Off-shell cubic hypermultiplet couplings to N=2 higher spin gauge superfields

We construct manifestly 4D, N = 2 supersymmetric and gauge invariant off-shell cubic couplings of matter hypermultiplets to the higher integer spin gauge Al = 2 multiplets introduced in arXiv:2109 .07639. The hypermultiplet is described by an ana- lytic harmonic 4D, Al = 2 superfield q+ with the physical component spins s = (1/2, 0) and an infinite number of auxiliary fields. The cubic coupling constructed has the schematic structure q(+)(H) over cap (++ )((s))q(+), where (H) over cap (++ )((s)) is a differential analytic operator of the highest degree (s - 1) accommodating the massless gauge N = 2 multiplet with the highest spin s. For odd s the gauge group generators and couplings are proportional to U(1)p G generator of the internal SU(2)p G symmetry of the hypermultiplet and so do not exist if SU(2)p G is unbroken. If this U(1)p G is identified with the central charge of 4D,N = 2 supersymmetry, a mass for the hypermultiplet is generated and the odd s couplings vanish in the proper massless limit. For even s the higher-spin gauge transformations and cubic superfield couplings can be defined for both massive and massless (central-charge neutral) hypermultiplets without including U(1)p G generator. All these features directly extend to the case of n hypermultiplets with the maximal internal symmetry USp(2n) x SU(2).