| Based on the(NRQCD)factorization theorem of non-relativistic quantum chromodynamics,the process of radiation decay from bottom quark to charm is studied in this paper,accompanied by a photon.According to the NRQCD factorization theorem,the decay width(amplitude)factor of the process is transformed into the product of a series of short-range coefficients and long-range matrix elements.The short distance coefficient can be calculated according to the strong interaction coupling constant as expansion,while the long range matrix element is non-perturbed.These different matrix elements are expanded according to the typical velocity v of the positive and inverse quarks in the heavy quark prime(where for charm prime v ^ 2?O.3 and diquarkrion v ^2?0.1),these matrix elements are expanded according to the typical velocity v of the positive and inverse quark in the heavy quark prime.Therefore,NRQCD is expanded according to the double expansion of as and v.The higher-order correction of the former is called radiation correction,and the higher-order correction of the latter is called relativistic correction.According to the need of precision,the theory can be truncated to a certain order.In this paper,the decay width of the QED and QCD processes is calculated,and two types of subprocesses are included:the QED and QCD processes.The QED process of the lead step is the tree diagram process.Due to the conservation of C-parity and the conservation of color charge,the leading-order contribution of the QCD process comes from a circle of graphs.The amplitude of the two sub-processes and the decay width of the process(including the interference contribution)will be calculated respectively.By using the NRQCD factorization theorem and the perturbation matching method,the short-range coefficients of the leading and sub-lead matrix elements of the two kinds of processes are respectively calculated.Wherein the short-range coefficients are refined to the leading step of the radiation correction.The paper uses manual derivation and computer programming to realize the calculation.The method comprises the following steps of:firstly,using a high-energy software package,FeynArts,to generate a Feyman graph and a Freeman amplitude of a process;then,using the FeyCalc to complete the calculation of the Dirac matrix trace and the index shrinkage that appear in the amplitude;and then using the Apart and the FIRE to perform tensor reduction on the Femann amplitude in the circle graph,so as to obtain a basic scalar circle graph integral;Then,the analytic expression of the integral of these scalar circles is calculated by PackageX,and the amplitude of the perturbation process is finally obtained.The short-range coefficient of the process amplitude is obtained by the matching method,and the decay width of the process is finally obtained.By selecting the appropriate input parameters,the paper makes a detailed phenomenological analysis and discussion.The results show that in the leading step of the relativistic expansion,the decay width of the QED process accounts for 7.98%of the total decay width,the contribution of the QCD process is 53.87%,and the interference contribution between the QED and the QCD is 38.15%.The contribution of the QED process to the total decay width is about 8.87%,the contribution of the QCD process is 53.0%,and the interference contribution between the QED and the QCD is 38.1%after the relativistic correction is included.The analysis shows that the relativistic correction of the process is relatively small and slightly reduces the branch ratio of the leading step contribution.The result of the calculation is less than the upper limit of the experimental decay width of 5.7×10-5,so there is no contradiction with the experiment,and the more accurate result of the experiment can test the prediction of the theory.The effect of the parameter error on the decay width and the decay width and the error of the decay of the Y(2S,3S)radiation to the envelope ?c are also considered. |
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