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

Abstract

We study the $f^{+}$ form factor for the semileptonic ${\bar{B}}_s\to K^{+}{\ell }^{-}\bar{\hat{I}}{½}_{\ell }$ decay in a constituent quark model. The valence quark estimate is supplemented with the contribution from the ${\bar{B}}^{\ast }$ pole that dominates the high $q^2$ region. We use a multiply-subtracted Omnès dispersion relation to extend the quark model predictions from its region of applicability near $q_{\max }^2=(M_{B_s}-M_K{)}^2\sim 23.75$ GeV${}^2$ to all $q^2$ values accessible in the physical decay. To better constrain the dependence of $f^{+}$ on $q^2$, we fit the subtraction constants to a combined input from previous light cone sum rule [Phys. Rev. D 78 (2008) 054015] and the present quark model results. From this analysis, we obtain $\hat{I}“({\bar{B}}_s\to K^{+}{\ell }^{-}\bar{\hat{I}}{½}_{\ell })=(5.45_{-0.80}^{+0.83})|V_{ub}{|}^2\times 10^{-9}\mathrm{MeV}$, which is about 20\% higher than the prediction based only on QCD light cone sum rule estimates. Differences are much larger for the $f^{+}$ form factor in the region above $q^2=15$ GeV${}^2$.

9 latex pages, 5 figures, 1 table