1. 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

2. 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

3. 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
Test radii difference to the level of 7.7s (the same level as the current discrepancy)!

4. 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

5. 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, (2010)
Test

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

7. Low Q2 data: JLab E08-007 and “LEDEX” polarization transfer data
5/18/2018
Low Q2 data:
JLab E and “LEDEX” polarization transfer data
Extract ratio GE/GM (~1% uncertainty, 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

8. 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"

9. 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

10. 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

11. 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] :
Linear fit error(stat) % % % % %
Truncation Error (GDip) 0.8% % % % %
Quadratic fit % % % % %
Error: % % % %
Cubic fit % % % % %
Error: % % %
Fits use ten 0.5% GE values for Q2 from 0 to Q2max
Test

12. 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, (2007)
Very low Q2 kinematics can have 1% cross sections yielding intercept (GM2) known to 25%
Test

13. 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

14. 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

15. 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

16. 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

17. 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)

18. 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

19. 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

20. 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

21. 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 = (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 vs fm

22. Absolute radius extraction
e-m Difference: 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

23. Relative radius extraction
e-m Difference: 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

24. 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 GeV2

25. 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