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We analyze the baryonic semilepton decay $\Lambda_{b} \rightarrow$ $\Lambda\mu^{+} \mu^{-}$ in the scalar leptoquark models with $X(3,2,7/6)$ and$X(3,2,1/6)$ states, respectively. We also discuss the effects of this two NPmodels on some physical observables. For some measured observables, like thedifferential decay width, the longitudinal polarization of the dilepton system,the lepton-side forward-backward asymmetry and the baryon-side forward-backwardasymmetry, we find, the prediction values of SM are consistent with the currentdata in the most $q^{2}$ ranges, where the prediction values of this two NPmodels can also keep consistent with the current data with $1\sigma$. However,in some $q^{2}$ ranges, the prediction values of SM are difficult to meet thecurrent data, but the contributions of this two NP models can meet them or keepcloser to them. For the double lepton polarization asymmetries, $P_{LT}$,$P_{TL}$, $P_{NN}$ and $P_{TT}$ are sensitive to the scalar leptoquark model$X(3,2,7/6)$ but not to $X(3,2,1/6)$. However, $P_{LN}$, $P_{NL}$, $P_{TN}$ and$P_{NT}$ are not sensitive to this two NP models.

Analysis of $\Lambda_{b} \rightarrow$ $\Lambda \mu^{+} \mu^{-}$ decay in scalar leptoquark model