Study Of B_c??(2S)K,?_c(2S)K,?(3770)K Decays With Perturbative QCD Approach

The standard model of particle physics is the fundamental theory,which come down to the Heliggs mechanism for producing particle mass and the quantum interaction and transformation fom the interaction between the lepton,quark and the three most basic gauge interactions,strong interaction,electromagnetic interaction and weak interaction.Specifically,that is to use gauge fields to describe the strong,the electromagnetic and the weak interactions in a unified way.The so-called gauge field is to transfer these three kinds of interacted medium particles gluon,W±,Z0 and photons.So far,almost all of its predictions are consistent with the experiment,and it belongs to the category of quantum field theory.And it's compatible with quantum mechanics and special relativity.When the four-fermion interaction of ? decay is studied,the effective Hamiltonian is obtained by integrating the intermediate bosons that transmit weak interactions in the standard model.The mixing of B mesons and the theoretical calculation and analysis of various decay processes show that the "low energy efficient Hamiltonian method" has been developed quite well.The core of this method is the calculation of Wilson coefficients,the evolution of renormalization groups and the calculation of Hadron transition matrix elements.After that,the effective Hamiltonian is expanded into a linear superposition of the four-quark operator and the magnetic moment operator in the domain by using the operator product expansion.The research method of this paper is the perturbation QCD(pQCD)theory based on the KT factorization.The core idea of the theory is to exchange a hard gluon between the spectator quark and the 4-quark operator aming to describe the weak interaction,that shows an equivalent interaction in the form of 6-quark.In this paper,we use perturbation theory to deal with such a hard gluon exchange process.Then the remaining nonperturbed parts are absorbed into the hadron wave function.In this paper,the meson wave function with the new relativistic correction and the single loop QCD radiation correction is used for the first time.Our calculated results of the decay branch ratio of Bc??/(2S)K,?c(2S)K are in good agreement with those obtained by other theoretical methods.The calculated results of the transition shape factor of Bc-?/(13D1)are also in good agreement with the results obtained by the light-cone QCD sum rule,which indicates that it is feasible to describe the radial and angular excited states of charmonium state(cc)by using harmonic oscillator wave function.?(3770)has important research value in the field of charm physics.Because the decay branch ratio of B??/(3770)K has been observed accurately in experiments to be 4.8 × 10-4 and some scholars have used QCD factorization method to calculate the decay branching ratio of B??(3770)K by 2S-1D mixing scheme with the calculated result 2.6 X 10-4,which is very close to the experimental observation.Based on this,we make a theoretical prediction of the decay branch ratio of decay process Bc ??/(3770)K by using the pQCD approach.For the sake of comparison,we calculate the decay branching ratio of Bc??/(3770)K when ?/(3770)is a pure D-wave state or a 2S-1D mixed state respectively.Finally,the decay branching ratios based on the two sets of mixing angle schemes are calculated respectively.The predicted results show that when?(3770)is regarded as a pure D-wave state,its decay branching ratio is in the order of 10-6,and when Bc is regarded as a mixing state of 2S-1D with a mixing angle-12 degrees,its decay branch ratio can be increased from 10-6 to 10-5,It shows that?(3770)may be a mixed state of 2S-1D.In addition,we also make a theoretical uncertainties analysis of the three decay channels,in which the largest and most important theoretical uncertainty derives from the hard scale that defines the contribution of the next-to-leading order correction.The calculation results show that the upper bound of the theoretical uncertainty is +13%and the lower bound is-6.9%,which indicates that the next-to-leading order correction is quite limited and can be safely ignored.