Difference between revisions of "Elong-13-09-30"

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===Larger x Range for Bosted===
 
===Larger x Range for Bosted===
  
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Using the kinematics for the SHMS <math>(E_{\mathrm{beam}}=6.60\mathrm{~GeV,~} E'=6.07\mathrm{~GeV,~}\theta_{e'}=9.51^{\circ})</math> to calculate the cross section and scanning over <math>0<x<2</math> with 200 bins, the Bosted cross-sections come out to:
+
Using the kinematics for the SHMS $(E_{\mathrm{beam}}=6.60\mathrm{~GeV,~} E'=6.07\mathrm{~GeV,~}\theta_{e'}=9.51^{\circ})$ to calculate the cross section and scanning over $0<x<2$ with 200 bins, the Bosted cross-sections come out to:
  
 
[[Image:2013-09-30-bosted-cs.png]]
 
[[Image:2013-09-30-bosted-cs.png]]
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[[Image:2013-09-30-fdil-compare.png]]
 
[[Image:2013-09-30-fdil-compare.png]]
  
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There is a discontinuity at <math>x=0.75</math>, which is caused by a (somewhat arbitrary) switch from Bosted's DIS code to his QE code at that point. The dilution factor is also different than shown above, because in the first plot shown on this page I accidentally left the kinematics set to the b1 experiment's (and not the Azz one).
+
There is a discontinuity at $x=0.75$, which is caused by a (somewhat arbitrary) switch from Bosted's DIS code to his QE code at that point. The dilution factor is also different than shown above, because in the first plot shown on this page I accidentally left the kinematics set to the b1 experiment's (and not the Azz one).
  
 
===Changes to Azz Statistics===
 
===Changes to Azz Statistics===
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[[Image:2013-09-30-Azz-fixed-dilution.png]]
 
[[Image:2013-09-30-Azz-fixed-dilution.png]]
  
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If we take the updated uncertainties and split them along <math>1.25\cdot A_{zz}</math> and <math>0.75\cdot A_{zz}</math>, then we get:
+
If we take the updated uncertainties and split them along $1.25\cdot A_{zz}$ and $0.75\cdot A_{zz}$, then we get:
  
 
[[Image:2013-09-30-Azz-fixed-dilution-split.png]]
 
[[Image:2013-09-30-Azz-fixed-dilution-split.png]]
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In the process of doing this study, it's occurred to me that I'm not entirely sure of the best way to put our data together since, with different kinematics, we'll have slightly different dilution factors. For b1, this is complicated by having multiple SHMS settings but lessened by a more stable dilution factor of ~0.3. For Azz, there are only two settings, but the dilution factor goes through a significant amount of change for each x bin. Further study is needed to account for this and to be able to combine the data properly.
 
In the process of doing this study, it's occurred to me that I'm not entirely sure of the best way to put our data together since, with different kinematics, we'll have slightly different dilution factors. For b1, this is complicated by having multiple SHMS settings but lessened by a more stable dilution factor of ~0.3. For Azz, there are only two settings, but the dilution factor goes through a significant amount of change for each x bin. Further study is needed to account for this and to be able to combine the data properly.
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==Cross Section Calculation==
 
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For previous calculations, I was using a simplified version of the cross-section where it was assumed that <math>F_2=2x\cdot F_1</math>, such that
 
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<math>\frac{d^2\sigma^u}{d\Omega dE'} = A_X \left( \frac{d\sigma}{d\Omega} \right) _{\mathrm{Mott}_{\mathrm{p}}} \left[ \frac{2\cdot \left(\frac{F_1^{X}}{A_X} \right)}{m_{p}}\right]\cdot \left[\tan^2\left( \frac{\theta_{e'}}{2} \right) + \frac{Q^2 }{2\nu^2} \right] </math>.<br>
 
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Since we're in a region that isn't DIS, I thought that the difference may be important so I incorporated <math>F_2</math> from Bosted and removed the assumption:
 
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<math>\frac{d^2\sigma^u}{d\Omega dE'} = A_X \left( \frac{d\sigma}{d\Omega} \right) _{\mathrm{Mott}_{\mathrm{p}}} \left[ \frac{2\cdot \left(\frac{F_1^{X}}{A_X} \right)}{m_{p}}\tan^2\left( \frac{\theta_{e'}}{2} \right) + \frac{\left( \frac{F_2^X}{A_X}\right) }{\nu} \right]</math>.<br>
 
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This increased the statistical uncertainty, particularly in the high-x region. It also lowered the rates dramatically, which gives us some room to play around with a lower <math>Q^2</math>.
 
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[[Image:2013-09-30-fixed-sigma-Azz-plots.png]]
 
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Although this changes the cross sections quite a bit,
 
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{| class="wikitable" style="text-align:center; border-collapse:collapse;" border="1"
 
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! <math>F_1</math> Only !! <math>F_1~&~F_2</math>
 
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|-
 
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| [[Image:2013-09-30-cs-f1-only.png]] || [[Image:2013-09-30-cs-f1-f2.png]]
 
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|- 
 
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|}
 
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The dilution factor is nearly identical.
 
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[[Image:2013-09-30-cs-fixed-fdil.png]]
 
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--[[User:Ellie|E. Long]] 20:16, 30 September 2013 (UTC)
 

Latest revision as of 13:55, 18 October 2023

Dilution Factor Comparisons

First Pass

I've been using the Bosted model to extract the dilution factor, but I hadn't previously plotted it against x. This was prompted when Patricia sent me a plot that she had created as she's working with a new model from Misak. The comparison for the new Azz, using the kinematics from the SHMS, is:

(Note: The kinematics for this are the same as the SHMS's highest x point for b1, not Azz as I originally thought)

2013-09-27-fdil-compare.png

Larger x Range for Bosted

Using the kinematics for the SHMS $(E_{\mathrm{beam}}=6.60\mathrm{~GeV,~} E'=6.07\mathrm{~GeV,~}\theta_{e'}=9.51^{\circ})$ to calculate the cross section and scanning over $0<x<2$ with 200 bins, the Bosted cross-sections come out to:

2013-09-30-bosted-cs.png

and the dilution, compared with the Misak model, comes out to:

2013-09-30-fdil-compare.png

There is a discontinuity at $x=0.75$, which is caused by a (somewhat arbitrary) switch from Bosted's DIS code to his QE code at that point. The dilution factor is also different than shown above, because in the first plot shown on this page I accidentally left the kinematics set to the b1 experiment's (and not the Azz one).

Changes to Azz Statistics

Previously, the dilution factor was assumed to be about 0.3. Since this is no longer the case, and the dilution factor has been changed to that shown in the Bosted plot above, the statistics for Azz (particularly in the high-x range) get larger.

2013-09-30-Azz-fixed-dilution.png

If we take the updated uncertainties and split them along $1.25\cdot A_{zz}$ and $0.75\cdot A_{zz}$, then we get:

2013-09-30-Azz-fixed-dilution-split.png

Combining Dilution Factors

In the process of doing this study, it's occurred to me that I'm not entirely sure of the best way to put our data together since, with different kinematics, we'll have slightly different dilution factors. For b1, this is complicated by having multiple SHMS settings but lessened by a more stable dilution factor of ~0.3. For Azz, there are only two settings, but the dilution factor goes through a significant amount of change for each x bin. Further study is needed to account for this and to be able to combine the data properly.

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