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

TL;DR

This paper investigates the renormalization of spin-1 resonances in effective field theory, analyzing different formalisms, loop corrections, and the emergence of additional unphysical poles.

Contribution

It provides a detailed renormalization procedure for spin-1 resonances in chiral effective theory, comparing formalisms and examining loop-induced unphysical states.

Findings

Loop corrections generate additional poles, including ghosts and tachyons.

Different formalisms for spin-1 particles are analyzed and compared.

A formal prescription for organizing counterterms and graphs is proposed.

Abstract

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-one 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 non-renormalizable 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.