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 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 applying the PMC scale setting, the decay widths for all those cases are almost independent of the initial renormalization scales. The PMC scales for ${\eta }_c$ and $h_c$ decays are below $1$ GeV, in order to achieve a confidential pQCD estimation, we adopt several low-energy running coupling models to do the estimation. By taking the MPT model, we obtain: $\Gamma ({\eta }_c\to LH)=25.09_{-4.28}^{+5.52}$ MeV, $\Gamma ({\eta }_b\to LH)=14.34_{-0.84}^{+0.92}$ MeV, $\Gamma (h_c\to LH)=0.54_{-0.04}^{+0.06}$ MeV and $\Gamma (h_b\to LH)=39.89_{-0.46}^{+0.28}$ KeV, where the errors are calculated by taking $m_c\in [1.40\mathrm{GeV},1.60\mathrm{GeV}]$ and $m_b\in [4.50\mathrm{GeV},4.70\mathrm{GeV}]$. These decay widths agree with the principle of minimum sensitivity estimations, in which the decay widths of ${\eta }_{c,b}$ are also consistent with the measured ones.

Comments: 5 pages, 1 figures. Typos corrected, to be published in Chin.Phys.Lett