$H\to \gamma \gamma$ to all orders in ${\alpha }_s$ in the large-${\beta }_0$ limit of QCD

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.

15 pages, 3 figures. Extended results to include the first two terms in the heavy-top expansion. Matches published version

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Cited by in corpus (2)

• Renormalization group summation and analytic continuation from spacelike to timeline regions
• Resurgent representation of the Adler function in the large-${\beta }_0$ approximation of QCD