Planar three-loop master integrals for $2 \to 2$ processes with one external massive particle

TL;DR

This paper provides analytic expressions for complex three-loop integrals relevant to 2-to-2 scattering processes with one massive external particle, facilitating precise calculations in particle physics.

Contribution

It introduces new analytic results for two integral families at three-loop order, expressed in Goncharov polylogarithms, suitable for phenomenological applications.

Findings

Analytic results for two tennis-court integral families

Expressions in Goncharov polylogarithms up to weight six

Real-valued polylogarithmic functions for physical kinematics

Abstract

We present analytic results for the two tennis-court integral families relevant to $2\to2$ scattering processes involving one massive external particle and massless propagators in terms of Goncharov polylogarithms of up to transcendental weight six. We also present analytic results for physical kinematics for the ladder-box family and the two tennis-court families in terms of real-valued polylogarithmic functions, making our solutions well-suited for phenomenological applications.