New Method for Data Treating in Polarization Measurements

TL;DR

This paper introduces a new method for analyzing polarization measurement data by deriving precise formulas for expected values and variances of spin asymmetry variables, accounting for background contributions.

Contribution

The paper presents novel formulas for expected values and variances of spin asymmetry variables, enabling data analysis without detector efficiency correction.

Findings

Variances of the variables are finite, unlike the Caushy distribution.

Expected value of the variable equals the physical asymmetry.

Asymptotic formulas are derived for large sample sizes.

Abstract

Precise formulas are derived for the expected values $<\xi>$, $<\eta>$ and variances $\delta \xi ^2$, $\delta \eta ^2$ of random variables $\xi$, $\eta$ describing the spin asymmetry of some reaction when a background process contribution is negligible and appreciable, respectively. The variances of $\xi$ and $\eta$ are proved to be finite. This property differs from that of the Caushy distribution which has an infinite variance. It is shown that $<\xi>$ is equal to the physical asymmetry which allows to find the asymmetry from experimental data without studying the detector efficiency. This is the base of the proposed method of data treating. Asymptotic formulas for $<\eta>$ and $\delta \eta ^2$ are also derived for a total number of events tending to infinity for a finite value of the background to signal ratio.