Searching for New Physics with $b\to sτ^+τ^-$ 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 $R_{K^*}$) and the charged-current transitions $b\to c\ell^-\barν_\ell$ (i.e., $R_D$, $R_{D^*}$ and $R_{J/ψ}$). LHCb has reported deviations from the Standard Model (SM) expectations in $b\to sμ^+μ^-$ 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 $R_{J/ψ}$ 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 $b\to sτ^+τ^-$ transitions. In this article we predict the branching ratios of $B\to Kτ^+τ^-$, $B\to K^{*}τ^+τ^-$ and $B_s\to ϕτ^+τ^-$ taking into account NP effects in the Wilson coefficients $C_{9(')}^{ττ}$ and $C_{10(')}^{ττ}$. Assuming a common NP explanation of $R_{D^{}}$ , $R_{D^{(*)}}$ and $R_{J/ψ}$, we show that a very large enhancement of $b\to sτ^+τ^-$ 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 $B_s\to τ^+τ^-$, $B_s\to ϕτ^+τ^-$ and $B\to K^{(*)}τ^+τ^-$ under these assumptions are in the observable range for LHCb and Belle II.