A lesson from $R_{\tau\tau}^{K^{(\ast)}}$ and $R_{\nu\nu}^{K^{(\ast)}}$ at Belle II

Abstract

Within the assumption of Left-Handed (LH) New Physics (NP), we review the relations between $\mathcal{B}(B\to K^{(\ast)} \tau^+\tau^-)$ and $\mathcal{B}(B\to K^{(\ast)} \nu\bar \nu)$ for several Beyond the Standard Model (BSM) scenarios, commonly considered to explain the Lepton flavor Universality (LFU) violation observed in charged and neutral-current semileptonic $B$ decays. We employ the latest $R_{D^{(\ast)}}$ world averages that include the recent LHCb measurement and assess the possibility of simultaneously explaining the $B$-anomalies without spoiling current bounds on di-neutrino and di-tau modes. This is particularly relevant in light of the upcoming results by Belle II on neutrinos and the continuing improvement in accuracy and sensitivity achieved in tau modes.