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Inspired by the recent hints of lepton flavor universality violation in    $$b\rightarrow s\ell \ell $$    b  →  s  ℓ  ℓand    $$b\rightarrow c\ell \nu $$    b  →  c  ℓ  νtransitions, we study lepton flavor violating exclusive    $$\Lambda _b\rightarrow \Lambda \ell _1^+\ell _2^-$$Λ  b   →  Λ   ℓ  1  +    ℓ  2  -(   $$\ell _1\ne \ell _2$$ℓ  1   ≠   ℓ  2) decay, which is forbidden in the Standard Model. Starting from a general effective Hamiltonian for a    $$b\rightarrow s\ell _1^+\ell _2^-$$    b  →  s   ℓ  1  +    ℓ  2  -transition that includes vector and axial-vector operators, and scalar and pseudo-scalar operators, we derive a two-fold decay distribution of    $$\Lambda _b\rightarrow \Lambda \ell _1^+\ell _2^-$$Λ  b   →  Λ   ℓ  1  +    ℓ  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.

Lepton flavor violating $$\Lambda _b\rightarrow \Lambda \ell _1\ell _2$$ decay