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Gauge invariant Ansatz for a special three-gluon vertex

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Abstract

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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Authors and Affiliations

  1. European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT) and Fondazione Bruno Kessler, Villa Tambosi, Strada delle Tabarelle 286, I-38123, Villazzano (TN), Italy

    D. Binosi

  2. Department of Theoretical Physics and IFIC, University of Valencia, Dr. Moliner str. 50, E-46100, Burjassot (Valencia), Spain

    J. Papavassiliou

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  1. D. Binosi
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ArXiv ePrint: 1102.5662

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Binosi, D., Papavassiliou, J. Gauge invariant Ansatz for a special three-gluon vertex. J. High Energ. Phys. 2011, 121 (2011). https://doi.org/10.1007/JHEP03(2011)121

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