We analyze in detail the angular distributions in $bar{B}to D^*ell bar u$ decays, with a focus on lepton-flavour non-universality. We investigate the minimal number of angular observables that fully describes current and upcoming datasets, and explore their sensitivity to physics beyond the Standard Model (BSM) in the most general weak effective theory. We apply our findings to the current datasets, extract the non-redundant set of angular observables from the data, and compare to precise SM predictions that include lepton-flavour universality violating mass effects. Our analysis shows that the current presentation of the experimental data is not ideal and prohibits the extraction of the full set of relevant BSM parameters, since the number of independent angular observables that can be inferred from data is limited to only four. We uncover a $sim4sigma$ tension between data and predictions that is hidden in the redundant presentation of the Belle 2018 data on $bar{B}to D^*ell bar u$ decays. This tension specifically involves observables that probe $e-mu$ lepton-flavour universality. However, we find inconsistencies in these data, which renders results based on it suspicious. Nevertheless, we discuss which generic BSM scenarios could explain the tension, in the case that the inconsistencies do not affect the data materially. Our findings highlight that $e-mu$ non-universality in the SM, introduced by the finite muon mass, is already significant in a subset of angular observables with respect to the experimental precision.
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