NNLO phase space master integrals for two-to-one inclusive cross sections in dimensional regularization

TL;DR

This paper computes all necessary phase space master integrals for 2->1 processes at NNLO in dimensional regularization, providing higher-order expansions and all-order threshold expressions crucial for precise QCD cross section calculations.

Contribution

It introduces new higher-order epsilon expansions and all-order threshold expressions for phase space integrals in 2->1 processes at NNLO, advancing precision in QCD calculations.

Findings

Expanded epsilon series beyond previous literature

Derived all-order threshold expressions using special functions

Facilitated NNLO renormalization and mass factorization in QCD

Abstract

We evaluate all phase space master integrals which are required for the total cross section of generic 2 -> 1 processes at NNLO as a series expansion in the dimensional regulator epsilon. Away from the limit of threshold production, our expansion includes one order higher than what has been available in the literature. At threshold, we provide expressions which are valid to all orders in terms of Gamma functions and hypergeometric functions. These results are a necessary ingredient for the renormalization and mass factorization of singularities in 2 -> 1 inclusive cross sections at NNNLO in QCD.