An analysis of $H\to \gamma \gamma$ up to three-loop QCD corrections

Abstract

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 $H\to \gamma \gamma$ 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 $\overline{\mathrm{MS}}$ 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 ${\mu }_r^{\mathrm{PMC}}=242.3$ GeV $\sim 2M_H$, 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., $\Gamma (H\to \gamma \gamma ){|}_{\mathrm{ATLAS}}=9.504_{-0.252}^{+0.226}$ keV and $\Gamma (H\to \gamma \gamma ){|}_{\mathrm{CMS}}=9.568_{-0.191}^{+0.195}$ keV, where the error is caused by the measured Higgs mass, i.e. the Higgs mass $M_H$ is taken as $125.5\pm 0.2_{-0.6}^{+0.5}$ GeV for ATLAS and $125.7\pm 0.3\pm 0.3$ GeV for CMS, respectively.

16 pages, 2 figures. References updated and discussion improved, to be published in J.Phys.G

References in corpus (8)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Eliminating the Renormalization Scale Ambiguity for Top-Pair Production Using the Principle of Maximum Conformality
• Renormalization Group Invariance and Optimal QCD Renormalization Scale-Setting
• Self-Consistency Requirements of the Renormalization Group for Setting the Renormalization Scale
• Application of the Principle of Maximum Conformality to the Top-Quark Forward-Backward Asymmetry at the Tevatron
• Complete Two-Loop Corrections to H -> gamma gamma
• Reanalysis of the BFKL Pomeron at the next-to-leading logarithmic accuracy

Cited by in corpus (12)

• Renormalization Group Invariance and Optimal QCD Renormalization Scale-Setting
• Degeneracy Relations in QCD and the Equivalence of Two Systematic All-Orders Methods for Setting the Renormalization Scale
• Application of the Principle of Maximum Conformality to the Top-Quark Charge Asymmetry at the LHC
• QCD corrections to the $B_c$ to charmonia semi-leptonic decays
• Setting the Renormalization Scale in pQCD: Comparisons of the Principle of Maximum Conformality with the Sequential Extended Brodsky-Lepage-Mackenzie Approach
• The Importance of Proper Renormalization Scale-Setting for Testing QCD at Colliders
• General Properties on Applying the Principle of Minimum Sensitivity to High-order Perturbative QCD Predictions
• Renormalization group improved pQCD prediction for ${\rm Y}(1S)$ leptonic decay
• Application of the Principle of Maximum Conformality to the Hadroproduction of the Higgs Boson at the LHC
• Properties of the decay $H\to \gamma \gamma$ using the approximate ${\alpha }_s^4$-corrections and the principle of maximum conformality
• Approximate N${}^5$LO Higgs boson decay width $\Gamma (H\to \gamma \gamma )$
• Reconsideration of the QCD corrections to the ${\eta }_c$ decays into light hadrons using the principle of maximum conformality