Data on some semi-leptonic decays of B have shown sizable tensions with the Standard Model (SM) predictions, through violations of lepton flavor universality. This effect is especially marked in the decays B → D* l ν_l , with l = e,μ,τ. Moreover the model independent analyses of the partial widths for l = τ give indications about the suitability of the various Dirac operators for describing the would-be interactions beyond the SM. This stimulates to study analogous decays, for example Λ_b → Λ_c τ ν_τ , which may confirm the anomaly and has the advantage of an initial polarization. Our analysis, together with a critical review of the current new physics models proposed, leads to indicating a preference among the Dirac operators. We suggest also to measure some observables which may help discriminating definitively among the different types of new physics. Among them, the polarization of final particles, like Λ_c or τ , deserves a particular place, since – apart from a nice theoretical result - it provides some T-odd observables, especially appropriate for discovering the effects we are looking for, and applicable also to the semi-leptonic decays of the top quark.