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

Abstract

Using the light-front quark model, we calculate the transition form factors, decay rates, and longitudinal lepton polarization asymmetries for the exclusive rare $B\to K{\ell }^{+}{\ell }^{-}(\ell =e,\mu ,\tau$) 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 $q^{+}=0$ frame and contaminated by the higher(or nonvalence) Fock states in $q^{+}\ne 0$ 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 $\mathrm{BR}(B\to K{\ell }^{+}{\ell }^{-})$ as $4.96\times 10^{-7}|V_{ts}/V_{cb}{|}^2$ for $\ell =e,\mu$ and $1.27\times 10^{-7}|V_{ts}/V_{cb}{|}^2$ for $\ell =\tau$.

Comments: 15 pages, 9 figures; added the figure for F_-(q^2) in Fig. 6; added the lengthy discussion and figure(Fig. 9) of VMD effect on LFQM near zero-recoil region; added some more references; version to appear in Phys. Rev. D