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arXiv · 1302.0307

The effect of an infrared divergent quark-antiquark interaction kernel on other Green functions

Reinhard Alkofer·Mario Mitter
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Abstract

The n-point Green functions of Landau gauge QCD are systematically investigated in a Dyson-Schwinger approach assuming a static linearly rising potential between fundamental color charges. Besides quarks also scalar matter in the fundamental representation is considered. Starting from the hypothesis of an 1/k^4 infrared divergent matter-antimatter vertex restrictions on the general color tensor structure of this divergence are derived. Consequences for the other four-point functions of QCD, resp., scalar QCD, are presented. Hereby Casimir scaling is found. It is shown that possible singular contributions to the three-point functions vanish due to cancellations within the color algebra. On the other hand, higher n-point functions inherit the infrared singularity of the matter-antimatter vertex in certain color channels. The presented results show that linear confinement is consistently possible in a Greens function approach, however, at the expense that the decoupling theorem is circumvented by infrared singularities.

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Reinhard Alkofer, Mario Mitter. 2013-02-01. The effect of an infrared divergent quark-antiquark interaction kernel on other Green functions. https://arxiv.org/abs/1302.0307

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