Complex poles and spectral function of Yang-Mills theory

Abstract

We derive general relationships between the number of complex poles of a propagator and the sign of the spectral function originating from the branch cut in the Minkowski region under some assumptions on the asymptotic behaviors of the propagator. We apply this relation to the mass-deformed Yang-Mills model with one-loop quantum corrections, which is identified with a low-energy effective theory of the Yang-Mills theory, to show that the gluon propagator in this model has a pair of complex conjugate poles or "tachyonic" poles of multiplicity two, in accordance with the fact that the gluon field has a negative spectral function, while the ghost propagator has at most one "unphysical" pole. Finally, we discuss implications of these results for gluon confinement and other non-perturbative aspects of the Yang-Mills theory.

arXiv comment18 pages, 20 figures, final version published in PRD

References in corpus (41)

• 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
• On the infrared behavior of Landau gauge Yang-Mills theory
• Constraints on the IR behavior of the gluon propagator in Yang-Mills theories
• Quark Confinement from Color Confinement
• Massive gluons and quarks and the equation of state obtained from SU(3) lattice QCD
• Landau gauge Yang-Mills correlation functions
• Infrared propagators of Yang-Mills theory from perturbation theory
• On the IR behaviour of the Landau-gauge ghost propagator
• Constraints on the IR behavior of the ghost propagator in Yang-Mills theories
• The Infrared Behaviour of the Pure Yang-Mills Green Functions
• Phenomenological Equations of State for the Quark-Gluon Plasma
• Analytic structure of the Landau gauge gluon propagator
• An Infrared Safe perturbative approach to Yang-Mills correlators
• The lattice Landau gauge gluon propagator: lattice spacing and volume dependence
• Lifting the Gribov ambiguity in Yang-Mills theories
• Lattice Gluon and Ghost Propagators, and the Strong Coupling in Pure SU(3) Yang-Mills Theory: Finite Lattice Spacing and Volume Effects
• The anomalous dimension of the composite operator A^2 in the Landau gauge
• Reconstructing the gluon
• Deconfinement transition in SU(N) theories from perturbation theory
• Two-point correlation functions of QCD in the Landau gauge
• Analytical study of Yang-Mills theory in the infrared from first principles
• Gluon Quasiparticles and the Polyakov Loop
• Gribov horizon and i-particles: about a toy model and the construction of physical operators
• How nonperturbative is the infrared regime of Landau gauge Yang-Mills correlators?
• Analytic structure of QCD propagators in Minkowski space
• Yang-Mills correlators at finite temperature: A perturbative perspective
• Polyakov Loop and Gluon Quasiparticles in Yang-Mills Thermodynamics
• Phase diagram of the lattice SU(2) Higgs model
• Some non-renormalization theorems in Curci-Ferrari model
• Yang-Mills correlators across the deconfinement phase transition
• Gauged supersymmetries in Yang-Mills theory
• Gauge-invariant description of Higgs phenomenon and quark confinement
• Quasigluon lifetime and confinement from first principles
• Gauge-independent Brout-Englert-Higgs mechanism and Yang-Mills theory with a gauge-invariant gluon mass term
• Dispersion relations for unphysical particles
• Confinement--deconfinement phase transition and gauge-invariant gluonic mass in Yang-Mills theory
• Gauge-independent Higgs mechanism and the implications for quark confinement
• Perturbative study of the QCD phase diagram for heavy quarks at nonzero chemical potential
• Mass-deformed Yang-Mills theory in the covariant gauge and its gauge-invariant extension through the gauge-independent BEH mechanism

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• The analytic structure of the lattice Landau gauge gluon and ghost propagators
• Spectrum and structure of octet and decuplet baryons and their positive-parity excitations
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• Complex poles and spectral functions of Landau gauge QCD and QCD-like theories
• Reflection positivity and complex analysis of the Yang-Mills theory from a viewpoint of gluon confinement
• Some remarks on the spectral functions of the Abelian Higgs Model
• Calculation of the non-perturbative strong coupling from first principles
• The BRST-invariant vacuum state of the Gribov-Zwanziger theory
• Neural network approach to reconstructing spectral functions and complex poles of confined particles
• Probing the singularities of the Landau-gauge gluon and ghost propagators with rational approximants
• On the complex structure of Yang-Mills theory
• The analytic structure of three-point functions from contour deformations
• Analytic continuation and physical content of the gluon propagator
• QCD phase diagram from the gluon propagator at finite temperature and density
• Effects of a quark chemical potential on the analytic structure of the gluon propagator
• Lorentz symmetry breaking in a Yang-Mills theory within the Gribov restriction
• A window on infrared QCD with small expansion parameters
• Non-Abelian extension of the aether term and the Gribov problem
• Causality, unitarity and stability in quantum gravity: a non-perturbative perspective
• Mean-field theory for self-interacting relativistic Luttinger fermions
• $B\to X_c\ell \bar{\nu }$ 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
• Extracting topological information from momentum space propagators