$bar B_sto K$ semileptonic decay from an Omn`es improved nonrelativistic quark model

We study the $f^+$ form factor for the $bar B_sto K^+ell^-bar u_ell$ semileptonic decay in a nonrelativistic quark model. The valence quark contribution is supplemented with a $bar B^*$-pole term that dominates the high $q^2$ region. To extend the quark model predictions from its region of applicability near $q^2_{rm max}=(M_{B_s}-M_K)^2$, we use a multiply-subtracted Omn`es 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 $bar B^*$-pole) in the high $q^2$ region. From this analysis, we obtain $Gamma(bar B_sto K^+ell^-bar u_ell)=(5.47^{+0.54}_{-0.46})|V_{ub}|^2times 10^{-9},{rm MeV}$, which is about 10% and 20% higher than predictions based on Lattice QCD and QCD light cone sum rules respectively.