Exclusive rare $B_s\to (K,\eta,\eta')\ell^+\ell^-$ decays in the light-front quark model

TL;DR

This paper calculates decay form factors, rates, and lepton polarization asymmetries for rare $B_s$ decays into $K$, $ a$, and $ a'$ mesons using the light-front quark model, providing predictions within the Standard Model.

Contribution

It introduces detailed calculations of rare $B_s$ decay observables using the light-front quark model, including $ a- a'$ mixing effects, which are novel in this context.

Findings

Predicted branching ratios for various $B_s$ decay channels.

Lepton polarization asymmetries are close to -1 for muons.

Branching ratios for $B_s o a$ decays are at the order of 10^{-8} to 10^{-6}.

Abstract

Using the light-front quark model, we calculate the transition form factors, decay rates, and longitudinal lepton polarization asymmetries for the exclusive rare $B_s\to (K,\eta^{(\prime)})(\ell^+\ell^-,\nu_{\ell}\bar{\nu_{\ell}}$ ($\ell=e,\mu,\tau$) decays within the standard model, taking into account the $\eta-\eta'$ mixing angle. For the mixing angle $\theta=-20^{\circ}$ ($-10^{\circ}$) in the octet-singlet basis, we obtain ${\rm BR}(B_s\to \eta\sum\nu_{\ell}\bar{\nu}_{\ell})=1.1 (1.7)\times 10^{-6}$, ${\rm BR}(B_s\to \eta\mu^+\mu^-)=1.5 (2.4)\times 10^{-7}$, ${\rm BR}(B_s\to \eta\tau^+\tau^-)=3.8 (5.8)\times 10^{-8}$, ${\rm BR}(B_s\to \eta'\sum\nu_{\ell}\bar{\nu}_{\ell})=1.8 (1.3)\times 10^{-6}$, ${\rm BR}(B_s\to \eta'\mu^+\mu^-)=2.4 (1.8)\times 10^{-7}$, and ${\rm BR}(B_s\to \eta'\tau^+\tau^-)=3.4 (2.6)\times 10^{-8}$, respectively. The branching ratios for the $B_s\to K(\nu_{\ell}\bar{\nu_{\ell}},\ell^+\ell^-)$ decays are at least an order of magnitude smaller than those for the $B_s\to \eta^{(\prime)}(\nu_{\ell}\bar{\nu_{\ell}},\ell^+\ell^-)$ decays. The averaged values of the lepton polarization asymmetries for $B_s\to (K,\eta^{(\prime)})\ell^+\ell^-$ are obtained as $\la P^K_L\ra_\mu=\la P^\eta_L\ra_\mu=\la P^{\eta'}_L\ra_\mu=-0.98$, $\la P^K_L\ra_\tau=-0.24$, $\la P^\eta_L\ra_\tau=-0.20$ and $\la P^{\eta'}_L\ra_\tau=-0.14$, respectively.