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

TL;DR

This paper investigates potential large enhancements in $b\to s\tau^+\tau^-$ decays due to new physics suggested by recent lepton flavor universality violation hints, predicting observable effects at current experiments.

Contribution

It predicts significantly increased branching ratios for $b\to s\tau^+\tau^-$ processes based on new physics explanations of existing anomalies, highlighting their observability.

Findings

Branching ratios could be enhanced by around three orders of magnitude.

Predicted decay rates are within reach of LHCb and Belle II.

Large LFU violation effects could be observed in $b\to s\tau^+\tau^-$ transitions.

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 $R_{K^*}$) and the charged-current transitions $b\to c\ell^-\bar\nu_\ell$ (i.e., $R_D$, $R_{D^*}$ 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 $R_{K^*}$, which together point at New Physics (NP) affecting muons with a high significance. Furthermore, hints for LFU violation in $R_{D^{(*)}}$ 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 $B\to K\tau^+\tau^-$, $B\to K^{*}\tau^+\tau^-$ and $B_s\to \phi \tau^+\tau^-$ taking into account NP effects in the Wilson coefficients $C_{9(')}^{\tau\tau}$ and $C_{10(')}^{\tau\tau}$. Assuming a common NP explanation of $R_{D^{}}$ , $R_{D^{(*)}}$ 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 $B_s\to \tau^+\tau^-$, $B_s\to \phi \tau^+\tau^-$ and $B\to K^{(*)}\tau^+\tau^-$ under these assumptions are in the observable range for LHCb and Belle II.