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

Abstract

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

Comments: 20 pages, 6 figures, minor revision. version to appear in Journal of Physics G