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arXiv · 1404.2545

The quark-gluon vertex in Landau gauge bound-state studies

Richard Williams
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Abstract

We present a practical method for the solution of the quark-gluon vertex for use in Bethe--Salpeter and Dyson--Schwinger calculations. The efficient decomposition into the necessary covariants is detailed, with the numerical algorithm outlined for both real and complex Euclidean momenta. A truncation of the quark-gluon vertex, that neglects explicit back-coupling to enable the application to bound-state calculations, is given together with results for the quark propagator and quark-gluon vertex for different quark flavours. The relative impact of the various components of the quark-gluon vertex is highlighted with the flavour dependence of the effective quark-gluon interaction obtained, thus providing insight for the construction of phenomenological models within Rainbow-Ladder. Finally, we solve the corresponding Green's functions for complex Euclidean momenta as required in future bound-state calculations.

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Richard Williams. 2014-04-09. The quark-gluon vertex in Landau gauge bound-state studies. https://doi.org/10.1140/epja/i2015-15057-4

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