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Three years ago, we proposed free off-shell models for N=2 superconformal higher-spin multiplets in arbitrary conformally flat backgrounds, constructed conserved conformal higher-spin supercurrents for a massless hypermultiplet, and sketched the Noether procedure to generate its cubic couplings to the superconformal higher-spin multiplets. This paper is devoted to completing the Noether procedure. Specifically, we: (i) describe the unique off-shell primary extensions of the conformal higher-spin supercurrents; (ii) embed the off-shell superconformal prepotentials given in arXiv: 2104. 10416 into primary unconstrained isotwistor multiplets; and (iii) present the unique gauge transformations of the hypermultiplet and the isotwistor prepotentials. An extension of the Noether procedure beyond the cubic level is also sketched, following the earlier N=1 superconformal approach of arXiv: 2208. 07783. Our construction is based on making use of the polar hypermultiplet within the projective-superspace setting.
Kuzenko et al. (Wed,) studied this question.
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