Dispersion relations for unphysical particles

Abstract

Generalized dispersion relations are discussed for unphysical particles, e.g. confined degrees of freedom that are not present in the physical spectra but can give rise to observable bound states. While in general the propagator of the unphysical particles can have complex poles and cannot be reconstructed from the knowledge of the imaginary part, under reasonable assumptions the missing piece of information is shown to be in the rational function that contains the poles and must be added to the integral representation. For pure Yang-Mills theory, the rational part and the spectral term are identified in the explicit analytical expressions provided by the massive expansion of the gluon propagator. The multi particle spectral term turns out to be very small and the simple rational part provides, from first principles, an approximate propagator that is equivalent to the tree-level result of simple phenomenological models like the refined Gribov-Zwanziger model.

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Cited by in corpus (14)

• Spectral functions of confined particles
• Reconstructing QCD Spectral Functions with Gaussian Processes
• Complex poles and spectral function of Yang-Mills theory
• The gluon propagator in linear covariant $R_{\xi }$ gauges
• Complex poles and spectral functions of Landau gauge QCD and QCD-like theories
• Quasigluon lifetime and confinement from first principles
• Calculation of the non-perturbative strong coupling from first principles
• The Nielsen identities in screened theories
• Analytic continuation and physical content of the gluon propagator
• Screened massive expansion of Schwinger-Dyson equations
• QCD phase diagram from the gluon propagator at finite temperature and density
• Extracting a model quark propagator's spectral density
• Screened massive expansion of the quark propagator in the Landau gauge
• One-loop analytic structure of the deep-infrared Landau-gauge gluon propagator at finite temperature