Phenomenological Studies Of Radiative Decays Of Charmonium To ??^?'?in The Framework Of Perturbative QCD

Since the discovery of the J/?,the charmonium physics has always been an active research field in charm physics,and is crucially important to improve our understanding of quantum chromodynamics(QCD),especially the interplay of perturbative with nonperturbative QCD.As one of the meaningful topics,the decays of charmonium have attracted continuous interests in theoretical and experimental investigations.In this thesis,within the framework of perturbative QCD,we study the Okubo-Zweig-Iizuka forbidden radiative decays of charmonium to ??(').Theoretically,these decays provide a clean environment to study the conversion of gluons into light mesons.Moreover,they are also closely related to the issues of ?-?' mixing,which are important ingredients for understanding many interesting phenomena related to the ? and ?' mesons.In addition,in the previous calculation of the decay widths of J/????('),the involved one-loop integrals were found to be very sensitive to the light quark masses of ?('),which is needed to be made clear.Our work in the thesis includes the following three parts:Firstly,the S-wave charmonium radiative decays J/????(')are revisited in detail.The involved five-point and four-point one-loop integrals are decomposed into a sum of three-point integrals,and then evaluated analytically with the light quark masses kept.We have found that the sum of these loop integrals is insensitive to the light quark masses and the branching ratios B(J/????('))barely depend on the shapes of ?(')distribution amplitudes.With the ?-?'mixing parameters extracted from low energy processes or from J????(')by means of non-perturbative matrix elements(0|G?vaGa,?v|?(')>,we could not get a ratio RJ/?=B(J/????')/B(J/????)that is in agreement with the experimental data.However,using the pa-rameters,especially the mixing angle ??33.5°±0.9°,extracted from the BaBar measured?*?-?' transition form factor at q2=112 GeV2,we obtain RJ/?=4.70,being in good agree-ment with RJ/?exp=4.65±0.21.As a crossing check,with ?exp(?(')???)and our results for B(J/????(')),we get?=33.9°±0.6°.Secondly,motivated by the latest experimental data,we study the P-wave charmonium radiative decays hc???(')in the framework of perturbative QCD,and evaluate analytically the one-loop integrals with the light quark masses kept.Interestingly,the branching ratios B(hc???('))are insensitive to both the light quark masses and the shapes of ?(')distribution amplitudes.And it is noticed that the contribution of the gluonic content of ?(')is almost equal to that of the quark-antiquark content of ?(')in the radiative decays hc???(').By employing the ratio Rhc=B(hc???)/B(hc????'),we extract the mixing angle ?=33.8°±2.5°,which is in clear disagreement with the Feldmann-Kroll-Stech result ?=39.0°±1.6° extracted from the ratio RJ/? with nonperturbative matrix elements<0|G?vaGa,?v|?(')>.but in consistent with?=33.5°±0.9° extracted from the ?*?-?' transition form factor and ?=33.9°±0.6° extracted from RJ/? in perturbative QCD.We have briefly discussed the possible reasons for the different values of the mixing angle determined from different processes.Thirdly,by using the covariant Salpeter wave function of P-wave charmonium hc,we im-prove our calculations for the radiative decays hc???(').Since the hard-scattering amplitude in the P-wave decays may be sensitive to the internal momentum qc,the convergence of the qc-expansion of the hard-scattering amplitude may become poor.In this calculation,the involved one-loop integrals are evaluated analytically with the full-dependence of the internal momen-tum of hc.It is then found that the branching ratios B(hc???(')barely depend on the light quark masses and the shapes of ?(')distribution amplitudes.As shown in the numerical results,the relativistic corrections associated with the internal momentum of hc can give a significant enhancement to the individual branching ratios B(hc???)and B(hc???'),but hardly affect their ratio Rhc,This means that the relativistic corrections associated with the internal momen-tum of hc in in the ratio cancel to a large extent.Using the mixing angle ?=33.5°±0.9°extracted from ?*?-?' transition form factor as input,we find that both the individual branching ratios B(hc???('))and their ratio Rhc are in good agreement with the corresponding experi-mental data.As a crossing check,using the ratio Rhc obtained with our improved calculations,we extract the mixing angle ?=33.8°±2.5°,which is obviously in line with our previous determination.