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

TL;DR

This paper conducts an angular analysis of the decay $B_s o f_2'(1525) o K^+ K^- \, \, \mu^+ \mu^-$ to investigate potential lepton flavor universality violation, providing predictions for various observables in the Standard Model and new physics scenarios.

Contribution

It offers the first detailed angular analysis of this decay mode as a probe for lepton flavor universality violation, including predictions of multiple observables under different new physics scenarios.

Findings

Predicted branching ratio and angular observables in SM and new physics models.

Identified potential deviations indicating lepton flavor universality violation.

Provided complementary insights to existing $b \to s \ell^+ \ell^-$ decay studies.

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.