Note on renormalization of the spin-1 resonance propagator at one loop order

TL;DR

This paper investigates the renormalization of the spin-1 resonance propagator at one loop in Resonance Chiral Theory, highlighting issues with unphysical poles and discussing symmetry roles in resonance dynamics.

Contribution

It provides explicit one-loop self-energy calculations and classifies propagator degrees of freedom, revealing the unavoidable emergence of unphysical poles.

Findings

Unavoidably generates negative norm ghosts or tachyons

Classifies propagating degrees of freedom

Discusses symmetry roles in resonance generation

Abstract

We study various aspects of the renormalization of the Resonance Chiral Theory at the one-loop level using a spin-one resonance propagator as a concrete example. We calculate explicitly the one-loop self-energy within the antisymmetric tensor field formalism, briefly discuss the general structure of the corresponding propagator obtained by means of the Dyson re-summation and give a classification of the propagating degrees of freedom. We find that additional pathological poles (negative norm ghosts or tachyons) are unavoidably generated and various scenarios according to their position are possible. We also briefly comment on the eventual dynamical generation of the opposite parity resonances which are frozen at the tree level and discuss the role of appropriate symmetry which could prevent such a scenario.