New physics in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mi>K</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:msup><mml:mi>τ</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>τ</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>: A model independent analysis

Abstract

In this work, we consider the implications of current $b\ensuremath{\rightarrow}s{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ ($\ensuremath{\ell}=e$, $\ensuremath{\mu}$) measurements on several $B\ensuremath{\rightarrow}{K}^{*}{\ensuremath{\tau}}^{+}{\ensuremath{\tau}}^{\ensuremath{-}}$ 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 $b\ensuremath{\rightarrow}s{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ 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 $B\ensuremath{\rightarrow}{K}^{*}{\ensuremath{\tau}}^{+}{\ensuremath{\tau}}^{\ensuremath{-}}$ branching fraction, the ${K}^{*}$ longitudinal fraction ${f}_{L}$, the tau forward-backward asymmetry ${A}_{\mathrm{FB}}$ and the optimized observables in the ${P}_{i}^{(\ensuremath{'})}$ basis. Further, we construct the $\ensuremath{\tau}\ensuremath{-}\ensuremath{\mu}$ lepton-flavor differences (${Q}^{\ensuremath{\tau}\ensuremath{\mu}}$) between these tau observables and their muonic counterparts in $B\ensuremath{\rightarrow}{K}^{*}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ decay. Moreover, we also consider lepton-flavor ratios (${R}^{\ensuremath{\tau}\ensuremath{\mu}}$) 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 ${Q}_{{P}_{3}}^{\ensuremath{\tau}\ensuremath{\mu}}$ and ${Q}_{{P}_{8}^{\ensuremath{'}}}^{\ensuremath{\tau}\ensuremath{\mu}}$ observables can be enhanced up to an order of magnitude, a twofold enhancement in ${Q}_{{A}_{\mathrm{FB}}}^{\ensuremath{\tau}\ensuremath{\mu}}$ is possible along with $\ensuremath{\sim}50%$ enhancement in ${R}_{{K}^{*}}^{\ensuremath{\tau}\ensuremath{\mu}}$ and $\ensuremath{\sim}25%$ in ${R}_{{A}_{\mathrm{FB}}}^{\ensuremath{\tau}\ensuremath{\mu}}$. Moreover, the branching ratio of $B\ensuremath{\rightarrow}{K}^{*}{\ensuremath{\tau}}^{+}{\ensuremath{\tau}}^{\ensuremath{-}}$ can be suppressed up to 25%. A precise measurement of these observables can also discriminate between a number of new physics solutions.

Topics & Concepts