Two-Loop QCD Corrections to Higgs $\rightarrow b + \bar{b} + g$ Amplitude

TL;DR

This paper calculates two-loop QCD corrections to the Higgs decay into a bottom quark, anti-bottom quark, and gluon, providing precise amplitudes crucial for understanding Higgs production with jets.

Contribution

It presents the first computation of two-loop QCD corrections for the Higgs to bar{b}g amplitude, including infrared structure and finite parts, advancing theoretical predictions for Higgs-associated processes.

Findings

Renormalized amplitudes exhibit correct infrared behavior.

Finite parts of amplitudes are explicitly calculated after subtraction.

Results improve precision in Higgs plus jet predictions.

Abstract

Exclusive observables involving Higgs boson in association with jets are often well suited to study the Higgs boson properties. They are rates involving cuts on the final state jets or differential distributions of rapidity, transverse momentum of the observed Higgs boson. While they get dominant contributions from gluon initiated partonic subprocesses, it is important to include the subdominant ones coming from other channels. In this article, we study one such channel namely the Higgs production in association with a jet in bottom anti-bottom annihilation process. We compute relevant amplitude $H\rightarrow b+\overline b+g$ up to two loop level in QCD where Higgs couples to bottom quark through Yukawa coupling. We use projection operators to obtain the coefficients for each tensorial structure appearing in this process. We have demonstrated that the renormalized amplitudes do have the right infrared structure predicted by the QCD factorization in dimensional regularization. The finite parts of the one and two loop amplitudes are presented after subtracting the infrared poles using Catani's subtraction operators.