Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2009-02-06
Physics
High Energy Physics
High Energy Physics - Phenomenology
10 pages, reference added, few typos corrected
Scientific paper
The propagator of confined quarks is calculated for timelike momenta by transforming Minkowski Greens functions to the Temporal Euclidean space. Based on the framework of the Schwinger-Dyson equations the QCD quark propagator is obtained in two approximations which differ by assuming behaviour of gluon propagator. In both studied cases we get universal result for the light quarks: The quark mass function becomes complex bellow expected perturbative threshold, the obtained absolute value of the infrared mass is $M\simeq \Lambda_{QCD} $ with the infrared phase $\simeq {\pi\over 2}$. Permanent confinement of quarks is maintained by generation of the complex mass function which prevents a real pole in the propagator. We will show that timelike dynamical Chiral Symmetry Breaking (CSB) solution is approximately, but non-trivially determined by the solution of gap equation in the standard Euclidean space.
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