Reflection positivity and complex analysis of the Yang-Mills theory from a viewpoint of gluon confinement

Abstract

In order to understand the confining decoupling solution of the Yang-Mills theory in the Landau gauge, we consider the massive Yang-Mills model which is defined by just adding a gluon mass term to the Yang-Mills theory with the Lorentz-covariant gauge fixing term and the associated Faddeev-Popov ghost term. First of all, we show that massive Yang-Mills model is obtained as a gauge-fixed version of the gauge-invariantly extended theory which is identified with the gauge-scalar model with a single fixed-modulus scalar field in the fundamental representation of the gauge group. This equivalence is obtained through the gauge-independent description of the Brout-Englert-Higgs mechanism proposed recently by one of the authors. Then, we reconfirm that the Euclidean gluon and ghost propagators in the Landau gauge obtained by numerical simulations on the lattice are reproduced with good accuracy from the massive Yang-Mills model by taking into account one-loop quantum corrections. Moreover, we demonstrate in a numerical way that the Schwinger function calculated from the gluon propagator in the Euclidean region exhibits violation of the reflection positivity at the physical point of the parameters. In addition, we perform the analytic continuation of the gluon propagator from the Euclidean region to the complex momentum plane towards the Minkowski region. We give an analytical proof that the reflection positivity is violated for any choice of the parameters in the massive Yang-Mills model, due to the existence of a pair of complex conjugate poles and the negativity of the spectral function for the gluon propagator to one-loop order. The complex structure of the propagator enables us to explain why the gluon propagator in the Euclidean region is well described by the Gribov-Stingl form.

33 pages, 25 figures, a version with the same contents as that published in Eur. Phys. J. C 80, 84 (2020)[33 pages] (although the style is different)

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Cited by in corpus (18)

• Landau gauge Yang-Mills propagators in the complex momentum plane
• Ghost spectral function from the spectral Dyson-Schwinger equation
• The analytic structure of the lattice Landau gauge gluon and ghost propagators
• Reconstructing confined particles with complex singularities
• Complex poles and spectral functions of Landau gauge QCD and QCD-like theories
• Spontaneous chiral symmetry breaking in the massive Landau gauge: realistic running coupling
• Some remarks on the spectral functions of the Abelian Higgs Model
• Probing the singularities of the Landau-gauge gluon and ghost propagators with rational approximants
• $H(4)$ tensor representations for the lattice Landau gauge gluon propagator and the estimation of lattice artefacts
• The analytic structure of three-point functions from contour deformations
• On the complex structure of Yang-Mills theory
• Effects of a quark chemical potential on the analytic structure of the gluon propagator
• A window on infrared QCD with small expansion parameters
• Complex poles, spectral function and reflection positivity violation of Yang-Mills theory
• Oscillators with imaginary coupling: spectral functions in quantum mechanics and quantum field theory
• Reconstructing propagators of confined particles in the presence of complex singularities
• Extracting topological information from momentum space propagators
• One-loop analytic structure of the deep-infrared Landau-gauge gluon propagator at finite temperature