$B \to D^{(*)} \tau \nu_{\tau}$ decay properties with RIQ model

In this work we compute the branching fraction of $B \to D^{(*)} \,\tau \, \nu_{\tau}$ and $B_s \to D_s^{(*)}\, \tau\, \nu_{\tau}$ within the Relativistic Independent Quark Model, emphasizing the harmonic potential model dependent analysis of these decay channels in the precision flavor physics era. Considering the experimental observation of longitudinal $\tau$-polarization and fraction of longitudinal polarization at LHCb and Belle, we have also investigated these observables within our model framework which are aligning well with the standard model expectations. We perform a comprehensive analysis of the form factors across the whole accessible kinematic range of $q^2$. Our results are consistent and compatible with other theoretical approaches as well as with the experimental measurements. Furthermore, we evaluated the clean ratios of $B_s$ to $B_0$ in the semimuonic mode that are in accordance with the LHCb measurements, and support the validity of the SU(3) flavor symmetry. Although the concept of new physics is facing a significant challenge at the current TeV scale, semileptonic $B$ decays, nevertheless, always serve as a valuable probe to study the decay dynamics.