Three-point functions of higher-spin supercurrents in 4D $\mathcal{N}=1$ SCFT: general formalism for arbitrary superspins

We analyse the general structure of the three-point functions involving conserved higher-spin ``vector-like" supercurrents $J_s(z):=J_{\alpha (s)\dot{\alpha }(s)}(z)$ in four-dimensional $\mathcal{N}=1$ superconformal field theory. Using the constraints of superconformal symmetry and superfield conservation equations, we utilise a computational approach to analyse the general structure of the three-point function $⟨J_{s_1}^{}(z_1)J_{s_2}^{\mathrm{\prime }}(z_2)J_{s_3}^{\mathrm{\prime }\mathrm{\prime }}(z_3)⟩$ and provide a general classification of the results. We demonstrate that the three-point function is fixed up to $2\min (s_i)+2$ independent conserved structures, which we propose to hold for arbitrary superspins. In addition, we show that the conserved structures can be classified as parity-even or parity-odd in superspace based on their transformation properties under superinversion.