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

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.

22 pages, 15 figures, revised version, ref. 54 corrected

References in corpus (11)

• A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
• Gluon and ghost propagators in the Landau gauge: Deriving lattice results from Schwinger-Dyson equations
• Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared
• Constraints on the IR behavior of the gluon propagator in Yang-Mills theories
• Infrared propagators of Yang-Mills theory from perturbation theory
• Constraints on the IR behavior of the ghost propagator in Yang-Mills theories
• Deconfinement transition in SU(2) Yang-Mills theory: A two-loop study
• Bayesian inference of non-positive spectral functions in quantum field theory
• Gauged supersymmetries in Yang-Mills theory
• Running coupling in the conformal window of large-Nf QCD
• Dispersion relations for unphysical particles

Cited by in corpus (15)

• Reconstructing QCD Spectral Functions with Gaussian Processes
• Ghost spectral function from the spectral Dyson-Schwinger equation
• Reconstructing confined particles with complex singularities
• The analytic structure of three-point functions from contour deformations
• On the complex structure of Yang-Mills theory
• The Nielsen identities in screened theories
• Analytic continuation and physical content of the gluon propagator
• Effects of a quark chemical potential on the analytic structure of the gluon propagator
• QCD phase diagram from the gluon propagator at finite temperature and density
• A window on infrared QCD with small expansion parameters
• Padé Approximants and the analytic structure of the gluon and ghost propagators
• Gauge invariant spectral analysis of quark hadronization dynamics
• $B\to X_c\ell \bar{\nu }$ Decay as a Probe of Complex Conjugate Poles
• One-loop analytic structure of the deep-infrared Landau-gauge gluon propagator at finite temperature
• Reconstructing propagators of confined particles in the presence of complex singularities