Two-Loop Hexa-Box Integrals for Non-Planar Five-Point One-Mass Processes

TL;DR

This paper computes non-planar two-loop five-point integrals essential for precise QCD corrections in processes involving W, Z, or Higgs bosons, using advanced differential equation techniques and analyzing their mathematical properties.

Contribution

It introduces a method to evaluate three non-planar hexa-box topologies with pure master integrals and explores their algebraic and analytic properties.

Findings

Derived compact alphabet expressions for non-planar integrals

Observed that extended Steinmann relations are generally violated

Provided high-precision numerical evaluations for phase space regions

Abstract

We present the calculation of the three distinct non-planar hexa-box topologies for five-point one-mass processes. These three topologies are required to obtain the two-loop virtual QCD corrections for two-jet-associated W, Z or Higgs-boson production. Each topology is solved by obtaining a pure basis of master integrals and efficiently constructing the associated differential equation with numerical sampling and unitarity-cut techniques. We present compact expressions for the alphabet of these non-planar integrals, and discuss some properties of their symbol. Notably, we observe that the extended Steinmann relations are in general not satisfied. Finally, we solve the differential equations in terms of generalized power series and provide high-precision values in different regions of phase space which can be used as boundary conditions for subsequent evaluations.