Difference between revisions of "Elong-13-10-01"
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! <math>F_1 \mathrm{~Only}</math> !! <math>F_1\mathrm{~and~}F_2</math> | ! <math>F_1 \mathrm{~Only}</math> !! <math>F_1\mathrm{~and~}F_2</math> | ||
|- | |- | ||
| − | | [[Image:2013-09-30-bosted-cs.png]] || [[Image:2013-09-30-cs-f1-f2.png]] | + | | [[Image:2013-09-30-bosted-cs.png|350px]] || [[Image:2013-09-30-cs-f1-f2.png|350px]] |
|- | |- | ||
|} | |} | ||
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The dilution factor is nearly identical. | The dilution factor is nearly identical. | ||
| − | [[Image:2013-09-30-cs-fixed-fdil.png]] | + | [[Image:2013-09-30-cs-fixed-fdil.png|350px]] |
==Cross Section Check for b1== | ==Cross Section Check for b1== | ||
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! HMS<br><math>\theta_{e'}=12.50^{\circ}</math><br><math>E'=7.31\mathrm{~GeV}</math> !! SHMS 1<br><math>\theta_{e'}=7.35^{\circ}</math><br><math>E'=6.80\mathrm{~GeV}</math> !! SHMS 2<br><math>\theta_{e'}=8.96^{\circ}</math><br><math>E'=7.45\mathrm{~GeV}</math> !! SHMS 3<br><math>\theta_{e'}=9.85^{\circ}</math> <br><math>E'=7.96\mathrm{~GeV}</math> | ! HMS<br><math>\theta_{e'}=12.50^{\circ}</math><br><math>E'=7.31\mathrm{~GeV}</math> !! SHMS 1<br><math>\theta_{e'}=7.35^{\circ}</math><br><math>E'=6.80\mathrm{~GeV}</math> !! SHMS 2<br><math>\theta_{e'}=8.96^{\circ}</math><br><math>E'=7.45\mathrm{~GeV}</math> !! SHMS 3<br><math>\theta_{e'}=9.85^{\circ}</math> <br><math>E'=7.96\mathrm{~GeV}</math> | ||
|- | |- | ||
| − | | [[Image:2013-10-01-b1-hms-cs.png]] || [[Image:2013-10-01-b1-shms-1-cs.png]] || [[Image:2013-10-01-b1-shms-2-cs.png]] || [[Image:2013-10-01-b1-shms-3-cs.png]] | + | | [[Image:2013-10-01-b1-hms-cs.png|350px]] || [[Image:2013-10-01-b1-shms-1-cs.png|350px]] || [[Image:2013-10-01-b1-shms-2-cs.png|350px]] || [[Image:2013-10-01-b1-shms-3-cs.png|350px]] |
|- | |- | ||
|} | |} | ||
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! HMS<br><math>\theta_{e'}=12.45^{\circ}</math><br><math>E'=5.80\mathrm{~GeV}</math> !! SHMS<br><math>\theta_{e'}=9.51^{\circ}</math><br><math>E'=6.07\mathrm{~GeV}</math> | ! HMS<br><math>\theta_{e'}=12.45^{\circ}</math><br><math>E'=5.80\mathrm{~GeV}</math> !! SHMS<br><math>\theta_{e'}=9.51^{\circ}</math><br><math>E'=6.07\mathrm{~GeV}</math> | ||
|- | |- | ||
| − | | [[Image:2013-10-01-Azz-hms-cs.png]] || [[Image:2013-10-01-Azz-shms-cs.png]] | + | | [[Image:2013-10-01-Azz-hms-cs.png|350px]] || [[Image:2013-10-01-Azz-shms-cs.png|350px]] |
|- | |- | ||
|} | |} | ||
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! <math>\theta_{e'}=8.00^{\circ}</math><br><math>E=6.519\mathrm{~GeV}</math> !! <br><math>\theta_{e'}=?^{\circ}</math><br><math>E=?\mathrm{~GeV}</math> | ! <math>\theta_{e'}=8.00^{\circ}</math><br><math>E=6.519\mathrm{~GeV}</math> !! <br><math>\theta_{e'}=?^{\circ}</math><br><math>E=?\mathrm{~GeV}</math> | ||
|- | |- | ||
| − | | [[Image:2013-10-02-cs-check-exp-1.png]] || [[Image:2013-10-02-cs-check-exp-2.png]] | + | | [[Image:2013-10-02-cs-check-exp-1.png|350px]] || [[Image:2013-10-02-cs-check-exp-2.png|350px]] |
|- | |- | ||
|} | |} | ||
Revision as of 14:13, 2 October 2013
Cross Section Calculation
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
<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>.
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:
<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>.
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>.
Although this changes the cross sections quite a bit,
| <math>F_1 \mathrm{~Only}</math> | <math>F_1\mathrm{~and~}F_2</math> |
|---|---|
 |
|
The dilution factor is nearly identical.
Cross Section Check for b1
To see if this could cause a problem for the b1 statistics, I did a study of the effects of changing the cross section calculation from the simplified to the full for the b1 kinematics.
| HMS <math>\theta_{e'}=12.50^{\circ}</math> <math>E'=7.31\mathrm{~GeV}</math> |
SHMS 1 <math>\theta_{e'}=7.35^{\circ}</math> <math>E'=6.80\mathrm{~GeV}</math> |
SHMS 2 <math>\theta_{e'}=8.96^{\circ}</math> <math>E'=7.45\mathrm{~GeV}</math> |
SHMS 3 <math>\theta_{e'}=9.85^{\circ}</math> <math>E'=7.96\mathrm{~GeV}</math> |
|---|---|---|---|
 |
 |
 |
|
Cross Section Check for Azz
Same as the section above, looking at the difference between the simplified cross section using only <math>F_1</math> and the full cross section using both <math>F_1</math> and <math>F_2</math>, but for the Azz kinematics.
| HMS <math>\theta_{e'}=12.45^{\circ}</math> <math>E'=5.80\mathrm{~GeV}</math> |
SHMS <math>\theta_{e'}=9.51^{\circ}</math> <math>E'=6.07\mathrm{~GeV}</math> |
|---|---|
 |
|
Comparison to Data
In order to see how my calculations line up with actual data, I've taken the deuterium information from the quasi-elastic scattering archive data page to compare with our measurements. There are two settings that line up with our
| <math>\theta_{e'}=8.00^{\circ}</math> <math>E=6.519\mathrm{~GeV}</math> |
<math>\theta_{e'}=?^{\circ}</math> <math>E=?\mathrm{~GeV}</math> |
|---|---|
 |
|
--E. Long 18:57, 2 October 2013 (UTC)
