Relations between three-point configuration space shear and convergence statistics

TL;DR

This paper establishes mathematical relations between shear and convergence three-point statistics in weak lensing, enabling better connection between observations and theory, and introduces a method for E/B-mode separation applicable to polarization fields.

Contribution

It derives new relations linking shear and convergence three-point statistics, facilitating improved analysis of weak lensing data and polarization fields.

Findings

Derived relations between shear and convergence three-point statistics.

Validated the consistency of these relations with existing results.

Formulated conditions for E/B-mode decomposition in lensing statistics.

Abstract

With the growing interest in and ability of using weak lensing studies to probe the non-Gaussian properties of the matter density field, there is an increasing need for the study of suitable statistical measures, e.g. shear three-point statistics. In this paper we establish the relations between the three-point configuration space shear and convergence statistics, which are an important missing link between different weak lensing three-point statistics and provide an alternative way of relating observation and theory. The method we use also allows us to derive the relations between other two- and three-point correlation functions. We show the consistency of the relations obtained with already established results and demonstrate how they can be evaluated numerically. As a direct application, we use these relations to formulate the condition for E/B-mode decomposition of lensing three-point statistics, which is the basis for constructing new three-point statistics which allow for exact E/B-mode separation. Our work applies also to other two-dimensional polarization fields such as that of the Cosmic Microwave Background.