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The Infrared Behaviour of the Pure Yang-Mills Green Functions

Ph. Boucaud·J. P. Leroy·A. Le Yaouanc·A. Y. Lokhov·J. Micheli·O. Pene·J. Rodriguez-Quintero·C. Roiesnel
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Abstract

We study the infrared behaviour of the pure Yang-Mills correlators using relations that are well defined in the non-perturbative domain. These are the Slavnov-Taylor identity for three-gluon vertex and the Schwinger-Dyson equation for ghost propagator in the Landau gauge. We also use several inputs from lattice simulations. We show that lattice data are in serious conflict with a widely spread analytical relation between the gluon and ghost infrared critical exponents. We conjecture that this is explained by a singular behaviour of the ghost-ghost-gluon vertex function in the infrared. We show that, anyhow, this discrepancy is not due to some lattice artefact since lattice Green functions satisfy the ghost propagator Schwinger-Dyson equation. We also report on a puzzle concerning the infrared gluon propagator: lattice data seem to favor a constant non vanishing zero momentum gluon propagator, while the Slavnov-Taylor identity (complemented with some regularity hypothesis of scalar functions) implies that it should diverge.

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Ph. Boucaud, J. P. Leroy, A. Le Yaouanc, A. Y. Lokhov, J. Micheli, O. Pene, J. Rodriguez-Quintero, C. Roiesnel. 2006-05-11. The Infrared Behaviour of the Pure Yang-Mills Green Functions. https://arxiv.org/abs/hep-ph/0507104

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