Polarization Figure of Merit for GlueX

There is a generic form for a figure of merit that is used for experiments which use polarized beams:

FOM = P²I

where P is the degree of polarization of the beam, and I is the beam current. As defined here, the FOM is only a relative measure; the absolute scale is arbitrary. This form is used by parity-violation experiments, but it is not limited to that particular case. The basic argument is that the statistical error on a measured asymmetry goes like 1/P and like 1/√N. These factors are squared in forming the FOM so that a comparison of FOM factors directly infers the cost or savings in beam time.

For a derivation of this form for the FOM in the case of linearly polarized photons in peripheral photoproduction, see this hand-written note. For plots of the FOM for varying conditions in GlueX, see the plots below.

• Fig. 1: Variation of the figure of merit for GlueX, as a function of varying radiator-collimator distance (x-axis) and collimator aperture (different curves). The vertical scale has been normalized to unity for the case of no collimation. Constant experimental conditions were maintained throughout these calculations by adjusting the beam current to keep the total hadronic rate in the detector constant at 370 KHz. The curves terminate at the point where further increasing the collimator distance would force the average tagging efficiency in the peak below 30% for that particular collimator aperture.

   

• Fig. 2: Variation of the figure of merit for GlueX, as a function of electron beam end-point energy (x-axis) with a 3.4 mm diameter collimator at 76 m from the radiator (green curve) and without collimation (black curve). The color codes and normalization are the same as were used for Fig. 1.