1. A Measurement of Two-Photon Exchange in Unpolarized Elastic Electron-Proton Scattering
James Johnson
Northwestern University & Argonne National Lab
For the Rosen07 Collaboration
I am the graduate student working on this particular experiment
Three experiments in the collaboration

2. Outline
The electromagnetic interactions of the proton are described by two form factors, GE (Q2) and GM(Q2)
Two methods of extraction, but their results don’t agree
Leading candidate is two-photon exchange
Parameterize the proton charge and magnetic moment distributions – in nonrel. Limit, Fourier transforms

3. Prior Experiments Rosenbluth Scattering
Measure electron-proton scattering
Factor out Mott cross section, and get a function linear in the squares of the form factors
τGM2 + εGE2
Polarization Transfer
Scatter longitudinally polarized electrons from unpolarized protons
The ratio GE/GM is proportional to pT/pL
Does not give form factors directly
Rosenbluth: angular dependant function
Tau – proportional to momentum transfer, Q^2 / (4*Mp^2)
Epsilon – angular dependant, virtual photon longitudinal polarization, (1 + 2*(1+tau) * tan^2 (theta_e/2))^-1
G_E/G_M = p_T/p_L * (E-E’)/(2*Mp) * tan(theta_e/2)

4. Disagreement Rosenbluth gives a ratio that stays flat
The errors on GE increase with Q2
Polarization transfer shows a decreasing ratio
Smaller errors at high Q2
Implies a difference between charge and magnetic distributions
It was suggested that there may be a problem inherent in the Rosenbluth method to cause these errors
J. Arrington, Phys. Rev. C69:022201, 2004
M. Jones et al, Phys. Rev. Lett. 84: , 2000
O. Gayou et al, Phys. Rev. Lett. 88:092301, 2002

5. Precision Rosenbluth JLab E01-001
Detect scattered protons instead of electrons
Same reaction, smaller angular dependant corrections
Precision comparable to polarization transfer
Agrees with electron Rosenbluth
The disagreement is real
High-precision measurement of the discrepancy
I. A. Qattan et. al, Phys. Rev. Lett. 94:142301, 2005

6. Magnitude of the Discrepancy
Shows the difference increasing as we increase Q^2
5-8% correction on reduced cross section
Solid line – fit to E ‘Super-Rosenbluth’
Dashed line – taken from polarization transfer ratio

7. Two-Photon Exchange
Both methods account for radiative corrections, but neither considers two-photon exchange
Difficult to Calculate
Rough qualitative agreement
Different ε dependence
Scale not predicted
Delta is the percentage change in the cross section

8. Rosenbluth 2007 JLab E05-017 HMS in Hall C at Jefferson Lab
4cm liquid hydrogen target for elastics
4cm aluminum dummy for endcap subtraction
May 8 – July 13, 2007
Add picture of HMS

9. Rosenbluth 2007 102 Kinematics points Q2 0.40-5.76 GeV2
13 points at Q2=0.983
10 points at Q2=2.284
Kinematics taken
Each solid, colored line is a different beam energy, data is where the lines intersect our Q^2 values
In particular, very low- and very high-epsilon points, where there is little previous data
16 Q^2 values
17 Ebeam values, range
At each Q^2, several points for an L-T seperation

10. Time of Flight Calibration
Acceptance cuts
Solid – full delta-β spectrum
Small dashes - Aerogel cut to exclude pions
Large dashes - Beta cut to exclude deuterons

11. Time of Flight Calibration
Six total calibrations
Three momentum ranges
Before/After discriminator replacement
Solid line – uncalibrated
Dashed line - calibrated

12. Aerogel Calibration Aerogel distinguishes π+ from heavier particles
Fit the position of the 1-photoelectron peak
Not possible on runs with low pion count due to interference from the pedestal

13. Analysis Steps Sum data & dummy runs at selected kinematic
Simulate elastics, pion photoproduction, compton scattering
Scale all to corrected charges
Fit dummy + simulations to the data
Extract ratio of simulation cross-section to actual cross-section

14. Charge Correction Included so far Not yet included
Computer & Electronics livetimes, Scintillator ¾ efficiency, Prescale, VDC tracking efficiency, BCM Calibration, Target boiling
Not yet included
Particle Identification efficiency, Proton Absorbtion, Beam offset

15. Charge Correction Particle Identification Efficiency Proton Absorption
Using delta-beta cut, need to find cut tails
Proton Absorption
Incomplete information on a few materials
Beam Offset
Surveyed using carbon target

16. Unpeeling Data/SIMC resolution mismatch Background xptar dependence
Non-gaussian tails in SIMC
Background
‘Dummy’ runs for endcap subtraction
Simulated pi-0 photoproduction
Solid – data
Black dotted – sum of dummy, simulations
Elastics – adding nongaussian tails
Resolution – xptar correction

17. Nonlinearity Tests
Rosenbluth expects linearity in ε, TPE would cause a deviation
E and NE11 show quadratic terms consistent with zero
Project P2 within ±0.020 for E05-017
NE-eleven is the best standard Rosenbluth, performed at SLAC
2.5 GeV^2
GeV^2
Projection is at Q^2 of 2.56 GeV2
NE11: L. Andivahis et al, Phys. Rev. D50:5491, 1994

18. Conclusion Projected Uncertainties More Q2 points Analysis underway
Shifted range down
Better separations at each Q2
Analysis underway
From proposal