Lepton flavor violating ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }{\mathrm{\ell }}_1{\mathrm{\ell }}_2$ decay

Inspired by the recent hints of lepton flavor universality violation in $b\to s\ell\ell$and$b\to c\ell\nu$ transitions, we study lepton flavor violating exclusive ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }{\mathrm{\ell }}_1^{+}{\mathrm{\ell }}_2^{-}$ (${\mathrm{\ell }}_1\mathrm{\ne }{\mathrm{\ell }}_2$) decay, which is forbidden in the Standard Model. Starting from a general effective Hamiltonian for a $b\to s{\mathrm{\ell }}_1^{+}{\mathrm{\ell }}_2^{-}$ transition that includes vector and axial-vector operators, and scalar and pseudo-scalar operators, we derive a two-fold decay distribution of ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }{\mathrm{\ell }}_1^{+}{\mathrm{\ell }}_2^{-}$. The distribution helps us to construct the differential branching ratio and the lepton side forward-backward asymmetry, which are studied in a vector leptoquark model. The parameter space of the vector leptoquark model is constrained by low energy observables.