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

The European Physical Journal C, Jan 2018

In the paper, we analyze the $$\eta _c$$ 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 $$\mathcal{{O}}(\alpha _s v^2)$$-order level has been included in the discussion, which gives about $$10\%$$ 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 $$n_{f}$$-terms, we transform the usual $$\overline{\mathrm{MS}}$$ pQCD series into the one under the minimal momentum space subtraction scheme. To compare with the prediction under conventional scale setting, $$R_\mathrm{{Conv,mMOM}-r}= \left( 4.12^{+0.30}_{-0.28}\right) \times 10^3$$, after applying the PMC, we obtain $$R_\mathrm{PMC,mMOM-r}=\left( 6.09^{+0.62}_{-0.55}\right) \times 10^3$$, where the errors are squared averages of the ones caused by $$m_c$$ and $$\Lambda _\mathrm{mMOM}$$. The PMC prediction agrees with the recent PDG value within errors, i.e. $$R^\mathrm{exp}=\left( 6.3\pm 0.5\right) \times 10^3$$. 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.

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Bo-Lun Du, Xing-Gang Wu, Jun Zeng, Shi Bu, Jian-Ming Shen. The $$\eta _c$$ decays into light hadrons using the principle of maximum conformality, The European Physical Journal C, 2018, 61, DOI: 10.1140/epjc/s10052-018-5560-3