Second Order QCD Corrections to Scalar and Pseudoscalar Higgs Decays into Massive Bottom Quarks

Abstract

Quark mass effects in ${\cal O}(α_s^2)$ QCD corrections to the decay rates of intermediate Higgs bosons are studied. The total hadronic rate and the partial decay rate into bottom quarks are analyzed for the Standard (scalar) Higgs boson as well as for pseudoscalar Higgs bosons. The calculations of three different contributions are presented. First, the flavour singlet diagrams containing two closed fermion loops are calculated for a nonvanishing bottom mass in the heavy top limit. Their leading contribution, which is of the same order as the quasi-massless nonsinglet corrections, and the subleading terms are found. Large logarithms arise due to the separation of the pure gluon final state from the bottom final states. Second, quadratic bottom mass corrections originating from nonsinglet diagrams are presented.Third, nonsinglet corrections induced by virtual heavy top quarks are calculated in leading and subleading orders. It is demonstrated that, in order $α_s^2$, the first contribution numerically dominates over the second and the third ones.