New Physics couplings from angular coefficient functions of $\bar B \to D^* (D \pi) \ell \bar \nu_\ell$

The Belle Collaboration has recently measured the complete set of angular coefficient functions for the exclusive decays $\bar B \to D^* (D \pi) \ell \bar \nu_\ell$, with $\ell=e,\,\mu$, in four bins of the parameter $w=\displaystyle\frac{m_B^2+m_{D^*}^2-q^2}{2m_B m_{D^*}}$, with $q$ the lepton pair momentum. Under the assumption that physics beyond the Standard Model does not contribute to such modes, the measurements are useful to determine the hadronic form factors describing the $B \to D^*$ matrix elements of the Standard Model weak current, and to improve the determination of $|V_{cb}|$. On the other hand, they can be used to assess the impact of possible new physics contributions. In a bottom-up approach, we extend the Standard Model effective Hamiltonian governing this mode with the inclusion of the full set of Lorentz invariant d=6 operators compatible with the gauge symmetry of the theory. The measured angular coefficient functions can tightly constrain the couplings in the generalized Hamiltonian. We present the first results of this analysis, discussing how improvements can be achieved when more complete data on the angular coefficient functions will be available.