The fate of $V_1$ vector leptoquarks: the impact of future flavour data

Abstract: Motivated by the recent experimental progress on the $B$-meson decay anomalies (in particular the angular observables in $B\to K^\ast\mu\mu$), we rely on a simplified-model approach to study the prospects of vector leptoquarks in what concerns numerous flavour observables, identifying several promising decay modes which would allow to (indirectly) probe such an extension. Our findings suggest that the confirmation of the $B$-meson decay anomalies, in parallel with positive signals (at Belle II or LHCb) for $\tau\to \phi \mu$, $B_{(s)}$-meson decays to $\tau^+ \tau^-$ and $\tau^+ \mu^-$ ($\tau^+ e^-$) final states, as well as an observation of certain charged lepton flavour violation decays (at COMET or Mu2e), would contribute to strengthen the case for this scenario. We also illustrate how the evolution of the experimental determination of $R_{D^{(*)}}$ could be instrumental in falsifying an explanation of the anomalous $B$-meson decay data via a vector $V_1$ leptoquark.