The Mono-Tau Menace: From $B$ Decays to High-$p_T$ Tails

We investigate the crossing-symmetry relation between $b\to c\tau^-\bar\nu$ decay and $b\bar c\to \tau^-\bar\nu$ scattering to derive direct correlations of New Physics in semi-tauonic $B$-meson decays and the mono-tau signature at the LHC ($pp\to\tau_h X$ + MET). Using an exhaustive set of effective operators and heavy mediators we find that the current ATLAS and CMS data constrain scenarios addressing anomalies in $B$-decays. Pure tensor solutions, completed by leptoquark, and right-handed solutions, completed by $W^\prime_R$ or leptoquark, are challenged by our analysis. Furthermore, the sensitivity that will be achieved in the high-luminosity phase of the LHC will probe $all$ the possible scenarios that explain the anomalies. Finally, we note that the LHC is also competitive in the $b\to u$ transitions and bounds in some cases are currently better than those from $B$ decays.