New physics in $B \to K^* \tau^+ \tau^-$: A model independent analysis

In this work we consider the implications of current $b \to s \ell^+ \ell^-$ ($\ell=e,\,\mu$) measurements on several $B \to K^* \tau^+ \tau^-$ observables under the assumption that the possible new physics can have both universal as well as nonuniversal couplings to leptons. For new physics solutions which provide a good fit to all $b \to s \ell^+ \ell^-$ data, we intend to identify observables with large deviations from the Standard Model (SM) predictions as well as to discriminate between various new physics solutions. For this we consider the $B \to K^* \tau^+ \tau^-$ branching fraction, the $K^*$ longitudinal fraction $f_L$, the tau forward-backward asymmetry $A_{FB}$ and the optimized observables in the $P_i^{(')}$ basis. Further, we construct the $\tau - \mu$ lepton-flavor differences ($Q^{\tau\mu}$) between these tau observables and their muonic counterparts in $B \to K^* \mu^+ \mu^-$ decay. Moreover, we also consider lepton-flavor ratios ($R^{\tau\mu}$) of all of these observables. We find that the current data allows for deviations ranging from 25% up to an order of magnitude from the SM value in a number of observables. For e.g., the magnitudes of $Q^{\tau \mu}_{P_3}$ and $Q^{\tau \mu}_{P'_8}$ observables can be enhanced up to an order of magnitude, a twofold enhancement in $Q^{\tau\mu}_{A_{FB}}$ is possible along with $\sim$50% enhancement in $R^{\tau\mu}_{K^*}$ and $\sim$25% in $R^{\tau\mu}_{A_{FB}}$. Moreover, the branching ratio of $B \to K^* \tau^+ \tau^-$ can be suppressed up to 25%. A precise measurement of these observables can also discriminate between a number of new physics solutions.