The QCD Corrections To The η_c Decays Into Light Hadrons Using The Principle Of Maximum Conformality

A key problem in making precise perturbative quantum chromodynamics(pQCD)predictions is to set the proper renormalization scale of the running coupling.The conventional scale setting method is usually using the kinematic scale(Q)of the process as the renormalization scale,and set the systematic error by assigning multiple of Q to fixed-order pQCD predictions.There is large limitation for this simple practice,breaking the renormalization group(RG)invariance,and introducing ambiguities of renormalization scale and renormalization scheme.Recently,a scale setting method named the Principle of Maximum Conformality(PMC)was suggested internationally,which is consistent with RG invariance.PMC,based on the renormalization scheme,sets the renormalization scale of high energy process systematically.By using PMC,we can systematically eliminate the ambiguities of renormalization scale and renormalization scheme,hence the precision of theoretical predictions are greatly improved.As an application,in this article,we analyze the_cηdecays into light hadrons at the next-to-leading order QCD corrections by applying the PMC.The relativistic correction at the(?)-order level has been included in the discussion for more precise prediction.To avoid the confusion of treatingn_f-terms,we transform the usual (?) pQCD series into the one under the minimal momentum space subtraction(miniMOM)scheme.We find the results under conventional scale setting shows large deviation from the experimental data,while the PMC prediction agrees with the recent PDG value within errors.Thus it demonstrates the importance of setting correct renormalization scale to a precise theoretical prediction.