Chiral moments make chiral measures

TL;DR

This paper introduces a new family of tensor-based, rotationally-invariant chiral measures that quantify the handedness of distributions, applicable to both theoretical models and experimental data.

Contribution

It develops a novel framework using tensorial moments and a new cross product to quantify chirality, with an open-source software implementation.

Findings

The measures effectively distinguish chiral from achiral distributions.

Application to photoionization data demonstrates practical utility.

Guidance on choosing optimal chiral measures for different distributions.

Abstract

We develop a family of chiral measures to quantify the chirality of a distribution and assign it a handedness. Our measures are built using the tensorial moments of the distribution, which naturally encode its spatial character, not only via its angular shape consistently with existing multipolar-moment approaches, but also its radial dependence. We combine these tensorial moments into a rotationally-invariant pseudoscalar using a newly-defined cross product and triple product for arbitrary symmetric tensors. We analyze these measures for a variety of toy-model distributions, providing intuition for the geometry and guiding the choice of chiral measure optimal for a given distribution. We also apply our measures to a physically-motivated example coming from photoionization in polychromatic chiral light. Our work provides a robust, flexible, intuitive, highly geometrical, and physically-driven framework for understanding and quantifying the chirality of a wide variety of distributions, together with an open-source software package that makes this toolbox readily applicable for the analysis of numerical or experimental data.