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On the absence and presence of pole(s) in fermion propagator in the simple model with mass.pdf

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On the absence and presence of pole(s) in fermion propagator in the simple model with mass

a r X i v : h e p - p h / 0 7 0 1 1 6 1 v 3 2 5 A p r 2 0 0 7 On the absence and presence of pole(s) in fermion propagator in the simple model with mass generation V. S?auli1 and F. Kleefeld2 1CFTP and Departamento de F??sica, Instituto Superior Te?cnico, Av. Rovisco Pais, 1049-001 Lisbon, Portugal 2Department of Theoretical Physics, Nuclear Physics Institute, R?ez? near Prague, CZ-25068, Czech Republic Within the Pauli-Villars regularization technique the fermion propagator is studied in the frame- work of Schwinger-Dyson equations in the Euclidean space. Making the generalization of Fukuda and Kugo proposals, the analytical continuation is performed into the timelike region of fourmomenta. The massive gauge boson is considered and the fermion propagator pole structure is discussed in detail. PACS numbers: 11.10.St, 11.15.Tk I. INTRODUCTION The natural nonperturbative framework for the study of infrared properties of QCD Green’s functions in the whole Minkowski space is the formalism of Schwinger-Dyson equations (SDEs). The complex of SDEs is an infinite tower of coupled integral equations which must be truncated to be tractable in practice. Most of the studies concerns the solution of SDEs in Quantum Chromodynamics [1] where it is believed they can give the correct description of chiral symmetry breaking and confinement. It is well known fact the the masses of the particles can be largely enhanced in strong coupling theory like QCD. The property and difficulty to extract a correct picture of dynamical mass generation attracts much attention in recent modeling of QCD [2, 3], Technicolors [4] and strong coupling models with spinless scalar bosons [5]. The models in two later cases represent the dynamical alternatives to Standard model Higgs mechanism. These models can break symmetry but avoid the introduction of negative scalar boson mass term for this purpose. In QCD, this is certainly the asymptotic freedom and its associated regulating character of the ultra