Two-Loop QCD Helicity Amplitudes for Higgs Production Associated with a Vector Boson through Bottom Quark Annihilation

TL;DR

This paper calculates two-loop QCD corrections to Higgs plus Z boson production via bottom quark annihilation, simplifying multiloop computations and providing numerical cross section estimates under NNLO approximations.

Contribution

It introduces a novel approach to project amplitudes onto Lorentz structures, reducing complexity in multiloop calculations for Higgs production processes.

Findings

Finite remainders verified through form factor decomposition.

D-dimensional form factor decomposition not necessary for physical observables.

Computed cross sections are significantly smaller than s-channel estimates.

Abstract

We present the two-loop QCD corrections to the amplitude of the Higgs production associated with a $Z$ boson via the bottom quark-antiquark annihilation channel with a non-vanishing bottom-quark Yukawa coupling. The computation is performed by projecting the D-dimensional scattering amplitude directly onto a set of Lorentz structures related to the linear polarisation states of the $Z$ boson. We cross-check the finite remainders through a computation based on conventional form factor decomposition. We show that for physical observables, an ultimate D-dimensional form factor decomposition of amplitudes is not necessary which has a huge potential to simplify a multiloop computation. We compute numerically the resulting cross sections under the soft-virtual approximation to NNLO and find it three orders of magnitude smaller than that of the s-channel.