Study Of B Meson Non-leptonic Decays With Perturbative QCD Factorization Approach

Since L.Lederman discovered the bound state particles y(bb)in Fermi laboratory and confirmed the existence of b quarks,it has opened up an era of B physics.In experiment,LHCb,Belle,BaBar and other experimental groups collected a large number of B meson decay cases each year,which allowed us to obtain the basic properties of B mesons.The study of B meson decay can not only verify the origin of CP violation,but also provide us with the exploration of the rich QCD dynamic mechanism in its decay process.In theory,many factorization approach have been developed,which are used to calculate the hadronic matrix elements in B meson decays.Among them,the perturbative QCD factorization approach based on KT factorization can deal with Feynman diagrams such as factorization diagram,non-factorization diagram,and annihilation diagram,and the only input parameters are wave functions of the considered mesons,which are non-perturbative and universal.In this paper,we calculate the B meson's three-body and two-body non-leptonic decays within the theoretical framework of the perturbative QCD factorization approach.The three-body decay process of B meson is generally dominated by intermediate vector and scalar resonance states,that is,by the process of quasi-two-body decay containing a resonance state and pseudoscalar meson.In general,due to the power suppressed effect,the heavy b quark decay kernel includes two virtual gluons in the lowest leading order in the three-body B meson decay.This make that the decay amplitude in this process is hard to directly calculate,and it is also nonsignificant.Therefore,we consider the two light mesons of the final decay state as light meson pairs,and introduce non-perturbative input of two-meson pairs distribution amplitudes,which the time-like scalar form factor in the meson pairs distribution amplitude includes the contribution of resonance and non-resonance.So the three-body decay of the B meson is simplified to the quasi-two-body decay.In our first work,we make a detailed theoretical study of Bs0??(3170)?+?-decay.The vector charmonium meson ?(3770)is mainly regarded as a mixed state of 2S-1D waves.Therefore,in our calculations,we will make the theoretical calculations for the contributions of S and D waves respectively,and two intermediate resonance states f0(980)and f0(1500)are considered.For the mixing angle of the 2S-1D wave,we choose the angle ?=-(12±2)°and ?=(27±2)?in the method of fitting the leptonic decay width and the non-relative potential model.In the conclusion,we give the branching ratio of the 2S and 1D wave respectively,and the results show that f0(980)is the main source of contribution in our considered decay mode.For the total S wave contribution,the theoretical calculation result of Bs0??(2S)?+?-is in good agreement with the experiment;and for the decay Bs0??(3170)?+?-,when we introduce the mixing angle ?=-12°,its branching ratio is increased approximately two times comparing with the result of Bs0??(1D)?+?-.Once this decay mode will be observed by the running experiment in the future time,it can help us understand the structure of ?(3770)and reveal the internal mechanism of three-body decays.In our second work,we make a predictive calculation for the rare decay mode Bs0?a0(980)a0(980)with taking both charged and neutral final state into account and regarding the scalar meson a0(980)as conventional qq structure for the first time in the pQCD approach.As we all known,the rare decay of the B mesons can testify the standard model and explore the rich field of QCD,which only have the contribution of the annihilation diagrams.Within the framework of QCD factorization approach,the contribution of the annihilation diagrams with endpoint divergence is generally uncalculated.However,the basic ideas of the perturbation QCD factorization approach is different for the QCD factorization approach,and it is considered that the above-mentioned endpoint divergence can be corrected by introducing the Sudakov factor.We calculate the branching ratio and CP violation parameters of Bs0?a0(980)a0(980)in our work,and find that the branching ratio and CP violation are relatively large.This will easy to be observed by the experiments and also the results will help us understand the internal structure of the light scalar mesons.