Phenomelnological Studies Of Electromagnetic Dalitz Decays Of Charmonia J/? And H_c In The Framework Of Perturbative QCD

The decays of charmonia into light hadrons have received a great deal of attention in the past few decades both on the experimental and theoretical aspects.They provide us with invaluable information about the Quantum Chromodynamics(QCD),which is the theory for describing the interactions between quarks and gluons.On the picture of QCD,the hadronic decays of charmonia are supposed to proceed predominantly via the cc annihilation with an intermediate state containing only gluons,which subsequently convert to light hadrons.Thus,these decays are ideal for the study of light hadron production mechanisms in high energy processes.In addition,using these decay processes,we can test the perturbative and nonperturbative properties of QCD.In this thesis,we present a phenomenological study of the electromagnetic(EM)Dalitz decays J/???(')l++-(l=e,?)and hc??(')l+l-(l=e,?)in the framework of per-turbative QCD.There exist mainly the following types of contributions to these processes:(i)In the large recoil momentum region,i.e.,q2(?)0,the contributions are dominated by the hard-scattering mechanism,which can be calculated in the framework of perturbative QCD.(ii)In the small recoil momentum region,i.e.,q2(?)qmax2,the involved transition form factors(TFFs)can be phenomenologically interpreted as the overlap of the incoming and outgoing hadronic wave functions.(iii)Near some resonance regions,such as q2(?)m?2,m?2,m?2,the resonance interaction between virtual photons and vector mesons is predominant,which can be universally described by a vector meson dominance(VMD)model.Firstly,we present a detailed study of the EM Dalitz decays J/???(')l+l-.In the large recoil region,these decay processes are investigated in detail within the perturbative QCD frame-work.With the help of the usual idea of factorization,the bound state effect of the initial J/?meson is factorized into the corresponding Bethe-Salpeter wave function,while the final ?(')mesons are described by the light-cone distribution amplitudes(DAs)due to the large recoil momentum.Then,the involved one-loop integrals are calculated analytically.Interestingly enough,we find that the TFFs f??(')(q2)are insensitive to the light quark masses and barely depend on the shapes of ?(')DAs,which are compatible with our previous studies of the ra-diative decays of J/? and hc.Furthermore,the soft contributions from the small recoil re-gion and the VMD corrections from some resonance regions have also been taken into account.We find that the VMD corrections are negligible in the branching ratios B(J/???(')e+e-).In addition,by using the calculated ratio RJe/?=B(J/???e+e-)/B(J/???'e+e-)and the decay widths ?(?(')???)as well as their experimental values,we extract the three phenomenological parameters for describing the ?-?' mixing,fq=(1.09 ± 0.01)f?,fs=(0.98±0.03)f? and ?=34.0°±0.6°,which are fairly consistent with the set of parameter values(fq=(1.09 ± 0.02)f?r,fs=(0.96 ± 0.04)f?,?=33.5°± 0.9°)extracted from the asymptotic TFFs of ?*?-?'.Moreover,the values of these phenomenological parameters are accord with our previous results(?=33.9° ±0.6° and ?=33.8°± 2.5°)extracted from the ratios RJ/?=B(J/???'?)/B(J/B(J/????)and Rhc=B(hc???)/B(hc??'?)in the radiative decays J/?-+?(')? and hc??(')?.However,they are clearly smaller than the mix-ing angle ?=40.6°± 0.9° extracted from low energy processes with nonperturbative methods.This implies that a smaller value of the mixing angle ?(?34°)may be favored in charmonium energy region.With the parameters of ?-?' mixing extracted from J/???(')e+e-,we obtain the branching ratios B(J/????+?-)=3.64 × 10-6,B(J/???'?+?-)=1.52 × 10-5 and their ratio RJ?/?=B(J/????+?-)/B(J/???'?+?-)=23.9%,where the uncertainty of the ratio is expected to be less than 5%.Secondly,the P-wave charmonium EM Dalitz decays hc??(')l+l-are studied along the same line as the S-wave charmonium EM Dalitz decays J/???(')l+l-.In accordance with the conclusions made in the last work,we also find that the TFFs fhc?(')(q2)are insensitive to the light quark masses and barely depend on the shapes of ?(')DAs in the large recoil momentum region.With the parameters of ?-?' mixing extracted from the EM Dalitz decays J/???(')e+e-,we obtain the branching ratios B(hc??e+e-)=7.35 × 10-6,B(hc???+?-)=3.47 × 10-6,B(hc??'e+e-)=2.09 × 10-5 and B(hc??'?+?-)=8.52 × 10-6,where the uncertainties(about 30%?40%)come mainly from Bexp(hc??(')-?).