Difference between revisions of "Experimental Sensitivity to Solenoidal Field"
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* 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 experimental run time ~ <math> R_{EM} </math> x width = 1/FOM. | * For constant sensitivity, 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 | + | 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: |
[[Image:Plot resolutions c5.png |thumb|left|300px|FOM ~ 1/(R_EM x omega width)]] | [[Image:Plot resolutions c5.png |thumb|left|300px|FOM ~ 1/(R_EM x omega width)]] | ||
Revision as of 18:18, 27 April 2010
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
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 ~
, where 
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 / ( x width)
- For constant sensitivity, the experimental run time ~ x width = 1/FOM.
We note that the calculated rates give 
, and 
, which leads to 
. See figure below:
