Infrared Resummation for Biased Tracers in Redshift Space

TL;DR

This work develops an IR-safe framework to model redshift-space distortions and bias within time-sliced perturbation theory (TSPT), enabling controlled resummation of non-linear BAO damping in biased tracers. By mapping real-space correlators to redshift space via a 1D fictitious flow, the authors derive leading and next-to-leading order IR resummation formulas for power spectra and bispectra, including deterministic bias through a velocity-derivative operator basis. The approach yields explicit expressions for the dressed linear spectrum and loop corrections, with a practical implementation strategy that leverages wiggly/smooth decompositions and operator exponentiation, and it shows improved agreement with N-body data over linear or LO-resummed predictions. The framework is generalizable to higher-point functions, supports real- and redshift-space analyses, and provides a robust theoretical baseline for BAO studies and full-shape analyses in redshift space.

Abstract

We incorporate the effects of redshift space distortions and non-linear bias in time-sliced perturbation theory (TSPT). This is done via a new method that allows to map cosmological correlation functions from real to redshift space. This mapping preserves a transparent infrared (IR) structure of the theory and provides us with an efficient tool to study non-linear infrared effects altering the pattern of baryon acoustic oscillations (BAO) in redshift space. We give an accurate description of the BAO by means of a systematic resummation of Feynman diagrams guided by well-defined power counting rules. This establishes IR resummation within TSPT as a robust and complete procedure and provides a consistent theoretical model for the BAO feature in the statistics of biased tracers in redshift space.

Figures (8)

• Figure 1: Examples of TSPT Feynman rules in redshift space.
• Figure 2: Examples of Feynman rules for wiggly and smooth elements in redshift space.
• Figure 3: Left panel: the dependence of the BAO damping factors $\Sigma^2$ and $\delta\Sigma^2$ on the separation scale $k_S$ at redshift zero (in the cosmological model of GilMarin:2012nb, $f=0.483$). Right panel: the dependence of two contributions to the damping factor on the angle $\mu$ between the Fourier wavevector and the line-of-sight; $k_S$ is fixed to $0.2\,h/$Mpc.
• Figure 4: The monopole ($\ell=0$) moment of the 2-point correlation function of matter in redshift space at $z=0$. Left panel: linear theory (orange, dashed) vs leading order (LO) IR resummed results for several choices of $k_S$ (blue). Right panel: LO for $k_S=0.2 h$/Mpc (blue, dashed) vs next-to-leading order (NLO) IR resummed results (black).
• Figure 5: The quadrupole ($\ell=2$) moment of the 2-point correlation function of matter in redshift space at $z=0$. Left panel: linear theory (orange, dashed) vs LO IR resummed results for several choices of $k_S$ (blue). Right panel: LO for $k_S=0.2 h$/Mpc (blue, dashed) vs NLO IR resummed results (black). The three NLO curves are virtually indistinguishable.