
Q2=0.03
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
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