# Modeling CMB Lensing Cross Correlations with {\sc CLEFT}

## TL;DR

This paper introduces the use of Convolution Lagrangian Effective Field Theory ({ extsc{CLEFT}}) for modeling cross correlations between CMB lensing and large-scale structure tracers at high redshift, demonstrating its accuracy over traditional methods.

## Contribution

It proposes a perturbative bias model using { extsc{CLEFT}} for high-redshift cross correlations, improving upon existing scale-independent bias approaches.

## Key findings

- { extsc{CLEFT}} provides unbiased estimates of $\sigma_8$ at high redshift.
- Traditional bias models are insufficient for upcoming survey precision.
- { extsc{CLEFT}} accurately models large-scale cross correlations in mock data.

## Abstract

A new generation of surveys will soon map large fractions of sky to ever greater depths and their science goals can be enhanced by exploiting cross correlations between them. In this paper we study cross correlations between the lensing of the CMB and biased tracers of large-scale structure at high $z$. We motivate the need for more sophisticated bias models for modeling increasingly biased tracers at these redshifts and propose the use of perturbation theories, specifically Convolution Lagrangian Effective Field Theory ({\sc CLEFT}). Since such signals reside at large scales and redshifts, they can be well described by perturbative approaches. We compare our model with the current approach of using scale independent bias coupled with fitting functions for non-linear matter power spectra, showing that the latter will not be sufficient for upcoming surveys. We illustrate our ideas by estimating $\sigma_8$ from the auto- and cross-spectra of mock surveys, finding that {\sc CLEFT} returns accurate and unbiased results at high $z$. We discuss uncertainties due to the redshift distribution of the tracers, and several avenues for future development.