Three-loop planar integrals for four-point one-mass processes

Abstract

In this contribution we will present analytic expressions for the two tennis-court integral families relevant to three-loop 2 → 2 scattering processes involving one massive external particle and massless propagators in terms of Goncharov polylogarithms of up to transcendental weight six. Additionally, we will also present analytic expressions for physical kinematics for the ladder-box family and the two tennis-court families in terms of real-valued polylogarithmic functions, making these results well-suited for phenomenological applications.