Study of Bs⟶ϕℓ+ℓ− Decays in the PQCD Factorization Approach with Lattice QCD Input

Abstract

In this paper, we studied systematically the semileptonic decays Bs⟶ϕl+l− with l−=e−,μ−,τ− by using the perturbative QCD (PQCD) and the “PQCD+Lattice” factorization approach, respectively. We first evaluated all relevant form factors Fiq2 in the low-q2 region using the PQCD approach, and we also took the available lattice QCD results at the high-q2 region as additional input to improve the extrapolation of Fiq2 from the low-q2 region to the endpoint qmax2. We then calculated the branching ratios and many other physical observables AFBl, FLϕ, S3,4,7, and A5,6,8,9 and the clean angular observables P1,2,3 and P4,5,6,8′. From our studies, we find the following points: (a) the PQCD and “PQCD+Lattice” predictions of BBs⟶ϕμ+μ− are about 7×10−7, which agree well with the LHCb measured values and the QCD sum rule prediction within still large errors; (b) we defined and calculated the ratios of the branching ratios Rϕeμ and Rϕμτ; (c) the PQCD and “PQCD+Lattice” predictions of the longitudinal polarization FL, the CP-averaged angular coefficients S3,4,7, and the CP asymmetry angular coefficients A5,6,8,9 agree with the LHCb measurements in all considered bins within the still large experimental errors; and (d) for those currently still unknown observables Rϕeμ,Rϕμτ,AFBl,P1,2,3, and P4,5,6,8′, we suggest LHCb and Belle-II Collaboration to measure them in their experiments.