Angular analysis of $B_s\to f_2^{\prime }(1525)(\to K^{+}{K}^{-}){\mu }^{+}{\mu }^{-}$ decays as a probe to lepton flavor universality violation

Abstract

The flavor anomalies reported in $R_K$, $R_{K^{\ast }}$, $P_5^{\prime }$ and $\mathcal{B}(B_s\to \varphi {\mu }^{+}{\mu }^{-})$ indicate lepton flavor universality violation in $b\to s{l}^{+}{l}^{-}$ quark level transition decays. The deviation from the SM prediction reported in the underlying flavor observables currently stand at the level of $2.5\sigma$, $2.4\sigma$, $3.3\sigma$ and $3.7\sigma$, respectively. In this context, we perform an angular analysis of the four-body differential decay of $B_s\to f_2^{\prime }(1525)(\to K^{+}{K}^{-}){\mu }^{+}{\mu }^{-}$ in a model independent effective field theory framework. The decay mode $B_s\to f_2^{\prime }(1525)l^{+}{l}^{-}$ undergoes similar $b\to s$ neutral current quark level transition and, in principle, can provide complementary information regarding lepton flavor universality violation in $b\to s{l}^{+}{l}^{-}$ quark level transition decays. We give predictions of various physical observables such as the branching ratio, the longitudinal polarization fraction, the forward-backward asymmetry, the angular observables $P_1$, $P_2$, $P_4^{\prime }$, $P_5^{\prime }$ and also the lepton flavor sensitive observables such as the ratio of branching ratio $R_{f_2^{\prime }}$, $Q_{F_L}$, $Q_{A_{FB}}$, $Q_1$, $Q_2$, $Q_4^{\prime }$, $Q_5^{\prime }$ for $B_s\to f_2^{\prime }(1525)(\to K^{+}{K}^{-}){\mu }^{+}{\mu }^{-}$ decays in the standard model and in the presence of several 1D and 2D new physics scenarios.

Comments: 25 pages, 7 figures, additional details updated