Analyzing $b\to u$ transitions in semileptonic $\bar{B}_s \to K^{*+}(\to K \pi)\ell^-\bar\nu_\ell$ decays

TL;DR

This paper analyzes the semileptonic decay B_s K^{*+} , incorporating SM and beyond SM effects, to extract V_{ub} and study angular observables for testing the SM's left-handed transition prediction.

Contribution

It provides a comprehensive analysis of B_s K^{*+}  decays, including new methods for extracting V_{ub} and form factor ratios, and proposes angular observables for testing the SM.

Findings

Estimated V_{ub} as (4.07  0.20)  10^{-3}

Identified angular observables to test the SM's left-handedness

Provided constraints on b s short-distance coefficients

Abstract

We study the semileptonic decay $\bar{B}_s \to K^{*+} \ell^-\bar\nu_\ell$, which is induced by $b\to u \ell^- \bar\nu_\ell$ transitions at the quark level. We take into account the standard model (SM) operator from $W$-boson exchange as well as possible extensions from physics beyond the SM. The secondary decay $K^{*+}\to K\pi$ can be used to study a number of angular observables, which are worked out in terms of short-distance Wilson coefficients and hadronic form factors. Our analysis allows for an independent extraction of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ub}|$ and for the determination of certain ratios of $\bar{B}_s\to K^*$ form factors. Moreover, a future precision measurement of the forward-backward asymmetry in the $\bar{B}_s \to K^{*+} \ell^-\bar\nu_\ell$ decay can be used to unambiguously verify the left-handed nature of the transition operator as predicted by the SM. We provide numerical estimates for the relevant angular observables and the resulting decay distributions on the basis of available form-factor information from lattice and sum-rule estimates. In addition, we pay particular attention to suitable combinations of angular observables in the decays $\bar{B}_s \to K^{*+}(\to K\pi)\ell^-\bar\nu_\ell$ and $\bar{B} \to K^{*0}(\to K\pi)\ell^+\ell^-$, and find that they provide complementary constraints on the relevant $b\to s$ short-distance coefficients. As a by-product, we perform a SM fit on the basis of selected experimental decay rates and hadronic input functions, which results in $|V_{ub}| = (4.07 \pm 0.20) \cdot 10^{-3}$.