Unconstrained off-shell superfield formulation of $4D, \mathcal{N}=2$ supersymmetric higher spins

We present, for the first time, the complete off-shell $4D, {\cal N}=2$ superfield actions for any free massless integer spin ${\bf s} \geq 2$ fields, using the ${\cal N}=2$ harmonic superspace approach. The relevant gauge supermultiplet is accommodated by two real analytic bosonic superfields $h^{++}_{\alpha(s-1)\dot\alpha(s-1)}$, $h^{++}_{\alpha(s-2)\dot\alpha(s-2)}$ and two conjugated complex analytic spinor superfields $h^{+3}_{\alpha(s-1)\dot\alpha(s-2)}$, $h^{+3}_{\alpha(s-2)\dot\alpha(s-1)}\,$, where $\alpha(s) := (\alpha_1\ldots \alpha_s), \dot\alpha(s) := (\dot\alpha_1\ldots \dot\alpha_s)$. Like in the harmonic superspace formulations of ${\cal N}=2$ Maxwell and supergravity theories, an infinite number of original off-shell degrees of freedom is reduced to the finite set (in WZ-type gauge) due to an infinite number of the component gauge parameters in the analytic superfield parameters. On shell, the standard spin content $({\bf s, s-1/2, s-1/2, s-1})$ is restored. For ${\bf s}=2$ the action describes the linearized version of "minimal" ${\cal N}=2$ Einstein supergravity.