Lepton flavour violating B meson decays via scalar leptoquark

We study the effect of scalar leptoquarks in the lepton flavour violating $B$ meson decays induced by the flavour changing transitions $b\to q{l}_i^{+}{l}_j^{-}$ with $q=s,d$. In the standard model these transitions are extremely rare as they are either two-loop suppressed or proceed via box diagrams with tiny neutrino masses in the loop. However, in the leptoquark model they can occur at tree level and are expected to have significantly large branching ratios. The leptoquark parameter space is constrained using the experimental limits on the branching ratios of $B_q\to l^{+}{l}^{-}$ processes. Using such constrained parameter space, we predict the branching ratios of LFV semileptonic $B$ meson decays, such as $B^{+}\to K^{+}({\pi }^{+})l_i^{+}{l}_j^{-}$, $B^+ \to (K^{* +}, \rho^+) l_i^+ l_j^-$and$B_s \to \phi l_i^+ l_j^-$, which are found to be within the experimental reach of LHCb and the upcoming Belle II experiments. We also investigate the rare leptonic $K_{L,S}\to {\mu }^{+}{\mu }^{-}(e^{+}{e}^{-})$ and $K_{L} \to \mu^\mp e^\pm$ decays in the leptoquark model.