On the computation of the spectral density of two-point functions: complex masses, cut rules and beyond

Abstract

We present a steepest descent calculation of the Kallen-Lehmann spectral density of two-point functions involving complex conjugate masses in Euclidean space. This problem occurs in studies of (gauge) theories with Gribov-like propagators. As the presence of complex masses and the use of Euclidean space brings the theory outside of the strict validity of the Cutkosky cut rules, we discuss an alternative method based on the Widder inversion operator of the Stieltjes transformation. It turns out that the results coincide with those obtained by naively applying the cut rules. We also point out the potential usefulness of the Stieltjes (inversion) formalism when non-standard propagators are used, in which case cut rules are not available at all.

16 pages, 4 .pdf figures. v2: version accepted for publication in Physical Review D

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Cited by in corpus (21)

• Källén-Lehmann spectroscopy for (un)physical degrees of freedom
• Gluon screening mass at finite temperature from Landau gauge gluon propagator in lattice QCD
• Landau gauge Yang-Mills propagators in the complex momentum plane
• Spectral representation of lattice gluon and ghost propagators at zero temperature
• A perturbative study of the QCD phase diagram for heavy quarks at nonzero chemical potential: two-loop corrections
• On the analytic structure of scalar glueball operators at Born level
• The No-Pole Condition in Landau gauge: Properties of the Gribov Ghost Form-Factor and a Constraint on the 2d Gluon Propagator
• Padé approximation and glueball mass estimates in 3d and 4d with N_c = 2,3 colors
• Some more details of minimal-Landau-gauge Yang-Mills propagators
• The (IR-)relevance of the Gribov ambiguity in SU(2) x U(1) gauge theories with fundamental Higgs matter
• Accessing the topological susceptibility via the Gribov horizon
• Dispersion relations for unphysical particles
• A study of the lightest glueball states in SU(2) Euclidean Yang-Mills theory in the maximal Abelian gauge
• The analytic structure of three-point functions from contour deformations
• Confined gluon from Minkowski space continuation of PT-BFM SDE solution
• Källén-Lehmann Spectral Representation of the Scalar SU(2) Glueball
• A BRST Characterization of the Broken Phase Observables of the Confining Complex Theory
• A path to confine gluons and fermions through complex gauge theory
• Aspects of the Gribov problem in Euclidean Yang-Mills theories
• Complex Chern-Simons and Gribov
• Gribov horizon, Polyakov loop and finite temperature