$\bar B_s\to K$ semileptonic decay from an Omn\`es improved nonrelativistic quark model

TL;DR

This paper improves predictions for the $ar B_s o K$ semileptonic decay form factor by combining a nonrelativistic quark model with an Omnès dispersion relation, fitting to sum rule and quark model data.

Contribution

It introduces a novel method combining a nonrelativistic quark model with an Omnès dispersion relation to accurately predict the decay form factor across the entire kinematic range.

Findings

Predicted decay width is approximately 10-20% higher than lattice and sum rule estimates.

The combined approach provides a more reliable form factor across all $q^2$ regions.

Results suggest potential revisions to existing decay rate predictions.

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 $\bar B^*$-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 $\Gamma(\bar B_s\to K^+\ell^-\bar\nu_\ell)=(5.47^{+0.54}_{-0.46})|V_{ub}|^2\times 10^{-9}\,{\rm MeV}$, which is about 10% and 20% higher than predictions based on Lattice QCD and QCD light cone sum rules respectively.