Exploring new physics in the angular distribution of $\bar{B}\to D^{\ast }(\to D\pi ){\tau }^{-}(\to V^{-}{\nu }_{\tau }){\bar{\nu }}_{\tau }$

Abstract

The decays $\bar{B}\to D^{\ast }{\tau }^{-}{\bar{\nu }}_{\tau }$ provide sensitive probes of new physics in the $b\to c\tau \nu$ transition. We discuss the effects of new physics in the decay chain $\bar{B}\to D^{\ast }(\to D\pi ){\tau }^{-}(\to V^{-}{\nu }_{\tau }){\bar{\nu }}_{\tau }$ where $V$ is a vector meson. We first present a comprehensive analysis of the five-dimensional angular distribution for the full decay chain $\bar{B}\to D^{\ast }(\to D\pi ){\tau }^{-}(\to {\rho }^{-}{\nu }_{\tau }){\bar{\nu }}_{\tau }$, 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 ${\theta }^{\ast }$, $E_{\rho }$, ${\theta }_{\rho }$, ${\chi }_{\rho }$, 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 $D^{\ast }$ polarization fractions and lepton-side forward-backward and azimuthal asymmetries, which isolate distinct combinations of helicity amplitudes. We also show that by decomposing the vector-meson energy spectrum into its longitudinal ($L$) and transverse ($T$) helicity sectors, two additional analyzing powers (${\alpha }_L$ and ${\alpha }_T$) related to the measurement of $\tau$ polarization $P_{\tau }^{D^{\ast }}(q^2)$ are obtained. Without information on the polarization of meson $V$, the spin analyzing power of $\rho$ is much larger than that of $a_1$ with ${\alpha }_{\rho }=0.45$ and ${\alpha }_{a_1}=0.02$. We further perform a numerical analysis using current experimental data on $R_{D^{\ast }}$ and the $D^{\ast }$ longitudinal polarization fraction $⟨F_L^{D^{\ast }}⟩$ to constrain the complex new-physics couplings $g_L$, $g_R$, $g_P$, and $g_T$, revealing the correlations among them.

revtex 4-1, 39 pages