Erratum to: Visible energy and angular distributions of the charged particle from the τ-decay in $$ b\to c\tau \left(\mu {\overline{\nu}}_{\mu }{\nu}_{\tau },\pi {\nu}_{\tau },\rho {\nu}_{\tau}\right){\overline{\nu}}_{\tau } $$ reactions

We study the $d^2 \Gamma_d /(d\omega d\cos\theta_d) $, $d\Gamma_d /d\cos\theta_d$ and $ d\Gamma_d /dE_d distributions, which are defined in terms of visible energy polar angle charged particle from $\tau-$decay $b\to c \tau\, (\mu \bar \nu_\mu \nu_\tau,\pi \nu_\tau,\rho\nu_\tau) \bar\nu_\tau$ reactions. The first two contain information on transverse tau-spin, tau-angular tau-angular-spin asymmetries $H_b\to H_c\tau\bar\nu_\tau$ parent decay and, a dynamical point view, they richer than commonly used one, dE_d) since latter only depends tau longitudinal polarization. pay attention to deviations with respect predictions standard model (SM) for these new observables, considering physics (NP) operators constructed using both right- left-handed neutrino fields, within an effective field-theory approach. present results $\Lambda_b\to\Lambda_c\tau\, \nu_\tau,\pi\nu_\tau,\rho\nu_\tau)\bar\nu_\tau$ $\bar B \to D^{(*)}\tau\, \nu_\tau,\pi\nu_\tau,\rho\nu_\tau) sequential decays discuss their use disentangle between different NP models. In this respect, we show that /d\cos\theta_d$, should be measured sufficiently good statistics, becomes quite useful, especially $\tau\to \pi \nu_\tau$ mode. carried out work could special relevance due recent LHCb measurement lepton flavor universality ratio ${\cal R}_{\Lambda_c}$ agreement SM. experiment identified $\tau$ its hadron into $\pi^-\pi^+\pi^-\nu_\tau$, result R}_{\Lambda_c}$, is conflict phenomenology $b$-meson sector, needs confirmation other reconstruction channels.