Two-loop renormalization and running of galaxy bias

TL;DR

This paper extends galaxy bias renormalization to two-loop order, providing explicit calculations and renormalization group equations, which improve theoretical modeling of galaxy clustering for cosmological analyses.

Contribution

It introduces a comprehensive two-loop renormalization framework for galaxy bias, including stochasticity and RGEs, advancing the precision of bias modeling in cosmology.

Findings

Explicit two-loop renormalization of bias operators

Derivation of RGEs for bias coefficients

Identification of operators with enhanced UV sensitivity

Abstract

We systematically extend the framework of galaxy bias renormalization to two-loop order. For the minimal complete basis of 29 deterministic bias operators up to fifth order in the density field and at leading order in gradient expansion we explicitly work out one- and two-loop renormalization. The latter is provided in terms of double-hard limits of bias kernels, which we find to depend on only one function of the ratio of the loop momenta. After including stochasticity in terms of composite operator renormalization, we apply the framework to the two-loop power spectrum of biased tracers and provide a simple result suitable for numerical evaluation. In addition, we work out one- and two-loop renormalization group equations (RGE) for deterministic bias coefficients related to bias operators constructed from a smoothed density field, generalizing previous works. We identify a linear combination of bias operators with enhanced UV sensitivity, related to a positive eigenvalue of the RGE. Finally, we present an analogy with the RGE as used in quantum field theory, suggesting that a resummation of large logarithms as employed in the latter may also yield useful applications in the study of large-scale galaxy bias.