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