Probing New Physics with $\bar{B}\to \rho (770){\ell }^{-}{\bar{\nu }}_{\ell }$ and $\bar{B}\to a_1(1260){\ell }^{-}{\bar{\nu }}_{\ell }$

Abstract

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.

LaTeX, 39 pages, 21 figures. Discussion of the $a_1$ mode extended. References added

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