Towards harmonic superfield formulation of N=4, USp(4) SYM theory with the central charge

We develop a superfield formulation of $\mathcal{N}=4$ supersymmetric Yang-Mills theory with gauged central charge in $USp(4)$ harmonic superspace. Component formulation of this theory was given by Sohnius, Stelle and West \cite{SSW80} but its superfield formulation has not been constructed so far. We construct the superfield action, corresponding to this model, and show that it reproduces the component action from \cite{SSW80}.