Adequate bases of phase space master integrals for $gg \to h$ at NNLO and beyond

TL;DR

This paper develops a systematic method to identify suitable bases of master integrals for Higgs production via gluon fusion at NNLO and beyond, simplifying their calculation using differential equations.

Contribution

It introduces a canonical form approach for phase space master integrals, demonstrating applicability at NNLO and N3LO, with detailed strategies for basis selection.

Findings

Successfully derived a canonical basis for all phase space master integrals at NNLO.

Extended the method to non-planar topologies at N3LO.

Provided practical examples and detailed procedures for basis selection.

Abstract

We study master integrals needed to compute the Higgs boson production cross section via gluon fusion in the infinite top quark mass limit, using a canonical form of differential equations for master integrals, recently identified by Henn, which makes their solution possible in a straightforward algebraic way. We apply the known criteria to derive such a suitable basis for all the phase space master integrals in afore mentioned process at next-to-next-to-leading order in QCD and demonstrate that the method is applicable to next-to-next-to-next-to-leading order as well by solving a non-planar topology. Furthermore, we discuss in great detail how to find an adequate basis using practical examples. Special emphasis is devoted to master integrals which are coupled by their differential equations.