Visible energy and angular distributions of the charged particle from the $τ-$decay in $b\to c τ\, (μ\bar ν_μν_τ,πν_τ,ρν_τ) \barν_τ$ reactions

Abstract

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