Exploring new physics in the angular distribution of $\bar{B}\to D^{\ast }(\to D\ddot{I}€)\ddot{I}{„}^{-}(\to V^{-}\hat{I}{½}_{\ddot{I}}„)\bar{\hat{I}}{½}_{\ddot{I}}„$

Abstract

The decays $\bar{B}\to D^{\ast }\ddot{I}{„}^{-}\bar{\hat{I}}{½}_{\ddot{I}}„$ provide sensitive probes of new physics in the $b\to c\ddot{I}„\hat{I}½$ transition. We discuss the effects of new physics in the decay chain $\bar{B}\to D^{\ast }(\to D\ddot{I}€)\ddot{I}{„}^{-}(\to V^{-}\hat{I}{½}_{\ddot{I}}„)\bar{\hat{I}}{½}_{\ddot{I}}„$ where $V$ is a vector meson. We first present a comprehensive analysis of the five-dimensional angular distribution for the full decay chain $\bar{B}\to D^{\ast }(\to D\ddot{I}€)\ddot{I}{„}^{-}(\to \ddot{I}{}^{-}\hat{I}{½}_{\ddot{I}}„)\bar{\hat{I}}{½}_{\ddot{I}}„$, exploiting the hadronic $\ddot{I}„$ decay to $\ddot{I}{}^{-}\hat{I}{½}_{\ddot{I}}„$ to circumvent the experimental challenge of direct $\ddot{I}„$ reconstruction. The differential decay rate is expressed in terms of measurable kinematic variables $\hat{I}{¸}^{\ast }$, $E_{\ddot{I}}$, $\hat{I}{¸}_{\ddot{I}}$, $\ddot{I}{‡}_{\ddot{I}}$, 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 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. Our formalism is also applicable to $\ddot{I}„\to a_1\hat{I}{½}_{\ddot{I}}„$, where the $3\ddot{I}€$ 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.

revtex 31 pages, 4 figures, 6 tables