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

TL;DR

This work computes the three-loop QCD corrections to the Hb\bar{b} Yukawa form factor in the massless-bottom limit, providing the analytic structure of the renormalized form factor $F_3$ across color channels. The calculation follows a standard multi-loop pipeline—diagram generation, Laporta-based IBP reduction to 22 master integrals, and analytic evaluation—yielding explicit $\epsilon$-expanded results and the complete infrared pole pattern. The pole structure, dictated by cusp and collinear anomalous dimensions, is shown to agree with universal infrared factorization predictions for the related ${\gamma^* q\bar{q}}$ form factor, reinforcing the consistency of the approach. These results enable N$^3$LO predictions for Higgs production via bottom-quark fusion and for fully differential Higgs decays to $b\bar{b}$, and they form a key component of threshold-resummed and soft-virtual analyses at this order.

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.