Higgs Rapidity Distribution in $b {\bar b}$ Annihilation at Threshold in N$^{3}$LO QCD

TL;DR

This paper calculates the Higgs boson rapidity distribution in bottom quark annihilation at N$^{3}$LO in QCD, providing a systematic framework and demonstrating the numerical impact of these advanced corrections at the LHC.

Contribution

It introduces a new framework for computing threshold corrections at N$^{3}$LO in QCD for Higgs production via bottom quark annihilation, utilizing recent theoretical results.

Findings

N$^{3}$LO corrections significantly affect the Higgs rapidity distribution.

The framework ensures systematic and accurate threshold correction calculations.

Numerical analysis shows notable impact on LHC Higgs production predictions.

Abstract

We present the rapidity distribution of the Higgs boson produced through bottom quark annihilation at third order in QCD using the threshold approximation. We provide a framework, based on the factorization properties of the QCD amplitudes along with Sudakov resummation and the renormalization group invariance, that allows one to perform the computation of the threshold corrections in a consistent, systematic and accurate way. The recent results on threshold N$^3$LO correction in QCD for the Drell-Yan production and on three loop QCD correction to Higgs form factor with bottom anti-bottom quark are used to achieve this task. We also demonstrate the numerical impact of these corrections at the LHC.