Elong-13-05-01-HERMES-Match
Matching HERMES F1d, dAzzd, and db1d
I wanted to double-check the code against the HERMES data, but this required a few extra steps. First, using the values for <math>A_{zz}^d</math> and <math>b_{1}^d</math> that they measured, along with the formula <math>b_1^d = -\frac{3}{2}A^d_{zz}F^d_1</math>, I found what they were using for <math>F^d_1</math>. The <math>F^d_1</math> they're using is per nucleon, and for HERMES' two highest x points (the rest are inaccessible to the Bosted code because for 0.012<x<0.063, 16.75<W2<42.87, which is outside the W range that the code can handle) they match the code relatively well:
| <x> | Q 2 | HERMES <math>F_1^d</math> | Bosted <math>\frac{F_1^d}{A_d}</math> |
| 0.128 | 2.33 | 1.018 | 0.620 (Outside Bosted "Good" range) |
| 0.248 | 3.11 | 0.496 | 0.486 |
| 0.452 | 4.69 | 0.161 | 0.171 |
This means that the way I was calculating the error <math>\delta b_1^d=\frac{3}{2}\delta A_{zz}^d F_1^d</math> was off by a factor of <math>A_d=2</math>. This was corrected.
Including the 1/2 term in the polarized cross-section (to stay consistent with HERMES' terminology), then <math>\delta A_{zz}^d = \frac{2}{f\cdot P_{zz}\sqrt{N_{\mathrm{Tot}}}}</math> where <math>P_{zz}=0.9</math>, <math>N_{\mathrm{Tot}} = 3,200,000</math> and <math>f=0.5</math>.
Looking at points from the HERMES data, I get:
The lowest point in <math>\delta b_1^d</math> doesn't match because of the difference in <math>F_1^d</math> noted above, although I'm not sure why I get a smaller error on the highest point in <math>\delta A_{zz}</math>. However, you may want to take these results with a grain of salt since this was all input using the SHMS code as I don't have code set up for the HERMES detector.
