The Study Of The Process E~-+e~+â†'J/Ψ+η_c

The lowest order cross sections in NRQCD framework of the exclusive production process of e-+e+â†'J/φ+ηc at the energy ranges of B factories are nearly one magnitude smaller than the data of two B factories. Latter works on this process point out that the effect of inner movement between cc in charmonium is unneglectable. It is showed that, describing J/φandηc by the light cone wave function which is relativistic, one can get a theoretical result which is comparable with the experiment data; in the NRQCD theoretical framework, to reduce the large discrepancy between theory and experiment, one must consider high order correction and relativistic effect.In this thesis, with the Bethe-Salpeter wave functions of J/φandηc, we calcu-late the cross section of the exclusive production process of e-+e+â†'J/φ+ηc. Our main purpose is to search a better theoretical framework to study the influence of the relativistic momentum of cc in charmonium on the cross section. The Bethe-Salpeter formalism is established in the framework of quantum field theory, therefore, it includes all relativistic effects. In this framework, the quark and antiquark can be off-shell, so the lowest order Feynman diagram which is different from the non-relativistic approximation and light-cone wave function theoretical framework is triangle diagram showed in Fig.1.4 in chapter one. Because of the conservation of four momentums, the three quark line can not be on-shell at the same time. It means that the lowest order Feynman diagram of other theoretical framework corresponds to the third order in our framework.The effective coupling vertexes of ccJ/φand ccηc can be derived from the Bethe-Salpeter wave functions of J/φandηc. Because of the differences between the spins of J/φandηc, there are different Dirac structures at different vertexes. There are many linearly-independent covariant sets in complete Dirac structure of vertex. To simplify the calculation, we just choose the leading order Dirac structure.The relativistic movement between cc is showed in the scalar part of Bethe- Salpeter wave function. The distribution of relativistic momentum between cc is rep-resented by parameterβ. In the process of calculation, we investigate the influence of distributions of relativistic momentum between cc on the cross sectionσby changing the value of the parameterβ. Whenβâ†'0,σâ†'0. It means that the contribution of this Feynman diagram vanishes, which is same as previous researches. Whenβbecomes very big, the cross section becomes very small, so our model is stable. When the value ofβis between 2 and 2.25,σcan reach, even go beyond the experimental data. When a is equal to the experiment data, the distribution of relativistic momentum between cc is quite wide, so the relativistic effect is significant. The conclusion shows that it is significant to study relativistic movement of cc in charmonium more carefully with similar produce processes.