Conserved higher spin supercurrents for arbitrary spin massless supermultiplets and higher spin superfield cubic interactions

We give an explicit superspace construction of higher spin conserved supercurrents built out of $4D,\mathcal{N}=1$ massless supermultiplets of arbitrary spin. These supercurrents are gauge invariant and generate a large class of cubic interactions between a massless supermultiplet with superspin $Y_1=s_1+1\mathrm{/}2$ and two massless supermultiplets of arbitrary superspin $Y_2$. These interactions are possible only for $s_1\ge 2Y_2$. At the equality, the supercurrent acquires its simplest form and defines the supersymmetric, higher spin extension of the linearized Bel-Robinson tensor.