Search for New Physics through the Observables of Semileptonic $B_{c}^+\to D^{\ast+}\ell^{+}\ell^{-}$ Decay
Motivated by the current flavor anomalies and the comparatively less explored nature of the $b\to d$ sector, we present a model-independent study of the rare semileptonic $B_c^{+}\to D^{\ast+}\ell^{+}\ell^{-}$ ($\ell=\mu,\tau$) decay, to investigate its sensitivity to New Physics effects. The analysis incorporates penguin-box contributions, long-distance resonance effects, and the sizable weak-annihilation amplitudes. Using the $B_c\to D^\ast$ transition form factors calculated in the covariant confined quark model and the weak-annihilation form factors obtained within the Bethe--Salpeter approach, we analyze the differential branching fraction, forward-backward asymmetry, longitudinal helicity fraction, and a comprehensive set of normalized angular observables in several one- and two-dimensional New Physics scenarios and compare our results with the Standard Model predictions. Notably, the branching fraction, forward-backward asymmetry, and the normalized angular coefficients such as, $\langle I_{2c}\rangle$, $\langle I_{3}\rangle$, $\langle I_{5}\rangle$, and $\langle I_{6s} \rangle$, show clear sensitivity to New Physics effects. Our results indicate that the decay $B_c^{+}\to D^{\ast+}\ell^{+}\ell^{-}$ serves as a complementary probe of the flavor structure of New Physics and can therefore be investigated in future measurements at LHCb and other high-luminosity flavor experiments.