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Symmetries in $B \to D^* \ell \nu$ angular observables

  • Algueró, Marcel
  • Descotes-Genon, Sébastien
  • Matias, Joaquim
  • Novoa Brunet, Martín
Publication Date
Mar 24, 2020
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We apply the formalism of amplitude symmetries to the angular distribution of the decays $B \to D^* \ell \nu$ for $\ell=e,\mu,\tau$. We show that the angular observables used to describe the distribution of this class of decays are not independent in absence of New Physics contributing to tensor operators. We derive sets of relations among the angular coefficients of the decay distribution for the massless and massive lepton cases which can be used to probe in a very general way the consistency among the angular observables and the underlying New Physics at work. We use these relations to access the longitudinal polarisation fraction of the $D^*$ using different angular coefficients from the ones used by Belle experiment. This in the near future can provide an alternative strategy to measure $F_L^{D^*}$ in $B \to D^* \tau \nu$ and to understand the relatively high value measured by the Belle experiment. Using the same symmetries, we identify two observables which should exhibit a tension if the experimental value of $F_L^{D^*}$ remains high. We discuss how these relations can be exploited for binned measurements. Finally we propose an alternative path to measure the lepton-flavour universality ratio $R_{D^*}$ by connecting it with $F_L^{D^*}$ and various angular coefficients.

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