Elong-13-05-01-HERMES-Match

Matching HERMES F₁^d, dA_zz^d, and db₁^d

I wanted to double-check the code against the HERMES data, but this required a few extra steps. First, using the values for $A_{zz}^d$ and $b_{1}^d$ that they measured, along with the formula $b_1^d = -\frac{3}{2}A^d_{zz}F^d_1$, I found what they were using for $F^d_1$. The $F^d_1$ 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 $F_1^d$	Bosted $\frac{F_1^d}{A_d}$
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 $\delta b_1^d=\frac{3}{2}\delta A_{zz}^d F_1^d$ was off by a factor of $A_d=2$. This was corrected.

Including the 1/2 term in the polarized cross-section (to stay consistent with HERMES' terminology), then $\delta A_{zz}^d = \frac{2}{f\cdot P_{zz}\sqrt{N_{\mathrm{Tot}}}}$ where $P_{zz}=0.9$, $N_{\mathrm{Tot}} = 3,200,000$ and $f=0.5$.

Looking at points from the HERMES data, I get:

The lowest point in $\delta b_1^d$ doesn't match because of the difference in $F_1^d$ noted above, although I'm not sure why I get a smaller error on the highest point in $\delta A_{zz}$. 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.