A gauge-technique Ansatz for the three gluon vertex of the background field method

Details A gauge-technique Ansatz for the three gluon vertex of the background field method A gauge-technique Ansatz for the three gluon vertex of the background field method

2011-03-03

arxiv.org/abs/1103.0643v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

10 pages, 2 figures. Contribution for the workshop "The many faces of QCD", 1-5 Nov 2010, Ghent, Belgium

Scientific paper

The vertex connecting one background gluon with two quantum ones constitutes a central ingredient in the gauge-invariant Schwinger-Dyson equation that determines the non-perturbative dynamics of the gluon propagator. This vertex satisfies a Ward identity with respect to the background gluon, and a Slavnov-Taylor identity with respect to the two quantum gluons. We present a complete Ansatz for this vertex, which satisfies both aforementioned identities. This entire construction depends crucially on a set of constraints relating the various form-factors of the ghost Green's functions appearing in the Slavnov-Taylor identity satisfied by the vertex. The validity of these constraints is demonstrated to all orders.

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