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Inspired by the recent hints of lepton flavor universality violation in $b\tos\ell\ell$ and $b\to c\ell\nu$ transitions, we study lepton flavor violatingexclusive $\Lambda_b\to\Lambda\ell_1^+\ell_2^-$ ($\ell_1\neq \ell_2$) decay,which is forbidden in the Standard Model. Starting from a general effectiveHamiltonian for a $b\to s\ell_1^+\ell_2^-$ transition that includes vector andaxial-vector operators, and scalar and pseudo-scalar operators, we derive atwo-fold decay distribution of $\Lambda_b\to\Lambda\ell_1^+\ell_2^-$. Thedistribution helps us to construct the differential branching ratio and thelepton side forward-backward asymmetry, which are studied in a vectorleptoquark model. The parameter space of the vector leptoquark model isconstrained by low energy observables.

Lepton flavor violating $\Lambda_b\to\Lambda\ell_1\ell_2$ decay