Renormalization Group Effects in the Process $H \longrightarrow \gamma \gamma$

TL;DR

This paper investigates the impact of renormalization group effects on the Higgs decay to two photons, incorporating two-loop running coupling effects to refine theoretical predictions relevant for collider experiments.

Contribution

It introduces the exact two-loop running coupling into calculations of the Higgs to gamma gamma decay width, improving the precision of the theoretical predictions in the MSSM.

Findings

The effective scale for the bottom contribution is close to α_s(10 m_b^2).

Including two-loop running coupling reduces scale uncertainty in the decay width.

Large tan β enhancements can significantly affect the partial width in extended Higgs sectors.

Abstract

The partial Higgs width $\Gamma (H \longrightarrow \gamma \gamma)$ is important at the LHC for Higgs masses in the MSSM mass window up to 140 GeV as a relatively background free signal of a fundamental scalar. At the photon photon mode at the NLC it would be the Higgs production mechanism . Two loop QCD corrections exist for the fermionic contribution and in the case of the bottom loop large non-Sudakov double logarithms can be resummed to all orders and contribute up to 12 % compared to the t-quark. In more complicated Higgs sectors, such as in the MSSM, large $\tan \beta$ enhancements of bottom type Yukawa couplings can potentially dominate even the whole partial width. A main uncertainty in all existing calculations is the scale of the strong coupling as it is only renormalized at the three loop level. In this paper we include the exact two loop running coupling to all orders into the bottom contribution. We find that the effective scale is close to $\alpha_s (10 m_b^2)$.