Abstract
In this work, we provide estimates of the branching ratios, direct CP asymmetries and triple product asymmetries in B_{(s)} rightarrow (pi pi )(Kpi ) decays in the perturbative QCD approach, where the pi pi and Kpi invariant mass spectra are dominated by the vector resonances rho (770) and K^*(892), respectively. Some scalar backgrounds, such as f_0(500,980) rightarrow pi pi and K^*_0(1430) rightarrow Kpi are also accounted for. The rho (700) is parametrized by the Gounaris-Sakurai function. The relativistic Breit-Wigner formula for the f_0(500) and Flatté model for the f_0(980) are adopted to parameterize the time-like scalar form factors F_S(omega ^2). We also use the D.V. Bugg model to parameterize the f_0(500) and compare the relevant theoretical predictions from different models. While in the region of Kpi invariant mass, the K^*_0(1430) is described with the LASS lineshape and the K^*(892) is modeled by the Breit-Wigner function. We find that the decay rates for the considered decay modes agree with currently available data within errors. As a by-product, we extract the branching ratios of two-body decays B_{(s)} rightarrow rho (770)K^*(892) from the corresponding four-body decay modes and calculate the relevant polarization fractions. Our prediction of longitudinal polarization fraction for B^0rightarrow rho (770)^0 K^*(892)^0 decay deviates a lot from the recent LHCb measurement, which should be resolved. It is shown that the direct CP asymmetries are large due to the sizable interference between the tree and penguin contributions, but they are small for the tree-dominant or penguin-dominant processes. The PQCD predictions for the “true” triple product asymmetries are small which are expected in the standard model, and consistent with the current data reported by the LHCb Collaboration. Our results can be tested by the future precise data from the LHCb and Belle II experiments.
Highlights
Multi-body B meson decays offer one of the best tools for studying direct C P violation and provide an interesting testing ground for strong interaction dynamical models
The situation of the “ C ”-type decay Bs0 → ρ0 K ∗(892)0 is more complicated: (a) as claimed in Ref. [88] that the widths of the resonant states and the interactions between the final state meson pairs will show their effects on the branching ratios, the new four-body prediction deviates from the previous calculations in the perturbative QCD (PQCD) approach, but agrees well with the corresponding results in the QCD factorization (QCDF) approach, soft-collinear-effective theory (SCET) and factorization-assisted topological amplitude approach (FAT) within errors; (b) the transverse polarization contribution in the PQCD approach is comparable to the longitudinal one due to the chirally enhanced annihilation and the hard scattering diagrams, which is quite different from those predictions in the QCDF approach, SCET and FAT
We have presented six helicity amplitudes of four-body decays B(s) → (π π )(K π ), where π π invariantmass spectrum is dominated by the vector ρ resonance and scalar f0(500), f0(980) resonances, and the vector K ∗
Summary
Multi-body B meson decays offer one of the best tools for studying direct C P violation and provide an interesting testing ground for strong interaction dynamical models. B(s) → V1V2, S1 S2, S1V2, V1 S2 decays (here V1,2 and S1,2 denote the vector and scalar mesons, respectively) are treated as two-body final states and have been studied in the two-body framework using QCD factorization (QCDF) [1,2,3,4,5,6], the perturbative QCD (PQCD) approaches [7,8,9,10,11,12,13,14,15,16,17,18,19], the soft-collinear-effective theory (SCET) [20,21,22,23,24,25] and the factorization-assisted topological amplitude approach (FAT) [26]. The Appendix collects the explicit PQCD factorization formulas for all the decay amplitudes
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
