1

The Proton at Low Q2

Ron Gilman*, Rutgers, The State University of New Jersey

Introduction & MotivationScattering Experiment TechniquesJefferson Lab ProgramProton Radius PuzzleSummary

*Supported by NSF PHY 09-69239

Outline

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Basics: Charge Distributions

Polarization

A standard problem in classical electromagnetic physics is calculating electric fields resulting from charge distributions.

Concepts like the root mean square (rms) radius are well defined: 〈 rE

2 〉 = ∫d3r r2 ρE(r), where ρE(r) is the normalized charge distribution.

When we start studying scattering theory in quantum mechanics, we learn that the scattering cross section from a charge distribution is the scattering cross section from a point particle times a form factor squared. The form factor is the Fourier transform of the charge distribution.

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Basics: Form Factors

Polarization

ρ(r) F(q2)

point: δ(r)/4π constant: 1

exponential: (Λ3/8π)e-Λr dipole: (1+q2/Λ2)-2

Gaussian: (a2/2π)3/2exp(-a2r2/2)

Gaussian: exp(-q2/2a2)

constant sphere: 3/(4πR3) for r<R

Oscillating: 3(qR)-3 (sinqR -

qRcosqR)

Experiments measure the form factors as functions of q2. These are observables that theories can calculate, and a basic property of proton, neutron, and nuclear structure, so interesting to measure. In NRQM, we can calculate the density from the FF.

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Basics: Small q expansion

Polarization

For small qR, and spherically symmetric distributions, one can expand the sin(qR) term in the Fourier transform to obtain:

F(q2) = 1 - q2<r>2/3! + q4<r>4/5! ...

to determine the rms radius, and higher moments of the charge distribution.

But there are two issues with this:

1) How well can the parameters be determined by a finite set of data?

2) Due to relativity, the rest frame charge distribution is not an observable.

So - we have a useful parameter commonly called the charge radius, that is not the charge radius.

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The Proton Radius

Polarization

For hadronic physicists, the proton (electric) radius is a fairly simple aspect of the structure of the proton, but it has not been one of the most interesting quantities to study.

There has been much greater interest in the high q2 / short range structure of the nucleon, to compare with quark models.

Also the radius has been considered relatively well known - the precision is already better than the theory - until recently. This was thanks largely to the work of Ingo Sick, atomic physics and electron scattering measurements had been brought into agreement:

CODATA atomic physics 0.8768 ± 0.0069

I. Sick electron scattering 0.895 ± 0.018

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The Jefferson Lab Program

Polarization

With the development of CEBAF in the 1980s and 1990s, it was recognized that major improvements could be made in our knowledge of the nucleon form factors, due to the high current, polarized electron beam - the accelerator physicists deserve much of the credit.

Major advances were also due to experiments fully utilizing polarization techniques developed by theorists in the 1960s, along with a new generation of polarimeters, advances in polarized targets, and improved implementation of ratio techniques.

This has allowed us to push the precise knowledge of proton and neutron structure of to "large" q2, several GeV2.

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ep Scattering Formulas: 1

currents

algebra

cross sections

with form factors:

and kinematic factors:

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The ProcedureMeasure cross sections

Perform radiative corrections

Do Rosenbluth separations - or - fit world data with form factor parameterization

The EM interaction is too strong!

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The ProcedureMeasure cross sections

Perform radiative corrections

Do Rosenbluth separations - or - fit world data with form factor parameterization

The electron is too light!

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Polarizations: 1Use polarizations for

form factor ratios

Sensitive to spin transport, insensitive to almost everything else ... but needs large

statistics

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Polarizations: 2

Measuring two angles at the same time allows a ratio to be made, reducing

sensitivity to PbPt, which can vary by 20% or more over time.

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The High Q2 Program at JLab?

With the proton polarimeter in Hall A: we learned

the proton electric and magnetic structures are not the same shape, the dipole, as was generally believed

the ratio GE/GM falls nearly linearly with Q2

2γ exchange effects are important, leading to a series of experiments in Halls A, B, C, OLYMPUS@DESY, Novosibirsk

With the polarized 3He target in Hall A, the neutron electric and magnetic form factors were much better determined at modest Q2

With the ratio technique in Hall B, the neutron magnetic form factor was determined to large Q2 to closely (10%) follow the dipole formula, with unprecedented precision

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The Proton Data

Red: old Rosenbluth data

Blue: JLab Hall A FPP data: Jones et al. PRL, Punjabi et al. PRC, Gayou et al. PRC, Gayou et al. PRL (Does not include recent results from Hall C by Meziane and by Puckett)

Black: "super-Rosenbluth"

Models of 2γ-exchange largely resolve the difference, moving the Rosenbluth results towards the polarization results.

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Why were we interested in low Q2 at JLab?

Articles appear studying the Zemach radius and corrections to Hydrogen hyperfine splitting - most sensitive to low Q2 FF

Friar and Sick, PLB 579 (2004)

Brodsky, Carlson, Hiller, and Hwang, PRL 96 (2005)

Friar and Payne, PRC 72 (2005)

Nazaryan, Carlson, and Griffioen, PRL 96 (2006)

Friedrich & Walcher fit, EPJA 17, 607, (2003)

2-dipole fit of the form factors leaves residual bumps, interpreted as evidence for meson-cloud effects

Not in agreement with newest data.

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Four experimentsBLAST - long planned program for low Q2 nucleon and deuteron structure with polarized beam - internal polarized target

Mainz A1 - unpolarized cross sections, 0.01 - 1 GeV2

E05-103 run 2006

FPP calibrations for low energy deuteron photodisintegration used to determine proton GE/GM

E08-007 run 2008

Dedicated FPP experiment to more systematically cover the 0.3 - 0.7 GeV2 range with higher statistics

E08-007 part II to run Nov 2011 Feb 2012 - May 2012 (along with g2p)

Dedicated polarized beam - polarized target measurements to cover the range about 0.015 - 0.16 GeV2 with high precision

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BLAST Low Q2 DataC.B. Crawford et al., Phys. Rev. Lett. 98, 052301 (2007)

BLAST FF ratio consistent with unity, within ≈2% uncertainties

Consistent with earlier fits / analyses / theory calculations

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E05-103 Low Q2 DataG. Ron et al., Phys. Rev. Lett. 99, 202002 (2007)

Our initial FPP results indicate the FF ratio is lower than previously believed, around 0.4 GeV2

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E05-103 Low Q2 DataG. Ron et al., Phys. Rev. Lett. 99, 202002 (2007)

Note that the fits ... have a range of slopes near the origin, not well constrained with data

Our initial FPP results indicate the FF ratio is lower than previously believed, around 0.4 GeV2

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E05-103 Low Q2 DataG. Ron et al., Phys. Rev. Lett. 99, 202002 (2007)

Combining Berger at al. PLB 35, 1971 dσ/dΩ with new FPP data in G. Ron et al PRL 98, we showed fits

tend to get GM about

right, but tend to over

predict GE

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Mainz A1 DataJ. Bernauer et al., Phys. Rev. Lett. 105, 242001 (2010)

The figure is from J. Bernauer’s Ph.D. thesis: Rosenbluth separation results compared to spline fit.

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E08-007 DataX. Zhan et al., PLB 705, 59 (2011).

M. Paolone et al., Phys Rev Lett 105, 072001, 2010 (Q2 = 0.8 GeV2)

Results essentially unchanged since online data.

About 1% total uncertainty on FF ratio.

Decreased ratio compared to earlier measurements prompted 2 years of thorough systematics studies: cuts, spin transport, backgrounds, ...

Major finding: with very high statistics here one sees changes in ratio as cuts are made very tight.

Reanalyzed G Ron data in very good agreement.

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Large Improvement in FF Ratio

RosenbluthPolarizationE08007 E03104

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E08-007 ImpactFit of world data except Mainz A1 data.

GE reduced up to ≈2% from 0.3 - 1 GeV2

GM increased ≈0.5% from 0.1 - 0.8 GeV2

FF ratio smaller by up to ≈2.5% from 0.3 - 0.8 GeV2

Slopes changed at Q2 = 0 changing ``radii’’.

AMT

w/ E08007

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But some tension between Mainz and JLab

Polarization

Note that the FF ratio agrees better than the individual form factors ... so the difference must arise from Mainz vs. world cross sections.

Is there an issue in the FF ratio at the low Q2 limit, or is it an end-point problem / statistics? We will know better once we have the polarized target results.

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E08-007 Phase II

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g2p + E08-007 part II

Major New Installation in Hall ALast run before 12 GeV shutdown

New Beam Diagnostics(BPM,BCM,Harps,Tungsten Calo)

Chicane

Polarized TargetLocal Dump

Septa

Strong Support from DOE and an additional ≈$200K of User Contributions

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g2p: Camsonne, Crabb, Chen, Slifer et al.

Fundamental spin observable never measured at low or moderate Q2

BC Sum Rule : violation suggested for proton at large Q2, but found satisfied for the neutron & 3He.

Spin Polarizability : Major failure (>8σ of χPT for neutron δLT. Need g2 isospin separation to solve.

Hydrogen HyperFine Splitting : Lack of knowledge of g2 at low Q2 is one of the leading uncertainties.

Proton Charge Radius : one of the leading uncertainties in extraction of <Rp> from μ−H Lamb shift.

BC

Su

m R

ule

Sp

in P

ola

riza

bili

ty δ

LT

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IssuesMajor Challenges 149 days lost to mechanical failures and design issues.Polarized target magnet repairSepta magnet redesign and later deterioration (was used in previous high dose experiment)Chicane structural support failureLocal Dump Cooling redesign

Major Achievements8 PhD students and 4 Post-DocsDAQ rate is Hall A record : 7-8 kHz/HRS with <30% deadtimeEntire new suite of beamline diagnostics for operation at 50nAPolarized target performance has been outstanding : <PT>=31%@2.5T and 85%@5T

VERY VERY

PRELIMINARY!Proton Elastic/Nitrogen Q.E.

Nitrogen Elastic

Δ-Resonance

Normalized Yield (Arb units) Transverse Asymmetry

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μGE/GM Projected Uncertainties

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μGE/GM Projected Uncertainties

Lost to targetmagnet

Lost to Septummagnet

Alreadytaken

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Hyperfine Splitting and Zemach radius

EHFS = (1+∆QED+∆pR+∆p

hvp+∆pμvp+∆p

WEAK+∆S) EFp = 1420.405 751 766 7(9)

MHz

Structure term ∆S = ∆Z + ∆POL, with ∆Z = -2amerZ(1+dradZ), and ∆POL an

inelastic structure correction dependent on g2p.

The Zemach radius is

FF rp [fm] rZ [fm]ΔZ

[ppm]

AMT 0.885 1.08 -41.43

AS 0.879 1.091 -41.85

Kelly 0.878 1.069 -40.99

F&W 0.808 1.049 -40.22

Dipole 0.851 1.025 -39.29

New 0.868 1.075 -41.22

Parameterizations vary by ≈2 ppm

Uncertainty from Q2 ≈ 0.01 - 1 GeV2

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Note on PV Experiments

For a given experimental asymmetry, with an oversimplified assumption of electric or magnetic dominance, A ≈ GpZ/Gpγ, so a reduced GE

p leads to a reduced GpZ and a reduced GE

s.

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While Low Q2 seemed important

Nucleon Structure

Impact on hyperfine splitting

Impact on parity violation

But it seemed that the differences were not all that large and the measurement not very important, until the proton radius puzzle arose in 2010.

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Proton Radius Puzzle

Polarization

Muonic hydrogen disagrees with atomic physics and electron scattering determinations of slope of FF at Q2 = 0.

``Slope’’ of GEp at Q2 = 0 (fm)

atom scattering combined

ep

CODATA: 0.8768

± 0.0060

Bernauer: 0.879 ± 0.008 Zhan: 0.870 ±

0.010combined: 0.8755 ± 0.0062

0.8761 ± 0.0046

μpPohl:

0.842 ± 0.001

? ?

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Possible Resolutions to the Puzzle / Critiques

The μp result is wrong. No doubts about the experiment, but some discussion about the theory and proton structure for extracting the proton radius.

The ep (scattering) results are wrong. The fit procedures are not good enough. Perhaps the data do not go to low enough Q2, and there are structures in the form factors.

Proton structure issues in theory. Theory critique of theory - off-shell proton in two-photon exchange leads to enhanced effects differing between μ and e, or leads to theoretically unjustified sticking-in-form-factor models.

Novel beyond-Standard-Model Physics differentiates μ and e. But constraints on novel physics exist, and there seems to be no generally accepted solution at present.

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PSI Muonic Hydrogen Measurements

Polarization

Possible issues: atomic theory & proton structure

R. Pohl et al., Nature 466, 09259 (2010): 2S➭2P Lamb shift ΔE (meV) = 209.9779(49) - 5.2262 rp

2 + 0.0347 rp3 ➮ rp = 0.842 ± 0.001.

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PSI Muonic Hydrogen Measurements

Polarization

Possible issues: atomic theory & proton structure

Proton structure: De Rujula suggested rp3 could be

anomalously large. Miller & Cloet and Distler, Bernauer & Walcher showed that this is inconsistent with

modern form factor fits. Wu & Kao showed if you add narrow peaks in unmeasured low-Q2 regions you can get different results. There is no reason at present to

believe such structures exist - and we would also expect them to affect the ep atom and scattering

determinations of the radii.

R. Pohl et al., Nature 466, 09259 (2010): 2S➭2P Lamb shift ΔE (meV) = 209.9779(49) - 5.2262 rp

2 + 0.0347 rp3 ➮ rp = 0.842 ± 0.001.

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Examples of Atomic Physics Calculations

Carlson & Vanderhaeghen (2011): box diagram corrections essentially agree with Pachucki and with Martynenko, although individual terms within the evaluation vary.

Hill & Paz (2011): Elastic contribution of C&V and others from SIFF model. Real part of inelastic not under good theoretical control and have nonphysical limiting behaviors in existing models. Numerical values given not all that different from others.

The SIFF criticism has also been made by Miller, Thomas, Carroll, & Rafelski, who point out that it has been made for many years.

But the issue remains under dispute.

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Mainz A1 ep Elastic Scattering

DataJ. Bernauer et al., PRL 105, 242001 (2010)

Cross sections ➭corrections form factors ➭fits radius

Figures from J. Bernauer’s Ph.D. thesis.

0.5% absolute uncertainty proposed, few % achieved, data normalized to GE = 1 at Q2 = 0.

Simulate radiation

Simulate backgroundFit cross sections directly

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Mainz A1 Data

From J. Bernauer’s Ph.D. thesis: spline fits tend to give r ≈ 0.875 fm, vs polynomial fits with r ≈ 0.883 fm. Uncertainties are statistics + linearly added systematics.

Reported r is an average of these, with statistical, systematic, and model uncertainties.

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Mainz A1 Data GE(Q2) = 1 - Q2r2/6 + ...

Low Q2 Mainz data: left - raw data, right- rebinned GE

Conclusion: in principle, the differences between r = 0.84 and 0.88 fm are large, but higher order terms obscure this

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e-μ UniversalityIn the 1970s / 1980s, there were several experiments that tested whether the ep and μp interactions are equal. They found 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 μpKostoulas et al. parameterization of μp vs. ep elastic differences

Entenberg et al DIS: σμp/σep ≈ 1.0±0.04 (±8.6% systematics)

no difference

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e-μ UniversalityThe 12C radius was determined with ep scattering and μC atoms. The results agree:

Cardman et al. eC: 2.472 ± 0.015 fmOffermann et al. eC: 2.478 ± 0.009 fmSchaller et al. μC X rays: 2.4715 ± 0.016 fmRuckstuhl et al. μC X rays: 2.483 ± 0.002 fmSanford et al. μC elastic: 2.32 +0.13

-0.18 fm

Perhaps carbon is right, e’s and μ’s are the same.

Perhaps hydrogen is right, e’s and μ’s are different.

Perhaps both are right - opposite effects for proton and neutron cancel with carbon.

But perhaps the carbon radius is insensitive to the nucleon radius, and μd or μHe would be a better choice.

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Example of Beyond Standard ModelBatell, McKeen, Pospelov propose new e/μ differentiating force with ≈ 100 MeV force carriers (guage boson V + complex scalar field), leading to large PV μp scattering. Two forces are needed to keep consistency with gμ-2 data.

Barger, Chiang, Keung, Marfatia indicate that the K → μν decay which could radiate V, and constrains its parameters.

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Possible Way to Resolve Puzzle:New ep Experiments

Obvious 1st guess: high energy proton beam (FNAL?) on atomic electrons, akin to low Q2 pion form factor measurements - difficult - only goes to 0.01 GeV2.

With MEIC/EIC, etc., obvious alternative in the longer term: use a ring with bending magnets to provide access to near 0 degree scattering - perhaps in several years

Very low Q2 JLab experiment, near 0o using ``PRIMEX’’ setup: A. Gasparian, D. Dutta, H. Gao et al.

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The ``PrimEx’’ Proposal

Low intensity beam in Hall B into windowless gas target.

Scattered ep and Moller electrons into HYCAL at 0o.

Lower Q2 than Mainz. Very forward angle, insensitive to 2γ, GM.

Conditionally approved by August 2011 PAC: ``Testing of this result is among the most timely and important measurements in physics.’’ Unlikely to run until 2016 or so (my estimate).

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"Our" proposal: μp Scattering at PSIArrington, Gilad, Gilman, Kohl, Meziani, Piasetzky, Ron,

Strauch

Directly test the most interesting possibility, that μp and ep scattering are different:

to higher precision than previously,

in the low Q2 region (same as Mainz and a JLab experiment now starting) for sensitivity to radius

with μ± to study possible 2γ mechanisms, but with improved sensitivity from low energy and large angle

measuring both μ±p and e±p to have direct comparison and a robust, convincing result.

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The Results!

πM1 channel, with pin = 115, 153, and 210 MeV/c: PID reasons.Choose θscatter = 20 - 100o: rates, backgrounds, systematics.ΔR = 4% ➭ ΔG’ = 8% ➭ Δσ’ = 16%.Statistics shown with estimated systematics lead to ΔR ≈ 0.01 fm for μ+, e±, but about 0.015 fm for μ-.Un-answered question: if radius differences are real, are cross section differences really this large?

projected μ+p

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More Results

Left: pseudo-random data (10o bins) showing effect of a large angle offset.Right: Estimate of uncertainties on extracted radius - systematic uncertainties dominateRelative e-μ radius has decreased uncertainties, estimated to be a factor of 2 or more.

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Experimental Issues Studied

Backgrounds: Moller & Bhabha scattering, π elastic scattering, π and μ decay in flight, scattering from cell wallsRate issues: determining event by event properties of 10 MHz of beam particles, singles rates in detectors, trigger ratesSystematic uncertainties: angle determination, beam momentum determination, multiple scattering effects, determining flux and efficiencyDetectors: GEMs, Sci-Fis, beam Cerenkov, wire chambers, threshold Cerenkov, scintillators, certain issues in triggering and DAQManagement: cost, time line, possible funding

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Some Systematics to Control

Left: should know central momentum to tenths of a percent, but can average over a few percent bin. Can “fit this out”.

Right: should know central angle to mr level, but can average over several mr. Can ``fit out’’ offset and correct cross sections for resolution.

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πM1 Channel - Nominal Characteristics≈100 - 500 MeV/c mixed beam of μ’s + e’s + π’s

-270 MeV/c

+160 MeV/c

Beam spot (nominal): 1.5 cm X x 1 cm Y, 35 mr X’ x 75 mr Y’

Momentum acceptance: 3% resolution: 0.1%

Dispersion at IFP: 7cm/%

Spots from 0.7x0.9 cm2 up to 16x10 cm2, and Δp/p from 0.1-3.0%, used previously.

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PSI Beam

Initial calculation by D. Reggiani confirms nominal beam parameters

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πM1 Channel - TargetUse 4-cm LH2 target, ≈ 0.3 g/cm2. (0.5% Lrad)

≈10x as much H as CH2 target with same multiple scattering.

θMS plane ≈ 10 mr @ 115 MeV/c, 6.5 mr @ 153 MeV/c, 4 mr @ 210 MeV/c.

Copy recent E906 target design?

MIT, Rutgers, PSI

Due to E loss in target, μ’s and e’s average over ≈ ±0.5 - 1% bin in momentum.

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π Decay Background μ’s from π decay go forward of detectors ➮ π decays near the target are not an issue. A simple GEANT gives a singles rate from 4 m of beam line in the wire chambers as 30, 150, 20 kHz. At the trigger level, these events are suppressed at least 3 orders of magnitude since they have a π RF time, and do not tend to strike two scintillator paddles that point back to the target.

210 MeV/c π→μν

153 MeV/c π→μν

115 MeV/c π→μν

At the analysis level, these events would be further suppressed by tracking back to the target, refined RF time determination, and lack of a GEM track. Their characteristics can be cross checked with empty target measurements.

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Hadronic Scattering of π

πp scattering rates calculated with cross sections from SAID and expected luminosities, assuming 2π azimuthal acceptance. Up to a few tens of kHz chamber rates, plus a DAQ rate issue for some kinematics, if not suppressed at the trigger level.

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μ Decay Background

Distribution of electrons from 153 MeV/c μ decay.

Distribution modified if μ polarized - here for S || p.

μ+ ➞ e+νμν gives several kHz track rate and ≈400 Hz e+

background trigger rate. Rejected at analysis level by requiring tracks from the target, and μ RF time from the detector - the decay electrons will be ≈ 0.8 ns faster than μ scattering events. Rate can be directly measured with empty target.

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Equipment for Test Run

UVa GEM cosmic test

Tel Aviv SciFi

South Carolina scintillators

CERN electronics in πM1

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Summary of Equipment

Beam Sci-Fi Tel Aviv, Rutgers 100 k

Beam GEMs Hampton, UVa existing

Beam Cerenkov Temple 50 k

Target MIT/... 300 k

Wire Chambers MIT 250 (200) k

Cerenkovs Jerusalem 100 k

ScintillatorsSo Carolina, Tel

Aviv220 k

Scintillators Hampton existing

Trigger Rutgers 100 k

DAQ - ?

US funding color coded: NSF or DOE

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Feb 2012 Proposal deferred pending Technical Review

June 30, 2012 Send Technical Design Report (TDR) to PSI

July 25, 2012 PAC/PSI Technical Review

September 2012 - spring

2013Funding proposals to US agencies*

fall 2012 test measurement in πM1 beamline

spring 2013 finalize designs

summer 2013 money arrives - start construction

fall 2014 start assembling equipment at PSI

late 2014 / early 2015

experiment ready to run

2015 1 + 5 month experiment run

* Tel Aviv + Jerusalem already applied for ERC advanced grant

Our "Aggressive" ScheduleIt can not be faster than this, it will likely be slower.

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Summary

Strong recent program in Low Q2 nucleon structure - form factors and spin structure.

Continued interest in slope of form factor at Q2 = 0, hyperfine splitting, parity violation, which are impacts of form factor measurements, as well as this aspect of nucleon structure for itself - e.g., is there a signature of the pion cloud?

Ongoing interest in future experiments to push precise measurements to even lower Q2.

A suggestion that GEn might go negative at high Q2.

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SummaryThe proton radius puzzle is a high-profile issue - APS plenary talk & invited sessions, PSAS2012 Symposium, Trento ECT* Workshop Nov 2012

Not clear what could be the explanation theoretically.

Not clear what could be the issue with experiments.

Electron scatterers interested in going to lower momentum.

A μp experiment which looks possible at PSI could confirm that μp and ep interactions are different, and whether it arises from 2γ exchange effects (μ+≠μ-) or possibly BSM physics (μ+≈μ-).

We have started thinking about how to set up and run the experiment; there is much more to do.

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A note on the neutron charge distribution

What are we to make of the neutron charge density at the origin being positive in the Breit frame but negative for the transverse density?

It seems intuitively obvious that as r → 0 or ∞ the sign of the charge density should be the same for the 3d and 2d transverse densities

It seems intuitive to think in the rest frame and to identify the Breit frame with the rest frame, however wrong this is.

It probably makes no sense to talks about the rest frame for a relativistic system anyway.

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Kelly Form Factors

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Why is ρ3d>0 when ρ<0 at r,b=0?Natural to assume they should have the same sign.

G Miller has suggested high Q2 data might change FT so ρT > 0 at b = 0.

ρBreit > 0 since GE > 0.

ρT < 0 since F1 < 0.

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Why is ρ3d>0 when ρ<0 at r,b=0?

Positive ρT requires positive F1, which requires GE grows relative to Q2GM. Seems unlikely. Since GM ≈ GD ≈ 1/Q2, GE grows absolutely. Seems unlikely.

Negative ρBreit requires only that GE goes sufficiently negative at high Q2.

One can generate nonsense that fits existing data and does this. Maybe future data will show this happens.

ρBreit > 0 since GE > 0.

ρT < 0 since F1 < 0.