Relativistic Contributions In Semileptonic Decays Of B_s Meson And B_c Meson

In the accurate calculation of particle physics,the relativistic correction is as im-portant as loop correction.Usually people only pay attention to the relativistic effects of light mesons,but ignore the relativistic effects of heavy mesons.Relativistic effects are usually calculated by a non-relativistic model combined with relative momentum(veloc-ity)expansion,and of course can also be calculated by a relativistic model.The former can only compute the lower order relativistic corrections,while the latter is often difficult to solve and therefore needs to take approximations.In this dissertation,the relativistic contribution in a meson decay is studied by the relative momentum expansion based on a relativistic model,the instantaneous Bethe-Salpeter equation.The Bethe-Salpeter equa-tion is derived from quantum field theory to describe relativistic two-body bound states.Although it has been approximated instantaneously in this dissertation,it still contains the most of relativistic effect,especially for the processes involving heavy mesons.We choose the semileptonic decays of B_cmeson to charmonium and B_smeson to charm strange meson.At the level of quark,these decays are both b?c,but their spectators are different.We expand the amplitude by the relative momentum between quark and diquark of the meson in the instantaneous Bethe-Salpeter model.The leading order of result is the non-relativistic term,and the difference between it and the complete decay width represents the relativistic contribution in this decay.Our results show that in the processes of B_c?(c?c)e??_e,the relativistic contributions are about 20%when the final states are S-wave,and the relativistic contributions are 14%�64%when the final states are P-wave.In the processes of B_s?(c?s)e??_e,the relativistic contributions are about 35%when the final states are S-wave,and the relativistic contributions are 28%�70%when the final states are P-wave.The relativistic effects in ground heavy mesons are not small,and the relativistic effects of some excited states are very large.The rapidity of convergence of the relative momentum expansion is not good in the process involving light quark.Therefore,heavy mesons should also be treated by a relativistic model.