Light-front quark model analysis of rare $B\to K{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ decays

Using the light-front quark model, we calculate the transition form factors, decay rates, and longitudinal lepton polarization asymmetries for the exclusive rare $B\to K{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}(\mathrm{\ell }=e,\mu ,\tau$) decays within the standard model. Evaluating the timelike form factors, we use the analytic continuation method in $q^{+}=0$ frame to obtain the form factors $F_{+}$ and $F_T$, which are free from zero-mode. The form factor $F_{-}$ which is not free from zero-mode in $q^+ = 0$frameandcontaminatedbythehigher(ornonvalence)Fockstatesin$q^+ \neq 0$ frame is obtained from an effective treatment for handling the nonvalence contribution based on the Bethe-Salpeter formalism. The covariance(i.e. frame-independence) of our model calculation is discussed. We obtain the branching ratios for $\mathrm{B}\mathrm{R}(B\to K{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-})$ as $4.96\times {10}^{-7}\mathrm{\mid }{V}_{ts}\mathrm{/}{V}_{cb}{\mathrm{\mid }}^2$ for $\mathrm{\ell }=e,\mu$ and $1.27\times 10^{-7}|V_{ts}/V_{cb}|^2$for$\ell=\tau$.