Difference between revisions of "Experimental Sensitivity to Solenoidal Field"

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(Figure-of-Merit)
(Figure-of-Merit)
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* 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
 
+
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
+
 
* 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,  
 
Therefore,  
 
* Sensitivity ~ time x luminosity / sqrt (time x luminosity x width) ~ sqrt (time x luminosity / width) ~  sqrt (time / (<math> R_{EM}</math> x width)   
 
* Sensitivity ~ time x luminosity / sqrt (time x luminosity x width) ~ sqrt (time x luminosity / width) ~  sqrt (time / (<math> R_{EM}</math> x width)   
* For constant sensitivity the time ~ <math> R_{EM} </math> x width = 1/FOM.
+
* For constant sensitivity, the experimental run time ~ <math> R_{EM} </math> x width = 1/FOM.

Revision as of 17:45, 27 April 2010

References

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

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. The validity for this FOM is based on the following argument:

  • Statistical sensitivity ~ 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,

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