| In this thesis, we calculate the decay width of XcJ(J=0,1,2) to vector meson pairs and pseudoscalar meson pairs in perturbative QCD(pQCD) framework. Since the c-quark is not so heavy as the b-and t-quark in the high energy process, the non-perturbative effects in the decays of charmonium become much more important than those in the decays of bottonium and topponium, and there is not a feasible scheme to deal with these non-perturbative effects so far. Therefore, some effectively phenomenological schemes are proposed, for example, the pQCD factorization. In the pQCD factorization scheme, the non-perturbative effect can be involved in the bound state wave function of the meson, and one can just calculate the hard-scattering amplitude for the decays of heavy flavored mesons, so the selection of the bound state wave function becomes crucial. The zero binding approximation (δ-approximation) for the bound wave function is an approach which is employed intensively in calculating the decay widths of heavy flavored mesons. The bound wave function with δ-approximation fails to describe the internal quark motion inside light mesons, since the quarks are highly relativistic. In order to include contributions from the internal quark motion, we employ Bethe-Salpter (B-S) wave functions, and obtain the non-relativistic form of B-S wave functions in the ladder approximation. In our calculation, the B-S wave functions of the initial and the final states are employed to account for the finite size correction to the δ-approximation. For the branching ratios of Xc0.2→PP decays, our results are all about an order smaller than the experimental values. The calculated branching ratios are comparable with the measured values for Sc0.2→VV decays. While for the decays of Xc1→VV, the branching fractions are nonzero and are at the same order as the measured values in magnitude. This indicates that the finite size correction to the δ-approximation can yield a significant contribution to the decays of Xc1→VV, which provides an explanation for the problem of evasion of helicity selection rule. |
