Abstract
In this work we investigate the effects of the Gribov prescription to get rid of zero-modes of the Faddeev-Popov operator, at one-loop order in perturbation theory, in the Landau-DeWitt gauge. Quantum fluctuations are taken around a transverse background gauge field. The one-loop effective action is explicitly computed, and the behavior of the gauge and ghost fields propagators are carefully investigated. At one-loop and for generic transverse background configurations the effective action is found to be \textit{not} background invariant, as expected, due to a non-vanishing background contribution. The gauge field propagator has the same form as in the case {where the} background is a trivial field, $i.e.$ with complex conjugate poles, which are modified by the corresponding gap equation. The ghost-anti-ghost propagator still displays its enhanced $\sim p^{-4}$ behavior.
Highlights
The description of all elementary forces of nature with the exception of gravity is encoded in the quantumfield-theoretic setting of the Standard Model of particle physics
The Gribov parameter, which is taken as a physical parameter in the standard refined Gribov-Zwanziger (RGZ) setup, receives nonphysical contributions from the background field already at one-loop order
At one-loop order for the vacuum energy, we could explicitly verify that the effective action can be rewritten in terms of the “total” gauge field Aμ 1⁄4 Aμ þ aμ as follows, ac
Summary
The description of all elementary forces of nature with the exception of gravity is encoded in the quantumfield-theoretic setting of the Standard Model of particle physics. This allowed for a “nonperturbative” BRST quantization rule which implements the restriction to a region free of a large set of Gribov copies in LCG and Curci-Ferrari gauges [54,57] giving a universal meaning to the horizon function [55]. The state-of-the-art quantization of Yang-Mills theories by restricting the configuration space of the path integral to the Gribov region in covariant gauges is summarized by a local, renormalizable, and BRST-invariant setup. The main goal of this work is to derive the leading order effective action, while taking into account the existence of infinitesimal Gribov copies in the LandauDeWitt gauge, for a generic transverse background Aaμ, by following Gribov’s original prescription. Important but lengthy derivations and Feynman rules are collected in the Appendices
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