On Leibniz superalgebras which even part is sl_2

This article deals with a Leibniz superalgebras $L=L_0\oplus L_1,$ whose even part is a simple Lie algebra ${\mathfrak{s}\mathfrak{l}}_2$. We describe all such Leibniz superalgebras when odd part is an irreducible Leibniz bi-module on ${\mathfrak{s}\mathfrak{l}}_2$. We show that there exist such Leibniz superalgebras with nontrivial odd part only in case of $dim{L}_1=2.$