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.
Highlights
The anomalies that recently emerged in the flavor sector challenge both the experimental analyses and the theoretical interpretations
The four-dimensional differential B → ρðππÞl−νl and B → a1ðρπÞl−νl decay distributions are computed in the Standard Model and in extensions involving new lepton-flavor universality violating semileptonic b → u operators
The questions raised by the anomalies in b → c semileptonic modes call for new analyses on the CKM suppressed semileptonic b → u modes, for which precise measurements are expected
Summary
The anomalies that recently emerged in the flavor sector challenge both the experimental analyses and the theoretical interpretations. It is unclear if the deviations that emerged in angular observables in B → KÃμþμ− [22,23] and in the rate of B0s → φμþμ− [24] can have a connected origin In addition to these tensions, the long-standing difference in the determination of the Cabibbo-KobayashiMaskawa (CKM) matrix element jVcbj from exclusive modes, in particular B → DÃl−νl, and from inclusive B → Xcl−νl observables (width and moments) still persists in new BABAR [25] and Belle analyses [26], with jVcbjexcl < jVcbjincl. LOPARCO experimental signatures have been studied, in particular, the four-dimensional differential B → DÃðDπ; DγÞl−νl decay distributions for the three lepton species have been scrutinized [32], following analyses that have pointed out the relevance of such distributions [33–36] It is worth wondering if similar deviations can appear in semileptonic b → u transitions. In the Appendixes, we collect the definitions of the hadronic matrix elements and the expressions of the angular coefficient functions for the two modes
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