5/18/2018 Extracting the proton charge radius from low-Q2 electron/muon scattering Graphic by Joshua Rubin, ANL (Guy Ron – HUJI - giving the talk for) John Arrington, Argonne National Laboratory PSI TDR, July 25th, 2012 Test

Bottom Line Many uncertainties are common to all extractions in the experiments: Cancel in e+/e-, m+/m-, and m/e comparisons Precise tests of TPE in e-p and m-p or other differences for electron, muon scattering Charge radius extraction limited by systematics, fit uncertainties Comparable to existing e-p extractions, but not better Separate Relative

The Real Bottom Line Many uncertainties are common to all extractions in the experiments: Cancel in e+/e-, m+/m-, and m/e comparisons Precise tests of TPE in e-p and m-p or other differences for electron, muon scattering Charge radius extraction limited by systematics, fit uncertainties Comparable to existing e-p extractions, but not better Relative Comparing e/mu gets rid of most of the systematic uncertainties as well as the truncation error. Projected uncertainty on the difference of radii measured with e/mu is 0.0045. Test radii difference to the level of 7.7s (the same level as the current discrepancy)!

Unpolarized Elastic e-N Scattering 5/18/2018 Unpolarized Elastic e-N Scattering Nearly all of the measurements used Rosenbluth separation sR = ds/dW [e(1+t)/sMott] = tGM2 + eGE2 t = Q2/4M2 e = [ 1 + 2(1+t)tan2(q/2) ]-1 Reduced sensitivity when one term dominates: GM if t << 1 GE if t >> 1 GE if GE2<<GM2 (neutron) Lack of free neutron target: Corrections for nuclear effects and proton contributions These limitations  slow progress after mid 1980s GE2 tGM2 q=180o q=0o Test

Low Q2 data: Mainz Wide range in q Q2 up to 1 GeV2 5/18/2018 Low Q2 data: Mainz Wide range in q Q2 up to 1 GeV2 ~1400 high-precision cross sections: ~0.2% statistics, <1% total pt-to-pt GE, GM obtained from global fit (GE shown to 0.2 GeV2) Fits include small (<0.5%) q-dependent systematic uncertainty Q2 [GeV2] J. Bernauer, et al., PRL 105, 242001 (2010) Test

Low Q2 data: JLab E08-007 and “LEDEX” polarization transfer data 5/18/2018 Low Q2 data: JLab E08-007 and “LEDEX” polarization transfer data Extract ratio GE/GM (~1% uncertainty, 0.3-0.7 GeV2) Less sensitive to TPE Deviation from mpGE/GM=1 begin at very low Q2 Test

Low Q2 data: JLab E08-007 and “LEDEX” polarization transfer data 5/18/2018 Low Q2 data: JLab E08-007 and “LEDEX” polarization transfer data Extract ratio GE/GM (~1% uncertainty, 0.3-0.7 GeV2) Less sensitive to TPE Deviation from mpGE/GM=1 begin at very low Q2 Updated global fit Improved form factors over Q2 range of the data Constrain normalization of different data sets over wider Q2 range Test

JLab radius extraction from ep scattering Fit directly to cross sections and polarization ratios Limit fit to low Q2 data Two-photon exchange corrections applied to cross sections New Mainz data not available when fit was performed Estimate model uncertainty by varying fit function, cutoffs Different parameterizations (continued fraction, inverse polynomial) Vary Q2 cutoff (0.3,0.4,0.5,1.0) Vary number of parameters (2-5 each for GE and GM ) In each case, vary radius while fit GE, GM, and normalization factors, map out Δχ2 vs <rE>2 Go to ”Insert (View) | Header and Footer" to add your organization, sponsor, meeting name here; then, click "Apply to All"

Some other issues Relative normalization of experiments: 5/18/2018 Some other issues Relative normalization of experiments: - Typical approach: fit normalizations and then neglect uncertainty (wrong) - Ingo Sick’s approach: vary based on quoted uncertainties (very conservative) Our approach: Fit normalization factors, vary based on remaining uncertainty Systematics  hard to tell how well we can REALLY determine normalization We set minimum uncertainty to 0.5% Most older extractions dominated by Simon, et al., low Q2 data - 0.5% pt-to-pt systematics - 0.5% normalization uncertainty All other experiments quote >1-1.5% systematic, normalization uncertainties Why is Simon, et al., so much better? Neglects uncertainty in Radiative Corr. We apply uncertainty consistent with other data sets Test

Difficulties in extracting the radius 5/18/2018 Difficulties in extracting the radius Very low Q2 yields slope but sensitivity to radius is low Larger Q2 values more sensitive, have corrections due to higher order terms in the expansion Want enough Q2 range to constrain higher terms, but don’t want to be dominated by high Q2 data; Global fits almost always give poor estimates of the radii Dipole Linear fit Test

Difficulties in extracting the radius (slope) 5/18/2018 Difficulties in extracting the radius (slope) 1-GE(Q2) Very low Q2 yields slope but sensitivity to radius is low Larger Q2 values more sensitive, have corrections due to higher order terms in the expansion Want enough Q2 range to constrain higher terms, but don’t want to be dominated by high Q2 data; Global fits almost always give poor estimates of the radii I. Sick, PLB 576, 62 (2003) Q2 [GeV2] : 0 0.01 0.04 0.09 0.15 0.23 Linear fit error(stat) 4.7% 1.2% 0.5% 0.3% 0.2% Truncation Error (GDip) 0.8% 3.3% 7.5% 12% 19% Quadratic fit 19% 4.5% 1.9% 1.1% 0.6% Error: 0 0.1% 0.6% 1.4% 3.1% Cubic fit 48% 11.5% 4.9% 2.8% 1.7% Error: 0 0 0.1% 0.2% 0.5% Fits use ten 0.5% GE values for Q2 from 0 to Q2max Test

Difficulties in extracting the radius (slope) 5/18/2018 Difficulties in extracting the radius (slope) Very low Q2 yields slope but sensitivity to radius is low Larger Q2 values more sensitive, have corrections due to higher order terms in the expansion Want enough Q2 range to constrain higher terms, but don’t want to be dominated by high Q2 data; Global fits almost always give poor estimates of the radii More important for magnetic radius, where the precision on GM gets worse at low Q2 values JA, W. Melnitchouk, J. Tjon, PRC 76, 035205 (2007) Very low Q2 kinematics can have 1% cross sections yielding intercept (GM2) known to 25% Test

Robustness of the results 5/18/2018 Robustness of the results Magnetic form factor, radius much more difficult to extract GE dominates the cross section at low Q2 Reduced sensitivity to GM High-Q2 data can dominate fit when low-Q2 data is less precise Extrapolation to e=0 very sensitive to q-dependent corrections Two-photon exchange Experimental systematics Cross section, electron momentum, radiative corrections all vary rapidly with scattering angle Relative normalization between data sets with different e ranges Test

Proton magnetic radius 5/18/2018 Proton magnetic radius Significant (3.4s) difference between Mainz and JLab results 0.777(17) fm 0.867(20) fm Need to fully understand this before we can reliably combine the electron scattering values? Figure from X. Zhan et al. Test

Proton magnetic radius 5/18/2018 Proton magnetic radius Significant (3.4s) difference between Mainz and JLab results 0.777(17) fm 0.867(20) fm Need to fully understand this before we can reliably combine the electron scattering values? Potentially a 2nd Gen experiment using polarized target to extract Magnetic Radius/FF Test

Proton magnetic radius 5/18/2018 Proton magnetic radius Updated TPE yields DR=0.026 fm 0.777(17)  0.803(17) Removing fits that may have insufficient flexibility: DR≈0.02 fm Mainz/JLab difference goes from 3.4s to 1.7s, less if include any TPE uncertainty RE value, uncertainty almost unchanged: 0.879(8)  0.876(8) Magnetic radius extraction has almost no effect on the extraction of the charge radius. Test

Future low-Q2 form factor measurements Phase II of JLab polarization measurement (Hall A at JLab) Very low Q2 cross section measurements (Hall B at JLab) Low Q2 measurements of e±, m± scattering cross sections (PSI)

JLab E08-007: Low Q2 Proton Form Factor 5/18/2018 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

PSI proposal: Projected results Charge radius extraction limited by systematics, fit uncertainties Comparable to existing e-p extractions, but not better Many uncertainties are common to all extractions in the experiments: Cancel in e+/e-, m+/m-, and m/e comparisons

PSI proposal: Projected results Charge radius extraction limited by systematics, fit uncertainties Comparable to existing e-p extractions, but not better Many uncertainties are common to all extractions in the experiments: Cancel in e+/e-, m+/m-, and m/e comparisons Precise tests of TPE in e-p and m-p or other differences for electron, muon scattering

Absolute radius extraction Previous extractions, uncertainties: X. Zhan (global) R=0.8750(100) J. Bernauer(MAINZ) R=0.8790(80) CODATA06 R=0.8768(69) Electron average: R=0.8772(46) Muonic hydrogen: R=0.8418(07) Difference = 0.0354(47) Naïve extraction for projected data: Assume GM known, GE = GDipole (with R=0.8099), use linear fit R=0.7863(8)(19)(236) All m+p settings, (statistical)(systematic)(truncation) R=0.7991(21)(65)(108) m+p, only 115 MeV/c setting Does not account for normalization uncertainties, uncertainty in G_M Dominated by truncation error [estimated by Rfit-Rinput] For linear fit, truncation always decreases radius  lower limit on radius Can apply correction (50% of estimate with 100% uncertainties) and do better e vs m difference  looking for 0.8099 vs. 0.7745 fm

Absolute radius extraction e-m Difference: 0.0354 fm 1) Improved extraction #1: All beam settings, quadratic fit, 3 norm. factors R=0.8069(63)(101)(40) m+, all data 2) Improved extraction #2: Fit lowest momentum setting only R=0.7099(45)(70)(100) m+, low-p setting In both cases, the truncation error is a significant overestimate For linear fit, we know the direction and approximate size of correction Can choose better fit function (continued fraction, z-pole expansion) Can combine 1) and 2) above Low-p setting has little impact on first extraction, so the two are essentially independent Improve statistical and systematic uncertainties Can combine l+ and l- measurements TPE uncertainties cancel Statistical uncertainty reduced

Relative radius extraction e-m Difference: 0.0354 fm Truncation error not relevant if comparing e+/e-, mu+/mu-, e/mu R=0.7863(35)(40) (0) all settings, linear fit, 3 normalizations # Fit Notes d<rE2>1/2 [fm] x104 1 All 3 settings - 125 2 Low-p only 130 3 Reduced truncation 100 4 Low-p m+ + m- 90 5 All 3 Relative uncertainties 47* 6 Relative 44 * Neglects TPE. The e+/e- and m+/m- comparisons are to extract TPE, and e/m comparisons test born+TPE in #5, born only in #6

Comparison to other experiments [Rinput=0.8099] Naïve: linear fit, neglect normalization R=0.7991(45)(70)(100) PSI (m+p, only 115 MeV/c setting [Q2<0.02]) R=0.8009(63)(113)(90) CLAS proposal [Q2<0.02] R=0.8033(39)(49)(66) MAINZ kinematics, Q2<0.01, 0.4% systematics (truncation error worse if more data is included) Improved: Fit to quadratic (PSI) or linear (CLAS/MAINZ) plus normalization factors R=0.8061(63)(101)(40) PSI (m+p, all data) R=0.7947(100)(243)(150) CLAS (linear fit better as truncation error does not dominate) R=0.7981(167)(187)(118) Mainz, Q2<0.01, linear fit [1 norm. factor] R=0.7948(85)(101)(151) Mainz, Q2<0.02, linear fit [6 norm. factors] CLAS: small Q2 range, only 2 normalization factors, small angle (small GM contribution): Applying out approach will likely overestimate uncertainty May not need to vary normalization if relative slope over measured Q2 range good enough Mainz: 0.4% systematic (my assumption) very optimistic when treated as uncorrelated equivalent to 0.1% systematic if rebin Q2 in steps of 0.001 GeV2

5/18/2018 Summary Inconsistency between muonic hydrogen and electron-based extractions Fits from scattering data must take care to avoid underestimating uncertainties, but current extractions of charge radius appear to be relatively robust Future experiments planned Better constrain GM at low Q2 Map out structure of GE at low Q2 Check TPE in both electron and muon scattering Directly compare electron and muon scattering cross sections Test