# Experimental Sensitivity to Solenoidal Field

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# 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)