Rare semileptonic $B\to K(\pi )l_i^{-}{l}_j^{+}$ decay in vector leptoquark model

We investigate the consequence of vector leptoquarks on the rare semileptonic lepton flavour violating decays of $B$ meson which are more promising and effective channels to probe the new physics signal. We constrain the resulting new leptoquark parameter space by using the branching ratios of $B_{s, d} \to l^+ l^-$,$K_L \to l^+ l^-$and$\tau^- \to l^- \gamma$ processes. We estimate the branching ratios of rare lepton flavour violating $B\to K(\pi )l_i^{-}{l}_j^{+}$ processes using the constrained leptoquark couplings. We also compute the forward-backward asymmetries and the lepton non-universality parameters of the LFV decays in the vector leptoquark model. Furthermore, we study the effect of vector leptoquark on $(g-2{)}_{\mu }$ anomaly.