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We investigate cubic interactions between a chiral superfield and higher spinsuperfield corresponding to irreducible representations of the $4D,\,\mathcal{N}=1$ super-Poincar\'{e} algebra. We do this by demanding aninvariance under the most general transformation, linear in the chiralsuperfield. Following Noether's method we construct an infinite tower of higherspin supercurrent multiplets which are quadratic in the chiral superfield andinclude higher derivatives. The results are that a single, massless, chiralsuperfield can couple only to the half-integer spin supermultiplets$(s+1,s+1/2)$ and for every value of spin there is an appropriate improvementterm that reduces the supercurrent multiplet to a minimal multiplet whichmatches that of superconformal higher spins. On the other hand a single,massive, chiral superfield can couple only to higher spin supermultiplets oftype $(2l+2\hspace{0.3ex},\hspace{0.1ex}2l+3/2)$ and there is no minimalmultiplet. Furthermore, for the massless case we discuss the component levelhigher spin currents and provide explicit expressions for the integer andhalf-integer spin conserved currents together with a R-symmetry current.

Higher Spin Superfield interactions with the Chiral Supermultiplet: Conserved Supercurrents and Cubic Vertices