The $$\eta _c$$ ηc decays into light hadrons using the principle of maximum conformality

Abstract

Abstract In the paper, we analyze the $$\eta _c$$ ηc decays into light hadrons at the next-to-leading order QCD corrections by applying the principle of maximum conformality (PMC). The relativistic correction at the $$\mathcal{{O}}(\alpha _s v^2)$$ O(αsv2) -order level has been included in the discussion, which gives about $$10\%$$ 10% contribution to the ratio R. The PMC, which satisfies the renormalization group invariance, is designed to obtain a scale-fixed and scheme-independent prediction at any fixed order. To avoid the confusion of treating $$n_{f}$$ nf -terms, we transform the usual $$\overline{\mathrm{MS}}$$ MS¯ pQCD series into the one under the minimal momentum space subtraction scheme. To compare with the prediction under conventional scale setting, $$R_\mathrm{{Conv,mMOM}-r}= \left( 4.12^{+0.30}_{-0.28}\right) \times 10^3$$ RConv,mMOM-r=4.12-0.28+0.30×103 , after applying the PMC, we obtain $$R_\mathrm{PMC,mMOM-r}=\left( 6.09^{+0.62}_{-0.55}\right) \times 10^3$$ RPMC,mMOM-r=6.09-0.55+0.62×103 , where the errors are squared averages of the ones caused by $$m_c$$ mc and $$\Lambda _\mathrm{mMOM}$$ ΛmMOM . The PMC prediction agrees with the recent PDG value within errors, i.e. $$R^\mathrm{exp}=\left( 6.3\pm 0.5\right) \times 10^3$$ Rexp=6.3±0.5×103 . Thus we think the mismatching of the prediction under conventional scale-setting with the data is due to improper choice of scale, which however can be solved by using the PMC.