Investigating the potential of $R_{K^{(\ast )}}^{\tau \mu }$ to probe lepton flavor universality violation

Abstract

In this work we study the potential of the lepton flavor ratios $R_K^{\tau \mu }\equiv \Gamma (B\to K{\tau }^{+}{\tau }^{-})/\Gamma (B\to K{\mu }^{+}{\mu }^{-})$ and $R_{K^{\ast }}^{\tau \mu }\equiv \Gamma (B\to K^{\ast }{\tau }^{+}{\tau }^{-})/\Gamma (B\to K^{\ast }{\mu }^{+}{\mu }^{-})$ to probe lepton flavor universality (LFU) violation in $\tau -\mu$ sector. We show that these ratios can deviate from their SM values even if the new physics couplings are universal in nature, i.e., having equal couplings to $e$, $\mu$ and $\tau$ leptons. Therefore in order to utilize these observables to probe LFU violation, we need to compare the allowed range of $R_{K^{(\ast )}}^{\tau \mu }$ for class of solutions with only universal couplings to leptons and solutions having both universal and non-universal components. For the current $b\to s\ell \ell$ ($\ell =e,\mu$) data, we find that these two class of solutions can be discriminated provided the measured value of $R_{K^{\ast }}^{\tau \mu }$ is greater than the SM prediction.

Comments: 8 pages, 2 figures; Published version