Higgs production and decay: Analytic results at next-to-leading order QCD

TL;DR

This work delivers closed analytic expressions at next-to-leading order QCD for Higgs processes with full mass dependence: H/A decays to two photons and the virtual corrections to gluon-fusion production, for both scalar and pseudoscalar Higgs bosons. The authors introduce the Expansion and Inversion method to convert existing one-dimensional integral representations into analytic formulas expressed in Harmonic Polylogarithms, validating the approach by reproducing known results and extending to pseudoscalar cases. Notably, the gluon-fusion case requires including a weight-4 Harmonic Polylogarithm in the basis to accommodate threshold behavior. The resulting expressions are suitable for fast phenomenological implementations and may inform algorithmic approaches to Feynman integral evaluation.

Abstract

The virtual two-loop corrections for Higgs production in gluon fusion are calculated analytically in QCD for arbitrary Higgs and quark masses. Both scalar and pseudo-scalar Higgs bosons are considered. The results are obtained by expanding the known one-dimensional integral representation in terms of m_H/m_q, and matching it with a suitably chosen ansatz of Harmonic Polylogarithms. This ansatz is motivated by the known analytic result for the Higgs decay rate into two photons. The method also allows us to check this result and to extend it to the pseudo-scalar decay rate.