Analytic decay width of the Higgs boson to massive bottom quarks at next-to-next-to-leading order in QCD

TL;DR

This paper provides an exact NNLO QCD calculation of the Higgs decay width to bottom quarks, improving precision and understanding of the decay process with implications for heavy scalar decays.

Contribution

It presents the first exact NNLO QCD result for Higgs decay to bottom quarks, including complex integral evaluations and threshold behavior analysis.

Findings

NNLO corrections reduce theoretical uncertainties.

Results match previous large momentum expansion in the small bottom mass limit.

Threshold expansion reveals unique power divergence structure.

Abstract

The Higgs boson decay to a massive bottom quark pair provides the dominant contribution to the Higgs boson width. We present an exact result for such a decay induced by the bottom quark Yukawa coupling with next-to-next-to-leading order (NNLO) QCD corrections. We have adopted the canonical differential equations in the calculation and obtained the result in terms of multiple polylogarithms. We also compute the contribution from the decay to four bottom quarks which consists of complete elliptic integrals or their one-fold integrals. The result in the small bottom quark mass limit coincides with the previous calculation using the large momentum expansion. The threshold expansion exhibits power divergent terms in the bottom quark velocity, which has a structure different from that in $e^+e^-\to t\bar{t}$ but can be reproduced by computing the corresponding Coulomb Green function. The NNLO corrections significantly reduce the uncertainties from both the renormalization scale and the renormalization scheme of the bottom quark Yukawa coupling. Our result can be applied to a heavy scalar decay to a top quark pair.