# Propagating Residual Biases in Cosmic Shear Power Spectra

## TL;DR

This paper derives a comprehensive expression for how shape measurement biases affect cosmic shear power spectra, highlighting new terms and the importance of forward modelling for large-scale analyses.

## Contribution

It introduces a full propagation framework for multiplicative and additive biases, including new terms related to selection effects and cross-correlations, and discusses computational challenges.

## Key findings

- Bias propagation scales as the fifth power of maximum multipole l.
- Shear power spectrum is mainly affected by the mean multiplicative bias and cross-correlation with additive bias.
- Second order bias terms are negligible if the mean multiplicative bias is zero.

## Abstract

In this paper we derive a full expression for the propagation of multiplicative and additive shape measurement biases into the cosmic shear power spectrum. In doing so we identify several new terms that are associated with selection effects, as well as cross-correlation terms between the multiplicative and additive biases and the shear field. The computation of the resulting bias in the shear power spectrum scales as the fifth power of the maximum multipole considered. Consequently the calculation is unfeasible for large l-modes, and the only tractable way to assess the full impact of shape measurement biases on cosmic shear power spectrum is through forward modelling of the effects. To linear order in bias parameters the shear power spectrum is only affected by the mean of the multiplicative bias field over a survey and the cross correlation between the additive bias field and the shear field. If the mean multiplicative bias is zero then second order convolutive terms are expected to be orders of magnitude smaller.