${\bar{B}}_s\to K$ semileptonic decay from an Omnès improved nonrelativistic quark model

Abstract

We study the $f^{+}$ form factor for the ${\bar{B}}_s\to K^{+}{\ell }^{-}{\bar{\nu }}_{\ell }$ semileptonic decay in a nonrelativistic quark model. The valence quark contribution is supplemented with a ${\bar{B}}^{\ast }$-pole term that dominates the high $q^2$ region. To extend the quark model predictions from its region of applicability near $q_{\max }^2=(M_{B_s}-M_K{)}^2$, we use a multiply-subtracted Omnès dispersion relation. We fit the subtraction constants to a combined input from previous light cone sum rule results in the low $q^2$ region and the quark model results (valence plus ${\bar{B}}^{\ast }$-pole) in the high $q^2$ region. From this analysis, we obtain $\Gamma ({\bar{B}}_s\to K^{+}{\ell }^{-}{\bar{\nu }}_{\ell })=(5.47_{-0.46}^{+0.54})|V_{ub}{|}^2\times 10^{-9}\mathrm{MeV}$, which is about 10% and 20% higher than predictions based on Lattice QCD and QCD light cone sum rules respectively.

Comments: 4 latex pages, 3 figures, 1 table. Talk presented at the "XI International Conference on Hyperons, Charm and Beauty Hadrons (BEACH 2014)", Birmingham (U.K.), July 2014