$H\to \gamma \gamma$ 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.

arXiv comment15 pages, 3 figures. Extended results to include the first two terms in the heavy-top expansion. Matches published version

References in corpus (19)

• HIGGS BOSON PRODUCTION AT THE LHC
• Renormalons
• Heavy Quark Effective Theory beyond Perturbation Theory: Renormalons, the Pole Mass and the Residual Mass Term
• Higgs production and decay: Analytic results at next-to-leading order QCD
• Naive nonabelianization and resummation of fermion bubble chains
• Resummation of $({\beta }_0{\alpha }_s{)}^n$ Corrections in QCD: Techniques and Applications to the $\tau$ Hadronic Width and the Heavy Quark Pole Mass
• MATAD: a program package for the computation of MAssive TADpoles
• Matching QCD and HQET heavy--light currents at two loops and beyond
• Analytic Results for Virtual QCD Corrections to Higgs Production and Decay
• Two-Photon Decay Widths of Higgs Particles
• Higgs - Two Photon Decay: QCD radiative correction
• Analytical Result for the Two-Loop QCD Correction to the Decay H --> 2 gamma
• Higher-order QCD corrections to hadronic $\tau$ decays from Padé approximants
• Complete three-loop QCD corrections to the decay H -> γγ
• Pole mass renormalon and its ramifications
• Reconciling the Contour-Improved and Fixed-Order Approaches for $\tau$ Hadronic Spectral Moments I: Renormalon-Free Gluon Condensate Scheme
• Higher order QCD results for the fermionic contributions of the Higgs-boson decay into two photons and the decoupling function for the MSbar renormalized fine-structure constant
• Exact quark-mass dependence of the Higgs-photon form factor at three loops in QCD
• Small-momentum expansion of heavy-quark correlators in the large-${\beta }_0$ limit and ${\alpha }_s$ extractions

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