IR-Safe and IR-Resummed Bispectra Before and After Reconstruction in Unified Lagrangian Perturbation Theory

TL;DR

This paper develops an analytic framework using Unified Lagrangian Perturbation Theory to model the dark matter bispectrum, capturing nonlinear effects and IR cancellations, crucial for interpreting future bispectrum data.

Contribution

It introduces a unified, IR-safe analytic approach for the dark matter bispectrum, including IR resummation and detailed BAO damping, extending previous methods.

Findings

Demonstrates exact IR cancellation in bispectrum calculations.

Provides analytic expressions for IR-resummed bispectra including BAO damping.

Captures complex BAO-scale modulations in pre- and post-reconstruction configurations.

Abstract

We develop a unified analytic framework for modeling the real-space dark matter bispectrum, including both auto and cross bispectra constructed from pre- and post-reconstruction density fields, based on Unified Lagrangian Perturbation Theory (ULPT). ULPT reorganizes the standard Lagrangian approach by separating the Jacobian deviation, which generates the nonlinear source bispectrum, from the displacement-mapping effect that determines how long-wavelength bulk flows distort observed configurations. Within this structure, we derive general one-loop ULPT expressions for the bispectrum and analyze their infrared (IR) behavior, demonstrating exact, nonperturbative IR cancellation and the natural emergence of an IR-resummed description of baryon acoustic oscillation (BAO) damping. In particular, ULPT enables a detailed and fully analytic treatment of the wiggle-wiggle contribution to the IR-resummed bispectrum, whose structure has remained comparatively unexplored in previous approaches. We further construct IR-resummed models for the cross bispectra of all pre- and post-reconstruction combinations. For configurations in which the displacement fields differ, ULPT captures not only the overall exponential damping but also the more intricate BAO-scale modulation characteristic of mixed pre/post bispectra. Our results clarify the physical origin of nonlinear BAO suppression and provide a compact theoretical framework in which the full ULPT bispectrum, once implemented numerically through displacement-mapping convolution integrals, will automatically encode all nonlinear BAO and IR effects. The framework developed here therefore offers a unified and IR-safe foundation for interpreting next-generation bispectrum measurements.