All planar three-loop Feynman integrals for the production of two vector bosons at hadron colliders

TL;DR

This paper computes all relevant planar three-loop master integrals for N3LO QCD corrections in vector boson production at hadron colliders, advancing precision calculations in particle physics.

Contribution

It provides a complete set of master integrals and their canonical differential equations for a key process at three loops, using novel finite field techniques.

Findings

Explicit expressions for all master integrals obtained.

Canonical differential equations reconstructed for each integral family.

Facilitates higher-order QCD calculations for collider physics.

Abstract

We compute all the planar three-loop master integrals relevant for the leading colour N3LO QCD corrections to the production of two massive or off-shell vector bosons at hadron colliders. These integrals are organised into nine four-point integral families with massless internal propagators and two external massive legs. For each family, we construct a basis of pure master integrals and we reconstruct the corresponding canonical differential equations using finite field techniques. We evaluate the master integrals by solving the differential equations using generalised power series expansions.