Higher order self-dual models for spin-3 particles in D=2+1

In D=2+1 dimensions, elementary particles of a given helicity can be described by local Lagrangians (parity singlets). By means of a soldering procedure, two opposite helicities can be joined together and give rise to massive spin-s particles carrying both helicities ±s (parity doublets), and such Lagrangians can also be used in D=3+1 to describe massive spin-s particles. From this point of view the parity singlets (self-dual models) in D=2+1 are the building blocks of real massive elementary particles in D=3+1. In the three cases s=1, 3/2, 2 there are 2s self-dual models of order 1,2,2s in derivatives. In the spin-3 case the fifth order model is missing in the literature. Here we deduce a fifth order spin-3 self-dual model and fill up this gap. It is shown to be ghost free by means of a master action which relates it with the top model of sixth order. We believe that our approach can be generalized to arbitrary integer spin-s in order to obtain the models of order 2s and 2s-1. We also comment on the difficulties in relating the fifth order model with their lower order duals.