Angular analysis of $B_s\, \to\, f_{2}'\,(1525)\,(\to K^+\,K^-)\,\mu^+ \,\mu^-$ decays as a probe to lepton flavor universality violation

Abstract

The flavor anomalies reported in $R_K$, $R_{K^*}$, $P_{5}^{\prime}$ and $\mathcal{B}(B_s\, \to\, \phi\, \mu^+\, \mu^-)$ 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.