Vector leptoquark mass limits and branching ratios of $ K_L^0, B^0, B_s \to l^+_i l^-_j $ decays with account of fermion mixing in leptoquark currents

The contributions of the vector leptoquarks of Pati-Salam type to the branching ratios of $K_L^0, B^0, B_s \to l \, l^{\prime}$ decays are calculated with account of the fermion mixing in the leptoguark currents of the general type. Using the general parametrizations of the mixing matrices the lower vector leptoquark mass limit $ m_V > 86 \,\, TeV $ is found from the current experimental data on these decays. The branching ratios of the decays $B^0, B_s \to l \, l^{\prime}$ predicted at $m_V = 86 \,\, TeV$ are calculated. These branching ratios for the decays $ B^0, B_s \to \mu^+ \mu^-, e \mu $ are close to the experimental data whereas those for the decays $B^0 \to e^+ e^-, e \tau, \mu \tau$, and $B_s \to e^+ e^-$ are by order of $2\div4$ less than their current experimental limits. For the decays $B_s \to e \tau, \mu \tau$ these branching ratios are of order $10^{-10}$ and $10^{-9}$ respectively. The predicted branching ratios will be usefull in the current and future experimental searches for these decays.