Compton polarimetry revisited

TL;DR

This paper revisits Compton polarimetry by calculating the average polarisation asymmetry from the Klein-Nishina cross section and introduces an optimal estimator for the polarisation fraction, showing modest improvements over simpler methods.

Contribution

It provides a detailed calculation of the polarisation asymmetry and develops a new moments-based estimator that enhances measurement precision in Compton polarimetry.

Findings

Average asymmetry decreases inversely with photon energy at high energies.

The new estimator improves statistical power by 10-20% over simple azimuthal fits.

Comparison with pair creation polarimetry shows larger improvements in that context.

Abstract

I compute the average polarisation asymmetry from the Klein-Nishina differential cross section on free electrons at rest. As expected from the expression for the asymmetry, the average asymmetry is found to decrease like the inverse of the incident photon energy asymptotically at high energy. I then compute a simple estimator of the polarisation fraction that makes optimal use of all the kinematic information present in an event final state, by the use of "moments" method, and I compare its statistical power to that of a simple fit of the azimuthal distribution. In contrast to polarimetry with pair creation, for which I obtained an improvement by a factor of larger than two in a previous work, here for Compton scattering the improvement is only of 10-20 %.