Renormalization and additional degrees of freedom within the chiral effective theory for spin-1 resonances

We study in detail various aspects of the renormalization of the spin-1 resonance propagator in the effective field theory framework. First, we briefly review the formalisms for the description of spin-1 resonances in the path integral formulation with the stress on the issue of propagating degrees of freedom. Then we calculate the one-loop 1-- meson self-energy within the resonance chiral theory in the chiral limit using different methods for the description of spin-1 particles, namely, the Proca field, antisymmetric tensor field, and the first-order formalisms. We discuss in detail technical aspects of the renormalization procedure which are inherent to the power-counting nonrenormalizable theory and give a formal prescription for the organization of both the counterterms and one-particle irreducible graphs. We also construct the corresponding propagators and investigate their properties. We show that the additional poles corresponding to the additional one-particle states are generated by loop corrections, some of which are negative norm ghosts or tachyons. We count the number of such additional poles and briefly discuss their physical meaning.