Hadronic Decays of the Spin-Singlet Heavy Quarkomium under the Principle of Maximum Conformality

Abstract

The principle of maximum conformality (PMC) provides a way to eliminate the conventional renormalization scale ambiguity in a systematic way. By applying the PMC scale setting, all non-conformal terms in a perturbative series are summed into the running coupling, and one obtains a unique, scale-fixed prediction at any finite order. In this study, we make a detailed PMC analysis for the spin-singlet heavy quarkoniums decay (into light hadrons) at the next-to-leading order. After applying the PMC scale setting, the decay widths for all those cases are almost independent of the initial renormalization scales. The PMC scales for ηc and hc decays are below 1 GeV; to achieve a confidential pQCD estimation, we adopt several low-energy running coupling models to carry out the estimation. By taking the MPT model, we obtain Γ (ηc → LH) = 25.09+5.52−4.28 MeV, Γ(ηb → LH) = 14.34+0.92−0.84 MeV, Γ(hc → LH) = 0.54+0.06−0.04 MeV and Γ(hb → LH) = 39.89+0.28−0.46 keV, where the errors are calculated by taking mc ∈[1.40 GeV, 1.60 GeV] and mb ∈[4.50 GeV, 4.70 GeV]. These decay widths agree with the principle of minimum sensitivity estimations, in which the decay widths of ηc,b are also consistent with the measured ones.