Searching for New Physics with $bto stau^+tau^-$ processes

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 $bto sell^+ell^-$ (i.e., $R_K$ and $R_{K^*}$) and the charged-current transitions $bto cell^-bar u_ell$ (i.e., $R_D$, $R_{D^*}$ and $R_{J/psi}$). LHCb has reported deviations from the Standard Model (SM) expectations in $bto smu^+mu^-$ 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 $bto stau^+tau^-$ transitions. In this article we predict the branching ratios of $Bto Ktau^+tau^-$, $Bto K^{*}tau^+tau^-$ and $B_sto phi tau^+tau^-$ taking into account NP effects in the Wilson coefficients $C_{9()}^{tautau}$ and $C_{10()}^{tautau}$. Assuming a common NP explanation of $R_{D^{}}$ , $R_{D^{(*)}}$ and $R_{J/psi}$, we show that a very large enhancement of $bto stau^+tau^-$ 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 $B_sto tau^+tau^-$, $B_sto phi tau^+tau^-$ and $Bto K^{(*)}tau^+tau^-$ under these assumptions are in the observable range for LHCb and Belle II.