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-by-order manner. At present, we make a detailed PMC analysis on the Higgs decay H → γγ up to three-loop QCD corrections. As an important point of deriving reliable PMC estimation, it is noted that only those {β_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 {β_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 {β_i}-terms into the coupling constant, we first transform the decay width in terms of top-quark \overlineMS 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 ∼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\rightarrow \gamma \gamma )|_ATLAS=9.504^{+0.226}_{-0.252} and \Gamma (H\rightarrow \gamma \gamma )|_CMS=9.568^{+0.195}_{-0.191} 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^{+0.5}_{-0.6} GeV for ATLAS and 125.7 ± 0.3 ± 0.3 GeV for CMS, respectively.