Spin-5/2 fields in hadron physics

Abstract

We show that the Lagrangian of the free spin-5/2 field in the spinor-tensor representation with the auxiliary spinor field depends on the three arbitrary parameters. The first two parameters are associated with the spin-3/2 and -1/2 sector of the theory while the latter one is related to the auxiliary degrees of freedom. We derive a corresponding propagator of the system which represents (2 x 2) matrix in the $({\psi }_{\mu \nu },\xi )$ space. The diagonal terms stand for the propagation of the spin-5/2 and auxiliary fields whereas the non-diagonal ones correspond to the ${\psi }_{\mu \nu }-\xi$ mixing. The resulting spin-5/2 propagator contains non-pole contributions coming from the spin-3/2 and -1/2 sector of the spinor-tensor representation. A general form of the interaction vertex involving spin-5/2 field is discussed on the example of the $\pi N{N}_{5/2}^{\ast }$ coupling. It is demonstrated that lower spin degrees of freedom can be removed from the theory by using higher order derivative coupling.