An analysis of H → γγ up to three-loop QCD corrections

The principle of maximum conformality (PMC) provides a convenient way for setting the optimal renormalization scales for high-energy processes, which can eliminate the conventional renormalization scale error via an order-byorder manner. At present, we make a detailed PMC analysis on the Higgs decay H -> gamma gamma up to three-loop QCD corrections. As an important point of deriving reliable PMC estimation, it is noted that only those {beta(i)}-terms that rightly determine the running behavior of coupling constant via the renormalization group equation should be absorbed into the coupling constant, and those {beta(i)}-terms that pertain to the quark mass renormalization and etc should be kept as a separate. To avoid confusion of separating and absorbing different types of {beta(i)}-terms into the coupling constant, we first transform the decay width in terms of top-quark (MS) over bar mass into that of on-shell mass and then apply the PMC scale setting. After applying PMC scale setting, the final estimation is conformal and is scheme-independent and scale-independent. Up to three-loop QCD corrections, we obtain a PMC scale mu(PMC)(r) = 242.3 GeV similar to 2M(H), which is optimal and highly independent of any choice of initial scale. Thus, we obtain a more accurate scale-independent prediction by taking the Higgs mass as the same as that of ATLAS and CMS measurements, i.e., Gamma (H -> gamma gamma)vertical bar(ATLAS) = 9.504(-0.252)(+0.226) and Gamma(H -> gamma gamma)vertical bar(CMS) = 9.568(-0.191)(+0.195) keV, where the error is caused by the measured Higgs mass, i.e. the Higgs mass M-H is taken as 125.5 +/- 0.2(-0.6)(+0.5) GeV for ATLAS and 125.7 +/- 0.3 +/- 0.3 GeV for CMS, respectively.