Two-loop helicity amplitudes for $H+$jet production to higher orders in the dimensional regulator

TL;DR

This paper advances the calculation of helicity amplitudes for Higgs plus jet production at higher orders in dimensional regularization, crucial for precise predictions at the upcoming High-Luminosity LHC.

Contribution

It computes one- and two-loop helicity amplitudes for H+jet production in an effective theory, introducing a new basis for tensor structures and master integrals, and solving differential equations with MPLs.

Findings

Derived and solved differential equations for master integrals.

Expressed form factors in terms of Multiple Polylogarithms.

Facilitates future higher-order QCD calculations for Higgs processes.

Abstract

In view of the forthcoming High-Luminosity phase of the LHC, next-to-next-to-next-to-leading (N$^3$LO) calculations for the most phenomenologically relevant processes become necessary. In this work, we take the first step towards this goal for H$+$jet production by computing the one- and two-loop helicity amplitudes for the two contributing processes, $H\to ggg$, $H\to q\bar{q}g$, in an effective theory with infinite top quark mass, to higher orders in the dimensional regulator. We decompose the amplitude in scalar form factors related to the helicity amplitudes and in a new basis of tensorial structures. The form factors receive contributions from Feynman integrals which were reduced to a novel canonical basis of master integrals. We derive and solve a set of differential equations for these integrals in terms of Multiple Polylogarithms (MPLs) of two variables up to transcendental weight six.