Gauge invariant Ansatz for a special three-gluon vertex

Details Gauge invariant Ansatz for a special three-gluon vertex Gauge invariant Ansatz for a special three-gluon vertex

2011-02-28

arxiv.org/abs/1102.5662v3

JHEP 1103:121,2011

Physics

High Energy Physics

High Energy Physics - Phenomenology

26 pages, 4 figures; v3: more typos corrected

Scientific paper

10.1007/JHEP03(2011)121

We construct a general Ansatz for the three-particle vertex describing the interaction of one background and two quantum gluons, by simultaneously solving the Ward and Slavnov-Taylor identities it satisfies. This vertex is known to be essential for the gauge-invariant truncation of the Schwinger-Dyson equations of QCD, based on the pinch technique and the background field method. A key step in this construction is the formal derivation of a set of crucial constraints (shown to be valid to all orders), relating the various form factors of the ghost Green's functions appearing in the aforementioned Slavnov-Taylor identity. When inserted into the Schwinger-Dyson equation for the gluon propagator, this vertex gives rise to a number of highly non-trivial cancellations, which are absolutely indispensable for the self-consistency of the entire approach.

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