N=8 invariant interaction of dynamical and semidynamical N=4 multiplets

We present a new model of N=8 mechanics with semidynamic supermultiplets. The model is constructed as an interaction of N=4 supermultiplets which carry an implicit N=4 supersymmetry. The initial field content consists of three dynamical (1,4,3) multiplets: one bosonic and two fermionic. To ensure implicit N=4 supersymmetry, we introduce the superfields describing three semidynamical (4,4,0) multiplets: one fermionic and two bosonic. To avoid the second-order Lagrangian for fermions from the fermionic (1,4,3) multiplets, we convert their velocities into new auxiliary fields. After conversion, these multiplets turn into semidynamical mirror (4,4,0) multiplets without noncanonical terms in the N=8 Lagrangian at the component level. The final N=8 multiplet content is (1,8,7)(8,8,0). As a first step to the ultimate N=4 superfield formulation of the model, we recall a natural description of the standard and mirror (4,4,0) multiplets in the framework of N=4,d=1 biharmonic superspace.