Difference between revisions of "Experimental Sensitivity to Solenoidal Field"

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(Figure-of-Merit)
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= References =
 
= References =
* [http://argus.phys.uregina.ca/cgi-bin/private/DocDB/ShowDocument?docid=1471 GlueX-doc-1471] Electromagnetic Background Rate Studies (for different solenoid magnet fields and FDC hole sizes)
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* [https://halldweb.jlab.org/doc-private/DocDB/ShowDocument?docid=1425 GlueX-doc-1425]  Magnetic Field Studies Status
* [http://argus.phys.uregina.ca/cgi-bin/private/DocDB/ShowDocument?docid=1425 GlueX-doc-1425] Magnetic Field Studies Status
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* [https://halldweb.jlab.org/doc-private/DocDB/ShowDocument?docid=1471 GlueX-doc-1471] Electromagnetic Background Rate Studies (for different solenoid magnet fields and FDC hole sizes)
* [http://argus.phys.uregina.ca/cgi-bin/private/DocDB/ShowDocument?docid=1469 GlueX-doc-1469] Studies of particle reconstruction for $\omega$ and X(2000) events
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* [https://halldweb.jlab.org/doc-private/DocDB/ShowDocument?docid=1469 GlueX-doc-1469] Studies of particle reconstruction for <math>\omega</math> and X(2000) events
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* [https://halldweb.jlab.org/doc-private/DocDB/ShowDocument?docid=1489 GlueX-doc-1489] Omega reconstruction / Justification for Bfield settings
  
 
= Figure-of-Merit =
 
= Figure-of-Merit =
We construct a Figure-of-Merit (FOM) based on the [http://argus.phys.uregina.ca/cgi-bin/private/DocDB/ShowDocument?docid=1471 calculated electromagnetic background rates] in the detector and the [http://argus.phys.uregina.ca/cgi-bin/private/DocDB/ShowDocument?docid=1469 resolution for reconstructing omega mesons]. The validity for this FOM is based on the following argument:
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We construct a Figure-of-Merit (FOM) based on the [https://halldweb.jlab.org/doc-private/DocDB/ShowDocument?docid=1471 calculated electromagnetic background rates] in the detector and the [https://halldweb.jlab.org/doc-private/DocDB/ShowDocument?docid=1469 resolution for reconstructing omega mesons], such that it will be inversely
* Statistical sensitivity ~ signal/sqrt(background)
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proportional to running time to attain a given statistical significance. The validity for this FOM is based on the following argument:
 +
* Statistical significance ~ signal/sqrt(background)
 
* signal ~ time x luminosity
 
* signal ~ time x luminosity
 
* background ~ time x luminosity x width of signal peak
 
* background ~ time x luminosity x width of signal peak
 
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In addition, we assume that the luminosity is limited by the rates in the detectors, which is dominated by electromagnetic background. Therefore
In addition, we assume that the luminosity is limited by the rates in the detectors which is dominated by electromagnetic background. Therefore
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* luminosity ~ <math>1/R_{EM}</math>, where <math>R_{EM}</math>  is the rate in one of the inner detectors, either the start counter or the FDC. (We use the start counter rate)
 
* luminosity ~ <math>1/R_{EM}</math>, where <math>R_{EM}</math>  is the rate in one of the inner detectors, either the start counter or the FDC. (We use the start counter rate)
 +
Therefore,
 +
* Significance ~ time x luminosity / sqrt (time x luminosity x width) ~ sqrt (time x luminosity / width) ~  sqrt (time / (<math> R_{EM}</math> x width) 
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* For constant significance, the experimental run time ~ <math> R_{EM} </math> x width = 1/FOM.
 +
We note that the calculated rates give <math> R_{EM} \sim 1/B^2 </math>, and  <math>\sigma_{\omega} \sim 1/B </math>, which leads to <math> FOM \sim B^3 </math>. See figure below:
  
Therefore,
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[[Image:Plot resolutions c5.png |thumb|left|300px|FOM ~ 1/(R_EM x omega width)]]
* Sensitivity ~ time x luminosity / sqrt (time x luminosity x width) ~ sqrt (time x luminosity / width) ~  sqrt (time / (<math> R_{EM}</math> x width) 
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* For constant sensitivity the time ~ <math> R_{EM} </math> x width = 1/FOM.
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Latest revision as of 16:52, 24 February 2017

References

  • GlueX-doc-1425 Magnetic Field Studies Status
  • GlueX-doc-1471 Electromagnetic Background Rate Studies (for different solenoid magnet fields and FDC hole sizes)
  • GlueX-doc-1469 Studies of particle reconstruction for \omega and X(2000) events
  • GlueX-doc-1489 Omega reconstruction / Justification for Bfield settings

Figure-of-Merit

We construct a Figure-of-Merit (FOM) based on the calculated electromagnetic background rates in the detector and the resolution for reconstructing omega mesons, such that it will be inversely proportional to running time to attain a given statistical significance. The validity for this FOM is based on the following argument:

  • Statistical significance ~ signal/sqrt(background)
  • signal ~ time x luminosity
  • background ~ time x luminosity x width of signal peak

In addition, we assume that the luminosity is limited by the rates in the detectors, which is dominated by electromagnetic background. Therefore

  • luminosity ~ 1/R_{{EM}}, where R_{{EM}} is the rate in one of the inner detectors, either the start counter or the FDC. (We use the start counter rate)

Therefore,

  • Significance ~ time x luminosity / sqrt (time x luminosity x width) ~ sqrt (time x luminosity / width) ~ sqrt (time / (R_{{EM}} x width)
  • For constant significance, the experimental run time ~ R_{{EM}} x width = 1/FOM.

We note that the calculated rates give R_{{EM}}\sim 1/B^{2}, and \sigma _{{\omega }}\sim 1/B, which leads to FOM\sim B^{3}. See figure below:

FOM ~ 1/(R_EM x omega width)