The $Hb\bar{b}$ form factor to three loops in QCD

TL;DR

This paper calculates the three-loop QCD corrections to the Higgs-bottom quark vertex function, which is essential for precise Higgs production and decay predictions involving bottom quarks.

Contribution

It provides the first complete three-loop QCD correction to the Higgs-bottom quark form factor in the massless quark limit.

Findings

Infrared pole structure matches QCD factorization predictions

Enables more accurate Higgs production and decay calculations

Advances theoretical understanding of higher-order QCD effects

Abstract

We compute the three-loop QCD corrections to the vertex function for the Yukawa coupling of a Higgs boson to a pair of bottom quarks in the limit of vanishing quark masses. This QCD form factor is a crucial ingredient to third-order QCD corrections for the production of Higgs bosons in bottom quark fusion, and for the fully differential decay rate of Higgs bosons to bottom quarks. The infrared pole structure of the form factors agrees with the prediction from infrared factorization in QCD.