${\cal N}{=}\,4$ supersymmetric multiparticle systems based on indecomposable multiplets

We construct new multiparticle models of $\mathcal{N}=4$ supersymmetric mechanics with spin degrees of freedom by employing nonlinear indecomposable supermultiplets ${\bf (1,4,3){\supset\hspace{-1.1em}+}(4,4,0)}$.

These systems are proper deformations of those associated with the standard irreducible $d=1, \mathcal{N}=4$ multiplets.

In this way we find a new $\mathcal{N}=4$ supersymmetric generalization of U$(2)$-spin rational Calogero system invariant under $d=1$ superconformal group OSp$(4|2)$.

One more deformed model reproduces $\mathcal{N}=4$ supersymmetric U$(2)$-spin hyperbolic Calogero system, up to a shift of the Hamiltonian by some U$(1)$ generators.