Complex poles and spectral functions of Landau gauge QCD and QCD-like theories

Yui Hayashi,Kei-Ichi Kondo

doi:10.1103/physrevd.101.074044

Abstract

In view of the expectation that the existence of complex poles is a signal of confinement, we investigate the analytic structure of the gluon, quark, and ghost propagators in the Landau gauge QCD and QCD-like theories by employing an effective model with a gluon mass term of the Yang-Mills theory, which we call the massive Yang-Mills model. In this model, we particularly investigate the number of complex poles in the parameter space of the model consisting of gauge coupling constant, gluon mass, and quark mass for the gauge group $SU(3)$ and various numbers of quark flavors $N_F$ within the asymptotic free region. Both the gluon and quark propagators at the best-fit parameters for $N_F=2$ QCD have one pair of complex conjugate poles, while the number of complex poles in the gluon propagator varies between zero and four depending on the number of quark flavors and quark mass. Moreover, as a general feature, we argue that the gluon spectral function of this model with nonzero quark mass is negative in the infrared limit. In sharp contrast to gluons, the quark and ghost propagators are insensitive to the number of quark flavors within the current approximations adopted in this paper. These results suggest that details of the confinement mechanism may depend on the number of quark flavors and quark mass.

Highlights

Color confinement, absence of color degrees of freedom from the physical spectrum, is one of the most fundamental and significant features of strong interactions
In view of the expectation that the existence of complex poles is a signal of confinement, we investigate the analytic structure of the gluon, quark, and ghost propagators in the Landau gauge quantum chromodynamics (QCD) and QCD-like theories by employing an effective model with a gluon mass term of the Yang-Mills theory, which we call the massive Yang-Mills model
We investigate the number of complex poles in the parameter space of the model consisting of gauge coupling constant, gluon mass, and quark mass for the gauge group SUð3Þ and various numbers of quark flavors NF within the asymptotic free region

Summary

Introduction

Absence of color degrees of freedom from the physical spectrum, is one of the most fundamental and significant features of strong interactions. It is a longstanding and challenging problem in particle and nuclear physics to explain color confinement in the framework of quantum field theory (QFT). Understanding analytic structures of the correlation functions will be of crucial importance to this end because a QFT describing physical particles can be reformulated in terms of correlation functions [1], and there are some proposals of confinement mechanisms whose criteria are expressed by them, e.g., [2]. The analytic structures of propagators encode kinematic information as the Källen-Lehmann spectral representation [3], which will be useful toward understanding confinement

Results

Discussion

Conclusion