1. GEp/GMp Group Meeting Chris Crawford May 12, 2005
I’m reporting on our measurement of the proton form factor ratio which was recently completed at MIT/Bates.

2. Elastic Cross Section
b = target spin angle w/r to the beam line

3. Asymmetry Super-ratio Method
Beam-Target Double Spin Asymmetry
Super-ratio
b = 45
I will now describe our technique. The experimental asymmetry depends on the beam and target asymmetries and the ratio of the polarized cross section over the unpolarized Rosenbluth part. There are two terms, one for longitudinal polarization to the q vector, and the other transverse term has G_E, not G_E^2.
If we measure both components of the polarized cross section at the same time and Q^2, then we can form a super-ratio where the polarization and Rosenbluth term cancel out. This is done by orienting the spin at 45 degrees, so that the right sector asymmetry is predominantly transverse while the left asymmetry is longitudinal.

4. Single-asymmetry Method
i = left,right sector
j = Q2 bin (1..n)
b = spin angle
Single-asymmetry Method
measure P first, use to calculate R
model-dependent
Super-ratio Method
2 equations in P, R
in each Q2 bin j
independent measure of polarization in each bin!
2n parameters Pj, Rj
Global Fit Method
fit for P, R1, R2, … from all Aij together
model independent
better statistics
n+1 parameters
can also fit for b

5. Cuts TOF WC available in utils/cuts_h3.C
Hpt – elliptical cut on timing & coplanarity – hpt-ntuple WC
flr-ntuple (+ and – track)
Hwc – elliptical cut on 5 redundant WC vars
Hwd – rectangular cut on same
Hwe – cut on invariant mass only (for RC)
available in utils/cuts_h3.C
each cut has parameter ns

6. Cosmics TOF Calibration
channels
L 9
L 6
L 3
L 0
R 0
R 3
R 6
channels

7. TOF Scintillator Cuts TOF paddle, proton TOF paddle, electron
The time-of-flight scintillators already do a clean separation of elastic events. This is a plot of coincidence events of an electron in one of the 16 right sector paddles with a proton in the left. Along the elastic ridge the proton and electron have roughly 90^\deg separation all the way from forward scattering to the back.
TOF paddle, electron

8. WC Offsets/Resolution/Cuts
pe-pe(qe)
pp-pp(qe)
qp-qp(qe)
pe qe fe ze
pp qp fp zp
fp-fp(fe)
z p- z p(ze)

9. Tracking Efficiency

10. Experimental Spin Asymmetry
context of high precision measurement:
bulk of data has been deuterium to date, hydrogen run planned for end of year.

11. Extractions of m GE/GM

12. .Radiative Corrections
2.5 sigma W cut: – 0.4 %
5.0 sigma W cut: – 0.8 %
7.5 sigma W cut: – 1.3 %
10. sigma W cut: – 2.0 %
(predominantly in the left sector asymmetry)

13. Single-Spin Asymmetry

14. Systematic Errors DQ2 (1.8%) Db (0.8%) comparison of qe and qp
difference between left/right sector errors most significant
TOF timing will help
Db (0.8%)
fieldmap: ° ± 1°
Hohler: ° ± 0.8°
Fit Method: 42° ± 3°
(1st 7 bins) 48° ± 4°
T20 analysis: 46.5° ± 3°

15. Q2 = 2M2(1-g)
TOF Q2

16. GE/GM by Dataset

17. GE/GM Monte Carlo

18. GE/GM Fine Bins

19. Beam and Target False Asymmetry

20. Target False Asymmetry

22. Systematic Checks
Monte Carlo
Time bins

23. World Data World Unpolarized Data
The spin ½ nucleon’s electromagnetic current has only 2 terms which conserve general symmetries, and Rosenbluth figured out in the 1950’s how two separate both of these from the single unpolarized cross section by varying the beam energy at fixed Q^2 point. Since then there has been a rich history of Rosenbluth extractions of G_e and G_m. I show here the unpolarized world data since But at cross section is dominated by G_m and high Q^2, which makes Rosenbluth separations above Q^2=1 very difficult. Plus, variation of the beam energy introduces extra uncertainties.

24. GE/GM — World Data
The technology of polarized beam and polarized target or recoil polarimetry has make possible a new generation of high precision measurements of the form factor. Now one can vary spin degrees of freedom instead of the beam energy, and rely on the interference term between G_e and G_m in the polarized cross section. The first such measurement was done at Bates using a polarized beam and a focal plane polarimeter for the recoil proton. These measurements were repeated at JLab to higher Q^2 and better precision.

25. GE/GM Results

26. Extraction of GE and GM

27. GE and GM Results
BLAST + World Data