The recent measurements on $R_D$, $R_{D^*}$ and $R_{J/psi}$ by three pioneering experiments, BaBar, Belle and LHCb, indicate that the notion of lepton flavour universality is violated in the weak charged-current processes, mediated through $b to c ell bar u_ell$ transitions. These intriguing results, which delineate a tension with their standard model predictions at the level of $(2-3)sigma$ have triggered many new physics propositions in recent times, and are generally attributed to the possible implication of new physics in $ b to c tau bar u$ transition. This, in turn, opens up another avenue, i.e., $ b to u tau bar u$ processes, to look for new physics. Since these processes are doubly Cabibbo suppressed, the impact of new physics could be significant enough, leading to sizeable effects in some of the observables. In this work, we investigate in detail the role of new physics in $B to (pi,rho,omega)tau bar u$ and $B_s to (K,K^*) tau bar u$ processes considering a model independent approach. In particular, we focus on the standard observables like branching fraction, lepton flavour non-universality (LNU) parameter, forward-backward asymmetry and polarization asymmetries. We find significant deviations in some of these observables, which can be explored by the currently running experiments LHCb and Belle-II. We also briefly comment on the impact of scalar leptoquark $R_2(3,2,7/6)$ and vector leptoquark $U_1(3,1,2/3)$ on these decay modes.
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