Difference between revisions of "Elong-13-05-01-HERMES-Match"

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(New page: ==Matching HERMES F<sub>1</sub><sup>d</sup>, dA<sub>zz</sub><sup>d</sup>, and db<sub>1</sub><sup>d</sup>== I wanted to double-check the code against the HERMES data, but this required a fe...)
 
 
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==Matching HERMES F<sub>1</sub><sup>d</sup>, dA<sub>zz</sub><sup>d</sup>, and db<sub>1</sub><sup>d</sup>==
 
==Matching HERMES F<sub>1</sub><sup>d</sup>, dA<sub>zz</sub><sup>d</sup>, and db<sub>1</sub><sup>d</sup>==
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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<''W''<sup>2</sup><42.87, which is outside the ''W'' range that the code can handle) they match the code relatively well:
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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<''W''<sup>2</sup><42.87, which is outside the ''W'' range that the code can handle) they match the code relatively well:
  
 
{| class="wikitable" style="text-align:center; border-collapse:collapse;" border="1"
 
{| class="wikitable" style="text-align:center; border-collapse:collapse;" border="1"
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| style="width: 100px;" | <''x''> || style="width: 100px;" | ''Q''<sup> 2</sup> || style="width: 100px;" | HERMES <math>F_1^d</math> || style="width: 100px;" | Bosted <math>\frac{F_1^d}{A_d}</math>
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| style="width: 100px;" | <''x''> || style="width: 100px;" | ''Q''<sup> 2</sup> || style="width: 100px;" | HERMES $F_1^d$ || style="width: 100px;" | Bosted $\frac{F_1^d}{A_d}$
 
|-  
 
|-  
 
| 0.128 || 2.33 || 1.018 || 0.620 (Outside Bosted "Good" range)
 
| 0.128 || 2.33 || 1.018 || 0.620 (Outside Bosted "Good" range)
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|}
 
|}
  
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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.
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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.
  
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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>.
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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:<br>
 
Looking at points from the HERMES data, I get:<br>
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[[Image:2013-05-01-HERMES.png]]
 
[[Image:2013-05-01-HERMES.png]]
  
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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.
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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.

Latest revision as of 13:49, 18 October 2023

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 $A_{zz}^d$ 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:

2013-05-01-HERMES.png

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.

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