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

Understand

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.