Investigating The Three-body Decays Of B_s~0→Sππ,Sπη,SK(?) In Perturbative QCD Factorization Approach

As one of the research focuses of particle physics,B physics plays an important role in testing the standard model and searching for new physical signals.In recent years,the research on the decay of B mesons has made good progress both theoretically and experimentally.With the further progress in the experiment of LHCb Collaboration and Belle Ⅱ Collaboration,more and more cases of the three-body hadron decay of B mesons have been found,and these cases need to be explained and predicted in theory.Therefore,the theoretical research on the three-body decay has attracted immense attention.Compared with the two-body decay of the B meson,the kinetic mechanism of the three-body decay is more complex,which makes it impossible to calculate the three-body decay process directly.Meanwhile,the common method is to convert the three-body decay into the two-body decay model by introducing scalar and vector intermediate resonances.On the other hand,there exists multiple degrees of freedom and energy scales in B physics,which makes the calculation relatively difficult.At the same time,a variety of factorization methods have been developed to calculate the decay of B mesons.Among them,the perturbative QCD factorization approach based on the kT factorization believes that the decay process of B meson is dominated by hard gluon exchange,while the perturbative part and the non-perturbative part in the decay process can be treated separately.The perturbative part can be calculated by perturbative theory,and the nonperturbative part can be absorbed into the universal hadron wave function.In this study,we use the perturbative QCD factorization approach to calculate the three-body Bs0→Sππ,Sπη,SKK decays,where S stands for the scalar meson.And this paper is divided into five parts,among which the first three parts are the basic theory,and the last two parts are the calculation process and main conclusions.In the first part,the history of particle physics,the significance and research status on the decay of B meson are reviewed briefly.The second part introduces the standard model theory and the basic theoretical framework of B meson decay.And the third part focuses on the perturbative QCD factorization approach used in the calculation of this work.In the fourth part,we investigate the branching ratios of Bs0→a0(980)[→KK,πη]a0(980),Bs0→f0(980)[→π+π-,K+K-]f0(980),and Bs0→f0(500)[→π+π-]f0(500)decays in the perturbative QCD factorization approach.Based on the isospin symmetry,we estimate the branching ratios of the Bs0→f0(980)[→π0π0]f0(980)and Bs0→ f0(500)[→π0π0]f0(500)decays.And the scalar mesons a0(980),f0(980),and fo(500)are considered as the lowest-lying qq state.In the meantime we think that the scalars f0(980)and f0(500)contain ss and(?)components in the quark model Through the calculation and analysis,the following conclusions are obtained:(1)For the Bs0→a0(980)[→KK,πη]a0(980)decays,the magnitude of the branching ratios are within the range 10-9～10-7.According to the branching ratio obtained,the relative partial decay width Γ(a0→K+K-)/Γ(a0→π0θ)is further studied in this paper with the narrow-width approximation.The obtained results are consistent with the existing data within the allowed error range.(2)By plotting the branching fractions of Bs0→f0(980)[→π+π-]f0(980)and Bs0→f0(500)[→π+π-]f0(500)decays dependent on the mixing Angle θ,we determine that the range of the mixing Angle 0 can be set as[15,82]and[105°,171°],which conforms to the requirements of the existing data.(3)When the mixing angle θ is taken as 300 to make numerical calculations,the branching ratios of Bs0→ f0(980)[→ππ,K+K-]f0(980)and Bs0→ f0(500)[→ ππ]f0(500)decays are at the order of 10-6～10-5.On this basis,we study the branching ratios of the sub-decay channel f0(980)→π+π-and f0(980)→ K+K-.The obtained results are still consistent with the experimental results in CLEO Collaboration within the allowable error range.(4)In this article,we graph the differential branching ratios of a partial decay channels on the invariant mass ω of the final state meson pair.The peak occurs around the pole mass of the intermediate resonance.The fifth party summarizes the whole paper and looks forward to the study of B meson decay.However,the branching ratios calculated in this paper lack relevant data experimentally.It is expected that these theoretical predictions can be verified in LHCb Collaboration and Belle-Ⅱ Collaboration in the future.