Hadronic Decays Of The Spin-singlet Heavy Quarkomium Under The Principle Of Maximum Conformality

A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. Recently, The principle of maximum conformality (PMC) provides a way to eliminate the conventional renormalization scale ambiguity in a systematic way. By applying PMC, all non-conformal terms in perturbative series are summed into the running coupling, and one obtains a unique, scale-fixed prediction at any finite order. In the paper, we make a detailed PMC analysis for the spin-singlet heavy quarkoniums decay (into light hadrons) at the next-to-leading order.After the PMC scale setting, the PMC scales for ηc and hc decays are below1GeV, in order to achieve a confidential pQCD estimation, we adopt several low-energy running coupling models to do the estimation. It is found that the results of all low-energy models are consistent with each other, which are caused by the fact that those models have similar behavioe around the region close to1GeV. For simplicity, we adopt MPT model to do a detail discussion on the heavy quarkonium decay properties and compare with the experimental data. After the PMC scale setting, the decay widths for all those cases are almost independent of the initial renormalization scales, in which the residual scale dependence are highly suppressed. By taking the MPT model, we obtain These decay widths agree with the principle of minimum sensitivity estimations, in which the decays of ηc,b are also consistent with the measured ones.