Elong-13-09-18
Optimizing Azz in QE and x>1 Range
Beam Energy = 2.2 GeV
HMS
SHMS
Beam Energy = 4.4 GeV
HMS
SHMS
Beam Energy = 6.6 GeV
HMS
SHMS
Beam Energy = 8.8 GeV
HMS
SHMS
Beam Energy = 11.0 GeV
HMS
SHMS
Optimization Results
Beam Energy = 2.2 GeV
Beam Energy = 4.4 GeV
Beam Energy = 6.6 GeV
Beam Energy = 8.8 GeV
Beam Energy = 11.0 GeV
(None for HMS -- rates drop off dramatically by the time it's in a good kinematics range) 
Fixed uncertainty due to large asymmetry
Previously, the code was using a simplified <math>\delta A_{zz} = \frac{4}{f \cdot Pzz \sqrt{N}}</math>. This gave all of the above uncertainties, as well as this one:
Going back through the uncertainty tech note, the assumption of a small asymmetry isn't made until after Eq. 28. Utilizing the full uncertainty (Eq. 28 and 25), <math>\delta A_{zz} = \frac{2}{f \cdot Pzz}\sqrt{\frac{N_{Pol}}{N_u^2}+\frac{N_{Pol}^2}{N_u^3}}</math>, the uncertainties change (very slightly) to:
Time Scan
Scanning over time and increasing it from 1 day to 2 weeks in intervals of one day, we get:
1 Week Measurement
Given one PAC week, using the SHMS and an 11 GeV beam on an 30% tensor polarized target, we can expect to get a good measurement from <math>0.8 > x > 1.8</math>
Beam Energy = 11.0 GeV
| <math><x></math> | <math>dA_{zz}^{stat}</math> | <math>dA_{zz}^{sys}</math> |
| 0.8 | 0.716E-02 | 0.526E-02 |
| 0.9 | 0.675E-02 | 0.120E-01 |
| 1.0 | 0.525E-02 | 0.249E-03 |
| 1.1 | 0.569E-02 | 0.307E-01 |
| 1.2 | 0.941E-02 | 0.667E-01 |
| 1.3 | 0.140E-01 | 0.924E-01 |
| 1.4 | 0.194E-01 | 0.998E-01 |
| 1.5 | 0.130E-01 | 0.100E+00 |
| 1.6 | 0.124E-01 | 0.100E+00 |
| 1.7 | 0.222E-01 | 0.100E+00 |
| 1.8 | 0.204E-01 | 0.100E+00 |
Beam Energy = 8.8 GeV
| <math><x></math> | <math>dA_{zz}^{stat}</math> | <math>dA_{zz}^{sys}</math> |
| 0.8 | 0.345E-02 | 0.526E-02 |
| 0.9 | 0.324E-02 | 0.120E-01 |
| 1.0 | 0.387E-02 | 0.249E-03 |
| 1.1 | 0.264E-02 | 0.307E-01 |
| 1.2 | 0.416E-02 | 0.667E-01 |
| 1.3 | 0.565E-02 | 0.924E-01 |
| 1.4 | 0.101E-01 | 0.998E-01 |
| 1.5 | 0.967E-02 | 0.100E+00 |
| 1.6 | 0.131E-01 | 0.100E+00 |
| 1.7 | 0.169E-01 | 0.100E+00 |
| 1.8 | 0.286E-01 | 0.100E+00 |
Beam Energy = 6.6 GeV
| <math><x></math> | <math>dA_{zz}^{stat}</math> | <math>dA_{zz}^{sys}</math> |
| 0.8 | 0.146E-02 | 0.526E-02 |
| 0.9 | 0.141E-02 | 0.120E-01 |
| 1.0 | 0.167E-02 | 0.249E-03 |
| 1.1 | 0.204E-02 | 0.307E-01 |
| 1.2 | 0.377E-02 | 0.667E-01 |
| 1.3 | 0.154E-02 | 0.924E-01 |
| 1.4 | 0.205E-02 | 0.998E-01 |
| 1.5 | 0.268E-02 | 0.100E+00 |
| 1.6 | 0.464E-02 | 0.100E+00 |
| 1.7 | 0.387E-02 | 0.100E+00 |
| 1.8 | 0.476E-02 | 0.100E+00 |
Beam Energy = 4.4 GeV
| <math><x></math> | <math>dA_{zz}^{stat}</math> | <math>dA_{zz}^{sys}</math> |
| 0.8 | 0.906E-03 | 0.526E-02 |
| 0.9 | 0.782E-03 | 0.120E-01 |
| 1.0 | 0.816E-03 | 0.249E-03 |
| 1.1 | 0.115E-02 | 0.307E-01 |
| 1.2 | 0.153E-02 | 0.667E-01 |
| 1.3 | 0.231E-02 | 0.924E-01 |
| 1.4 | 0.247E-02 | 0.998E-01 |
| 1.5 | 0.108E-02 | 0.100E+00 |
| 1.6 | 0.127E-02 | 0.100E+00 |
| 1.7 | 0.149E-02 | 0.100E+00 |
| 1.8 | 0.234E-02 | 0.100E+00 |
Beam Energy = 2.2 GeV
| <math><x></math> | <math>dA_{zz}^{stat}</math> | <math>dA_{zz}^{sys}</math> |
| 0.8 | 0.954E-03 | 0.526E-02 |
| 0.9 | 0.895E-03 | 0.120E-01 |
| 1.0 | 0.661E-03 | 0.249E-03 |
| 1.1 | 0.900E-03 | 0.307E-01 |
| 1.2 | 0.135E-02 | 0.667E-01 |
| 1.3 | 0.137E-02 | 0.924E-01 |
| 1.4 | 0.134E-02 | 0.998E-01 |
| 1.5 | 0.119E-02 | 0.100E+00 |
| 1.6 | 0.160E-02 | 0.100E+00 |
| 1.7 | 0.169E-02 | 0.100E+00 |
| 1.8 | 0.220E-02 | 0.100E+00 |
--E. Long 21:13, 19 September 2013 (UTC)
