Exploring new physics in the angular distribution of $\bar B\rightarrow D^*(\rightarrow D\pi)\tau^-(\rightarrow V^-\nu_\tau)\bar\nu_\tau$

Abstract

The decays $\bar{B}\rightarrow D^*\tau^{-}\bar{\nu}_\tau$ provide sensitive probes of new physics in the $b\rightarrow c\tau\nu$ transition. We discuss the effects of new physics in the decay chain $\bar{B}\rightarrow D^*(\rightarrow D\pi)\tau^{-}(\rightarrow V^-\nu_\tau)\bar{\nu}_\tau$ where $V$ is a vector meson. We first present a comprehensive analysis of the five-dimensional angular distribution for the full decay chain $\bar{B}\rightarrow D^*(\rightarrow D\pi)\tau^{-}(\rightarrow \rho^-\nu_\tau)\bar{\nu}_\tau$, exploiting the hadronic $\tau$ decay to $\rho^-\nu_\tau$ to circumvent the experimental challenge of direct $\tau$ reconstruction. The differential decay rate is expressed in terms of measurable kinematic variables $\theta^*$, $E_\rho$, $\theta_\rho$, $\chi_\rho$, and $q^2$ -- with complete coefficient functions provided for scalar, pseudoscalar, vector, axialvector, and tensor new-physics interactions. From this distribution we construct a set of integrated observables, including the $D^*$ polarization fractions and lepton-side forward-backward and azimuthal asymmetries, which isolate distinct combinations of helicity amplitudes. We further perform a numerical analysis using current experimental data on $R_{D^*}$ and the $D^*$ longitudinal polarization fraction $\langle F_L^{D^*}\rangle$ to constrain the complex new-physics couplings $g_L$, $g_R$, $g_P$, and $g_T$, revealing the correlations among them. Our formalism is also applicable to $\tau \to a_1 \nu_\tau$, where the $3\pi$ final states mainly come from the $a_1$ meson. The framework established here provides a powerful tool for disentangling new-physics scenarios with future high-statistics data.