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

Abstract

In this work we consider the implications of current $b\to s{\ell }^{+}{\ell }^{-}$ ($\ell =e,\mu$) measurements on several $B\to K^{\ast }{\tau }^{+}{\tau }^{-}$ 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 $B\to K^{\ast }{\tau }^{+}{\tau }^{-}$ branching fraction, the $K^{\ast }$ longitudinal fraction $f_L$, the tau forward-backward asymmetry $A_{FB}$ and the optimized observables in the $P_i^{{(}^{\prime })}$ basis. Further, we construct the $\tau -\mu$ lepton-flavor differences ($Q^{\tau \mu }$) between these tau observables and their muonic counterparts in $B\to K^{\ast }{\mu }^{+}{\mu }^{-}$ 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 $Q_{P_3}^{\tau \mu }$ and $Q_{P_8^{\prime }}^{\tau \mu }$ observables can be enhanced up to an order of magnitude, a twofold enhancement in $Q_{A_{FB}}^{\tau \mu }$ is possible along with $\sim$50% enhancement in $R_{K^{\ast }}^{\tau \mu }$ and $\sim$25% in $R_{A_{FB}}^{\tau \mu }$. Moreover, the branching ratio of $B\to K^{\ast }{\tau }^{+}{\tau }^{-}$ can be suppressed up to 25%. A precise measurement of these observables can also discriminate between a number of new physics solutions.

arXiv comment14 pages, 6 figures; Published version

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