The one-loop bispectrum of galaxies in redshift space from the Effective Field Theory of Large-Scale Structure

TL;DR

This paper derives the theoretical framework and counterterms for the one-loop bispectrum of galaxies in redshift space within the Effective Field Theory of Large-Scale Structure, addressing renormalization subtleties.

Contribution

It provides the first derivation of kernels and counterterms for the one-loop bispectrum in real and redshift space, including biased tracers, with detailed renormalization procedures.

Findings

Derived kernels and counterterms for one-loop bispectrum

Addressed renormalization subtleties in velocity and momentum

Validated the theoretical framework with initial data analyses

Abstract

We derive the kernels and the Effective Field Theory of Large-Scale Structure counterterms for the one-loop bispectrum of dark matter and of biased tracers in real and redshift space. This requires the expansion of biased tracers up to fourth order in fluctuations. In the process, we encounter several subtleties related to renormalization. One is the fact that, in renormalizing the momentum, a local counterterm contributes non-locally. A second subtlety is related to the renormalization of local products of the velocity fields, which need to be expressed in terms of the renormalized velocity in order to preserve Galilean symmetry. We check that the counterterms we identify are necessary and sufficient to renormalize the one-loop bispectrum at leading and subleading order in the derivative expansion. The kernels that we originally present here have already been used for the first analyses of the one-loop bispectrum in BOSS data [1, 2].