Final analysis
<math>Q^2</math>
From Kiad
Left average: <math>Q^{2} = 0.09330</math> GeV<math>{}^{2}</math> Right average: <math>Q^{2} = 0.08751</math> GeV<math>{}^{2}</math>
Averaging the two weighting <math>\frac{N}{\sigma^2}</math>, over three data sets of the left and right arms are up with the direct average, left arm up, and right arm up, I get
Average: <math>Q^{2} = 0.09064</math> GeV<math>{}^{2}</math>
Polarimetry
Compton
87.41 +/- 0.12 (stat) +/- 1.32 (sys) % (waiting for updated numbers)
Moller
90.32 +/- 0.07 (stat) +/- 1.12 (sys) %
Taking a weighted average between the two
89.10 +/- 1.12%
Compton
Mindy's HAPLOG post:
http://ace.phys.virginia.edu:8080/HAPPEX/2582
Final result: 87.41 +/- 0.12 (stat) +/- 1.32 (sys) %
chi^2/NDoF = 1.09 for 13 points over the experiment
Compton slug-by-slug:
Systematic Error
| Rel Uncer. (%) | |||
|---|---|---|---|
| Laser Pol. | 0.07 | http://ace.phys.virginia.edu:8080/HAPPEX/2530 | |
| Gain shift | 1.3 | email from Megan Friend, see below | |
| Collimator Pos. | 0.02 | http://ace.phys.virginia.edu:8080/HAPPEX/2568 | |
| Nonlinearity | 0.3 | http://ace.phys.virginia.edu:8080/HAPPEX/2569 | |
| TOTAL | 1.51 |
Systematic Error Notes
- From Megan over gain shift:
I don't think I'm going to be able to get a number for the gain shift during PREX, although it should scale linearly with signal-background size. Using the 1% gain shift we saw during HAPPEX (signal+bkg to background = 122e6 to 53e6), that would give us a 0.8% gain shift for PREX (signal+bkg to background = 48e6 to 30e6 at 1kHz * 3.3 to convert to 30Hz). This would give us a change in the final polarization number of 1.3%, if it's folded into the background subtraction ( which comes from comparing a background subtraction of (48e6-30e6*(1.008))/(48e6-30e6) ). So I'd say the possible gain shift gives you a 1.3% systematic error.
- From Megan over radiative correction:
I just ran through the PREX data to add in a radiative correction, and I get that this increases the analyzing power by 0.3% (from 0.01828903 to 0.01834393). This is consistent with what I've seen, so I think it's safe to add that in there.
There is an increase in analyzing power of 0.3%, which corresponds to a decrease in beam polarization by 0.3%. Therefore, the final analyzing power should multiply by (1+0.003) due to A_real = A_exp * (1+0.3%)
w/o the radiative correction:
analyzing power = 0.01824526 +- 0.00002583 (sta.)
w/ the radiative correction:
analyzing power = 0.018299996 +- 0.00002583 (sta.)
Moller
http://www.jlab.org/~moller/e02-006.html
Just taking the last 4 runs, which are relevant for production data taking:
Final result weighted average: 90.32 +/- 0.07 (stat) +/- 1.12 (sys) %
Systematic Error
Sasha's report at the Jan 2011 collaboration meeting
| Uncer. (%) | |
|---|---|
| Fe Pol. | 0.25 |
| Targ Discrep. | 0.5 |
| Targ Saturation | 0.3 |
| Analyzing power | 0.3 |
| Levchuk | 0.5 |
| Targ temp | 0.02 |
| Dead time | 0.3 |
| Background | 0.3 |
| Others | 0.5 |
| Current diff | 0.3 |
| TOTAL | 1.12 |
Finite Acceptance
The radiative effects/multiple scattering/etc. leads to an effective drop in the measured <math>Q^2</math> by 0.68%
From HAMC, the asymmetry as a function of <math>Q^{2}</math> can be well represented by a third order polynomial:
<math> A = -0.1607 + 203.3Q^{2} -15260Q^{4} + 402200Q^{6}</math>
http://www.jlab.org/~riordan/20110417/AvsQ2.png
Using <math>Q^{2}_{obs} = 0.009359</math> GeV<math>{}^2</math> and <math>Q^{2}_{vertex} = 0.009296</math> GeV<math>{}^2</math>, the fractional difference between <math>A_{obs}</math> and <math>A_{vertex}</math> is 0.20%.
Background
Inelastic
See Kiad's presentation
http://ace.phys.virginia.edu:8080/HAPPEX/2583
The acceptance for the first excited state of Pb is <0.1%. It's expected to have an asymmetry ~1.3 of the elastic asymmetry so it is totally negligable.
The first excited state of carbon is outside our acceptance and does not contribute
Carbon
In progress
Rescattering
In progress
Nonlinearity
http://ace.phys.virginia.edu:8080/HAPPEX/2597
Transverse Asymmetry
The transverse polarization of the beam was about 1 degree:
http://ace.phys.virginia.edu:8080/HAPPEX/2596
Using the regressed transverse lead result here:
http://ace.phys.virginia.edu:8080/HAPPEX/2575
| Left arm | <math> 0.227 \pm 0.654 </math> ppm |
| Right arm | <math> 0.138 \pm 0.901 </math> ppm |
| Average | <math> 0.196 \pm 0.529 </math> ppm |
To average over the run, I take a weighted average with <math>N/\sigma^2</math> over three data sets. The first data set is both arms up, where I used the average transverse asymmetry, the second is left only where I use the left value, and the third is right only where I use the right value.
Multiplying the result by <math>\sin 1^\circ</math>, I get:
<math>0.0034 \pm 0.0095</math>ppm
For a 0.5ppm asymmetry, this is a 0.7% correction.
