Motivated by the recent observation of lepton universality violation in the flavour changing charged current transitions , we intend to scrutinize the lepton non-universality effects in rare semileptonic meson decays involving the quark level transitions . In this regard, we envisage the model-independent approach and consider the generalized effective Lagrangian in the presence of new physics and constrain the new parameters by using the experimental branching fractions of $B_u^+ \to l^+ \nu_lB^- \to \pi^0 \mu^- \bar \nu_\mul=e, \mu, \tau$. We then estimate the branching ratios and forward-backward asymmetries of processes, where $P(=K, \pi, \eta^{(\prime)})V(=K^*, \rho)$ is the vector meson. We also find out various lepton non-universality parameters in these processes in the presence of new physics.

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