Impact of 3D polarization profiles on spin-dependent measurements in colliding beam experiments
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mpact of 3D Polarization Profiles on SpinDependent Measurements in Colliding Beam Experiments1 A. Bazilevsky and W. Fischer Brookhaven National Laboratory, Upton, New York 11973, USA Abstract—We derive the effect of 3dimensional polarization profiles on the measured polarization in pola rimeters, as well as the observed polarization and the polarizationweighted luminosity (figure of merit) in single and double spin measurements in colliding beam experiments. DOI: 10.1134/S1063779614010134 1
1. INTRODUCTION
During beam acceleration and storage the polar ization profiles (variation of polarization P versus phase space coordinates) develop, which affect the polarization measured in a polarimeter, and the polar ization and figure of merit (FOM) in colliding beam experiments. In the recently published paper [1] we analytically derived formulas to quantify these effects for 3dimensional Gaussian profiles. Below we briefly review these results and concentrate more on the prac tical consequences for the polarization related param eters derived from the polarimeter measurements and used in the physics spin asymmetry results.
dinate in all dimensions (both position and momen tum or angle). For two colliding beams we introduce polarization moments m
Polarimeter usually measures the average beam polarization over all particles in a bunch, hence polar ization average is weighted with intensity distribution over all dimensions of a bunch. For Gaussian profiles it can be expressed: P0 P = , ( 1 + Rx ) ( 1 + Ry ) ( 1 + Rs )
(2)
where m and n are nonnegative integers and the angle brackets indicates the luminosityweighted average over the polarization function. PB and PY denote the polarizations of the two beams, respectively (called “Blue” and “Yellow” at RHIC). In this notation aver age polarizations and figures of merit in a collider experiment can be expressed as
2. POLARIZATIONS AND FOMS As was shown by measurements in RHIC intensity and polarization profiles can be well approximated by Gaussian distributions. We introduce the parameter R separately in all three dimensions, which is a ratio of the variances σ2 of the intensity over polarization pro 2 2 files: R = σ I /σ P . Without any polarization profiles we have σP → ∞ and hence R = 0. The typical values of R in RHIC for 250 GeV beams in transverse direction are ~0.2, while in the longitudinal direction it was found to be insignificant (~
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