Study of B s ⟶ ϕ

In this paper, we studied systematically the semileptonic decays $B_s⟶\varphi l^{+}{l}^{-}$ with $l^{-}=\left(e^{-},{\mu }^{-},{\tau }^{-}\right)$ by using the perturbative QCD (PQCD) and the “PQCD+Lattice” factorization approach, respectively. We first evaluated all relevant form factors $F_i\left(q^2\right)$ in the low- $q^2$ region using the PQCD approach, and we also took the available lattice QCD results at the high- $q^2$ region as additional input to improve the extrapolation of $F_i\left(q^2\right)$ from the low- $q^2$ region to the endpoint $q_{\max }^2$ . We then calculated the branching ratios and many other physical observables $A_{\text{FB}}^l$ , $F_L^{\varphi }$ , $S_{3,4,7}$ , and $A_{5,6,8,9}$ and the clean angular observables $P_1$