Analytic Results for Virtual QCD Corrections to Higgs Production and Decay

TL;DR

This work delivers analytic NLO QCD corrections for Higgs production via gluon fusion $gg \to H$ and decay to two photons $H \to \gamma\gamma$ in a general framework where the Higgs couples to external particles through colored fermions and scalars. The authors express the two-loop virtual corrections in compact Harmonic Polylogarithms, provide new Master Integrals, and perform mass-regime expansions to ensure broad applicability, including both MS-bar and on-shell schemes. They also perform independent checks in the pseudoscalar sector, computing $A \to \gamma\gamma$ and $gg \to A$, and confirm consistency with prior results while extending to OS top masses. The combination of the Laporta reduction and differential equations techniques yields analytic results suitable for fast numerical implementation, enhancing precision Higgs phenomenology at the LHC and beyond.

Abstract

We consider the production of a Higgs boson via gluon-fusion and its decay into two photons. We compute the NLO virtual QCD corrections to these processes in a general framework in which the coupling of the Higgs boson to the external particles is mediated by a colored fermion and a colored scalar. We present compact analytic results for these two-loop corrections that are expressed in terms of Harmonic Polylogarithms. The expansion of these corrections in the low and high Higgs mass regimes, as well as the expression of the new Master Integrals which appear in the reduction of the two-loop amplitudes, are also provided. For the fermionic contribution, we provide an independent check of the results already present in the literature concerning the Higgs boson and the production and decay of a pseudoscalar particle.

Figures (3)

• Figure 1: The Feynman diagrams for the decay process $H,A \to \gamma \gamma$. Diagrams (a)--(d) have a fermion, labeled by "f", running in the loop, while diagrams (e)--(n) have a scalar, labeled by "s".
• Figure 2: The Feynman diagrams for the production mechanism $gg \to H,A$. Diagrams (a)--(h) have a fermion, labeled by "f", running in the loop, while diagrams (i)--(x) have a scalar, labeled by "s".
• Figure 3: The Master Integrals necessary for the computation of the two-loop QCD corrections to $gg \to H$ and $H \to \gamma \gamma$.