Two-loop divergences of scattering amplitudes with massive partons

TL;DR

This paper completes the analysis of two-loop infrared divergences in scattering amplitudes involving massive and massless partons, deriving universal functions that describe three-parton correlations and their behavior near production thresholds.

Contribution

It provides the analytic calculation of the universal functions F_1 and f_2 at two loops, advancing the understanding of infrared singularities in non-abelian gauge theories with massive particles.

Findings

F_1 and f_2 are suppressed as O(m^4/s^2) for small masses.

Both functions diverge logarithmically near heavy particle pair production thresholds.

The two-loop anomalous-dimension matrix for q q̄ → t t̄ near threshold is non-diagonal in the s-channel basis.

Abstract

We complete the study of two-loop infrared singularities of scattering amplitudes with an arbitrary number of massive and massless partons in non-abelian gauge theories. To this end, we calculate the universal functions F_1 and f_2, which completely specify the structure of three-parton correlations in the soft anomalous-dimension matrix, at two-loop order in closed analytic form. Both functions are found to be suppressed like O(m^4/s^2) in the limit of small parton masses, in accordance with mass factorization theorems proposed in the literature. On the other hand, they are unsuppressed and diverge logarithmically near the threshold for pair production of two heavy particles. As an application, we calculate the two-loop anomalous-dimension matrix for q q_bar --> t t_bar near threshold and show that it is not diagonal in the s-channel singlet-octet basis.