Searching for New Physics with $b\to s{\tau }^{+}{\tau }^{-}$ processes

Abstract

In recent years, intriguing hints for the violation of Lepton Flavour Universality (LFU) have been accumulated in semileptonic $B$ decays, both in the neutral-current transitions $b\to s{\ell }^{+}{\ell }^{-}$ (i.e., $R_K$ and $R_{K^{\ast }}$) and the charged-current transitions $b\to c{\ell }^{-}{\bar{\nu }}_{\ell }$ (i.e., $R_D$, $R_{D^{\ast }}$ and $R_{J/\psi }$). LHCb has reported deviations from the Standard Model (SM) expectations in $b\to s{\mu }^{+}{\mu }^{-}$ processes as well as in the ratios $R_K$ and $R_{K^{\ast }}$, which together point at New Physics (NP) affecting muons with a high significance. Furthermore, hints for LFU violation in $R_{D^{(\ast )}}$ and $R_{J/\psi }$ point at large deviations from the SM in processes involving tau leptons. Together, these hints for NP motivate the possibility of huge LFU-violating effects in $b\to s{\tau }^{+}{\tau }^{-}$ transitions. In this article we predict the branching ratios of $B\to K{\tau }^{+}{\tau }^{-}$, $B\to K^{\ast }{\tau }^{+}{\tau }^{-}$ and $B_s\to \varphi {\tau }^{+}{\tau }^{-}$ taking into account NP effects in the Wilson coefficients $C_{9{(}^{\prime })}^{\tau \tau }$ and $C_{10{(}^{\prime })}^{\tau \tau }$. Assuming a common NP explanation of $R_{D^{}}$ , $R_{D^{(\ast )}}$ and $R_{J/\psi }$, we show that a very large enhancement of $b\to s{\tau }^{+}{\tau }^{-}$ processes, of around three orders of magnitude compared to the SM, can be expected under fairly general assumptions. We find that the branching ratios of $B_s\to {\tau }^{+}{\tau }^{-}$, $B_s\to \varphi {\tau }^{+}{\tau }^{-}$ and $B\to K^{(\ast )}{\tau }^{+}{\tau }^{-}$ under these assumptions are in the observable range for LHCb and Belle II.

7 pages, 1 figure

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