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Motivated by the recent observation of lepton universality violation in theflavour changing charged current transitions $b \to c l \bar{\nu}_l$, we intendto scrutinize the lepton non-universality effects in rare semileptonic $B$meson decays involving the quark level transitions $b \to u l \bar{\nu}_l$. Inthis regard, we envisage the model-independent approach and consider thegeneralized effective Lagrangian in the presence of new physics and constrainthe new parameters by using the experimental branching fractions of $B_u^+ \tol^+ \nu_l$ and $B^- \to \pi^0 \mu^- \bar \nu_\mu$ processes, where $l=e, \mu,\tau$. We then estimate the branching ratios and forward-backward asymmetriesof $B_{(s)} \to P (V)l \bar{\nu}_l$ processes, where $P(=K, \pi,\eta^{(\prime)})$ denotes the pseudoscalar meson and $V(=K^*, \rho)$ is thevector meson. We also find out various lepton non-universality parameters inthese processes in the presence of new physics.

Model independent investigation of rare semileptonic b \to u l \bar{\nu}_l decay processes