Research On The Charmonium Decay Process Of η_c→γγ

Quantum chromodynamics（QCD）is a theory used to describe strong interactions.The coupling constant is small at high momentum transfers and can be studied using perturbative quantum chromodynamics（pQCD）,In pQCD theory,it can be expanded by any physical observable measurement in terms of coupling and constant perturbation.Renormalization group invariance requires that the observed quantity should not depend on the selection of renormalization indices.However,in traditional schemes,renormalization indices are usually chosen as the typical indices of the process,and the dependence of renormalization indices exists in finite order calculation of pQCD.The uncertainty of renormalization indices is an important source of error in QCD theoretical language.The principle of maximum conformal（PMC）provides a systematic method to solve the renormalization scale dependence problem.In this paper,PMC method is used to calculate the second order leading order（NNLO）QCD correction of the S-wave（lowest charmonium state）charmonium decay to two-photon under the nonrelativistic QCD（NRQCD）framework.In order to obtain a reliable prediction,we take the process from the non-physical （?） scheme to the physical V scheme using the method of PMC scale setting,we obtain the PMC scale of the form factor in the decay process as μrPMC=6.739 GeV.In the traditional method,people usually choose renormalization scale as the mass of charm quark,and PMC energy is much larger than traditional energy.The convergence of the obtained PMC conformal series is greatly improved,and the resulting theoretical prediction eliminates the renormalization scale uncertainty,and the calculated decay width is Γ（ηc→γγ）=5.134-0.326+0.333 keV,where the uncertainty comes from the charm quark mass mc=1.5±0.1 GeV.The world mean value（PDG）gives the decay width of the process as Γ（ηc→γγ）=5.15±0.35 keV.The predicted results in this paper are in good agreement with the experimental results.In addition,the coupling constant αs is a free parameter in QCD,and the expression of the physical observables can be expanded in terms of the coupling constantαs,which plays an important role in obtaining the physical observables.At present,many experimental and theoretical groups extract the coupling constant αs through different platforms.In this paper,the determination of the coupling constant based on event shape physical quantity is studied the e+e-collision platform.The traditional method simply sets the renormalization scale as μr=s^1/2,and can only extract a value of αs under a given scale,which is the main source of error when the renormalization scale is selected.In contrast,the PMC scale is not a single value,but changes with the change of eventshape value.By comparing theory and experiment,we can extract the coupling constant of the scale in a wide region.As the uncertainty of the energy scale is eliminated,the precision of the extracted coupling constant is greatly improved.