Physical spectrum from confining propagators in a Yang-Mills-inspired toy model

Full text: Recently there has been significant advances in the direction of understanding the infra-red regime of Yang- Mills theories through the analysis of the consequences brought about by the so-called Gribov Copies. The Gribov-Zwanziger (GZ) action was constructed with the aim of eliminating these reminiscent gauge copies from the path integral, generating essentially a new nonperturbative mass scale, that then protects the infra-red domain. A refinement of this theory (RGZ) was proposed by the inclusion of dimension 2 condensates and the propagators generated in this case present complex poles, each associated with the 'propagation' of an i-particle, signaling gluon confinement. These propagators describe with great success precise lattice data in the infrared regime. One of the most important questions about confining theories is how they generate a physical spectrum out of confined elementary particles. Inspired by these developments in the physics of Gribov Copies, we study in a scalar toy model of i-particles how interactions may produce physical propagating modes from the combination of these unphysical (confined) objects. Departing from confining propagators of the GZ type at tree level, we include a quartic interaction and demonstrate the appearance of poles in the spectral representation of two-point correlators of composite operators, associated with pairs of i-particles. We discuss results for dimension 2, 3 and 4 and also compare these findings with analogous models with real particles (with positive mass). (author)