$H\to \gamma\gamma$ to all orders in $\alpha_s$ in the large-$\beta_0$ limit of QCD

TL;DR

This paper computes QCD corrections to Higgs to diphoton decay in the large-$eta_0$ limit, providing all-order insights into leading-$n_f$ contributions and renormalon effects, with explicit high-loop results.

Contribution

It presents the first two terms in the heavy-top expansion for this decay process in the large-$eta_0$ limit, enabling all-order analysis of leading-$n_f$ contributions.

Findings

Explicit leading-$n_f$ coefficients at 6 and 7 loops.

Analytic all-order expressions for leading-$n_f$ contributions.

Insights into the size of higher-order QCD corrections.

Abstract

In this note, we present the result for the QCD corrections to the decay of the Higgs boson into two photons in the large-$\beta_0$ limit of QCD, providing the first two terms in the heavy-top expansion. From our results, one can easily read off the exact leading-$n_f$ QCD contributions in analytic form to all orders in the strong coupling, $\alpha_s$, where $n_f$ is the number of massless quarks, and identify the leading renormalon singularities. We give explicit results for the leading-$n_f$ coefficients at 6 and 7 loops and use the large-$\beta_0$ result to speculate about the size of yet unknown (but small) higher-order contributions to the QCD series.