Probing New Physics with $\bar B \to \rho(770) \, \ell^- \bar \nu_\ell$ and $\bar B \to a_1(1260) \, \ell^- \bar \nu_\ell$

The $B$ meson semileptonic modes to $\rho(770)$ and $a_1 (1260)$ are useful to pin down possible non Standard Model effects. The 4d differential $\bar B \to \rho(\pi \pi) \ell^- \bar \nu_\ell$ and $ \bar B \to a_1 (\rho \pi) \ell^- \bar \nu_\ell$ decay distributions are computed in SM and in extensions involving new Lepton Flavour Universality violating semileptonic $b \to u$ operators. The Large Energy limit for the light meson is also considered for both modes. The new effective couplings are constrained using the available data, and several observables in $\bar B \to \rho(\pi\pi) \ell^- \bar \nu_\ell$ in which NP effects can be better identified are selected, using the angular coefficient functions. The complementary role of $\bar B \to \rho(\pi \pi) \ell^- \bar \nu_\ell$ and $\bar B \to a_1 (\rho \pi) \ell^- \bar \nu_\ell$ is discussed.
Comment: LaTeX, 39 pages, 21 figures. Discussion of the $a_1$ mode extended. References added