Infrared propagators of Yang-Mills theory from perturbation theory

Tissier, Matthieu; Wschebor, Nicolás

doi:10.1103/physrevd.82.101701

Cited by 220 publications

(344 citation statements)

References 31 publications

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“…We also demonstrate that, within perturbation theory, correlation functions of YM fields are identical to those obtained in a massive extension of the usual FP gauge-fixed action, which is a particular case of the Curcci-Ferrari (CF) model [12]. This provides a solid first-principle field theoretical justification for the phenomenological approach recently proposed in [13,14].…”

Section: Introductionsupporting

confidence: 65%

“…We see that the action (16), with (13) and (21)- (23), thus describes a collection of n gauged supersymmetric nonlinear sigma models [19]. It is invariant under the super gauge transformation…”

Section: Defining Further the "Super Gauge Transform"mentioning

confidence: 99%

“…The gluon and ghost two-point vertex functions have been computed at one-loop in the CF model [13,14] with dimensional regularization. The corresponding one-loop expressions for the present theory can thus be obtained from these papers by replacing the bare gluon mass m 2 0 → nβ 0 .…”

Section: Renormalization Group Flowmentioning

confidence: 99%

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Lifting the Gribov ambiguity in Yang-Mills theories

Serreau¹

2013

Proceedings of XTH Quark Confinement and the Hadron Spectrum — PoS(Confinement X)

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We propose a new one-parameter family of Landau gauges for Yang-Mills theories which can be formulated by means of functional integral methods and are thus well suited for analytic calculations, but which are free of Gribov ambiguities and avoid the Neuberger zero problem of the standard Faddeev-Popov construction. The resulting gaugefixed theory is perturbatively renormalizable in four dimensions and, for what concerns the calculation of ghost and gauge field correlators, it reduces to a massive extension of the Faddeev-Popov action. We study the renormalization group flow of this theory at one-loop and show that it has no Landau pole in the infrared for some -including physically relevant -range of values of the renormalized parameters.

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Section: Introductionsupporting

confidence: 65%

Section: Defining Further the "Super Gauge Transform"mentioning

confidence: 99%

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Lifting the Gribov ambiguity in Yang-Mills theories

Serreau¹

2013

Proceedings of XTH Quark Confinement and the Hadron Spectrum — PoS(Confinement X)

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“…Tissier and Wschebor [8] have shown that straightforward one-loop perturbation theory applied to Yang-Mills theory with a gluon mass term yields results for the gluon and ghost propagators that reproduce surprisingly well the propagators found on the lattice in three and four space-time dimensions in the IR regime. It is apparent, however, that a renormalization group improvement is necessary for a quantitative description of the ultraviolet (UV) regime in four space-time dimensions, and also for a quantitatively good fit to the propagators in the IR regime in three dimensions.…”

mentioning

confidence: 75%

“…In the case of the coupling constant, this means that the IR fixed point is trivial. The triviality of the fixed point explains the success of straightforward perturbation theory in the IR regime (in four dimensions) [8]. On the other hand, the fact that the mass parameter tends to zero does not mean that one recovers a massless theory in the deep IR: the scale dependence of the gluon field renormalization constant leads to a finite limit of the gluon propagator at zero momentum.…”

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confidence: 99%

Callan-Symanzik equations for infrared Yang-Mills theory

Weber

Dall’Olio

2017

EPJ Web Conf.

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Abstract. Dyson-Schwinger equations have been successful in determining the correlation functions in Yang-Mills theory in the Landau gauge, in the infrared regime. We argue that similar results can be obtained, in a technically simpler way, with Callan-Symanzik renormalization group equations. We present generalizations of the infrared safe renormalization scheme proposed by Tissier and Wschebor in 2011, and show how the renormalization scheme dependence can be used to improve the matching to the existing lattice data for the gluon and ghost propagators.Historically, the first semi-analytical method that has made it possible to access the deep infrared (IR) regime of Landau gauge Yang-Mills theory, have been Dyson-Schwinger equations. The first solutions of these equations that have been found show a scaling behavior of the propagators in the IR [1]. Several years later, another type of solutions of the same equations was discovered [2], with a massive gluon propagator and a finitely enhanced ghost propagator in the IR (decoupling solutions). To date, Dyson-Schwinger equations are still the main tool for the (semi-)analytical exploration of the IR regime of Yang-Mills theory.In a parallel development that actually initiated much earlier with Gribov's observation of the existence of gauge copies in his famous 1978 paper [3] and was later worked out in great detail by Zwanziger [4], the theoretical foundations of IR Yang-Mills theory in the Landau gauge were laid. While this so-called Gribov-Zwanziger scenario seemed to confirm the existence of the scaling solutions, a more recent refinement [5] favors the decoupling type of solutions. Finally, the results of simulations of Yang-Mills theory in the Landau gauge on huge lattices [6] have been interpreted by most workers in the field as confirming the realization of the decoupling type of solutions in three and four space-time dimensions.In this contribution, we will present a different technique for the exploration of the IR regime of Yang-Mills theory. We intend to reproduce the results of lattice simulations in the Landau gauge that restrict the gauge field configurations to the (first) Gribov region, but make no attempt to reach the fundamental modular region. The restriction to the Gribov region implies the breaking of BRST invariance in the continuum formulation [4]. The most important consequence of the broken BRST invariance for the IR regime is the appearance of a mass term for the gluon field [5]. Indeed, the addition of a gluonic mass term to the Yang-Mills action has been shown to reproduce all the solutions (two types of scaling solutions and the decoupling solution) found before with the help of DysonSchwinger equations when solving the Callan-Symanzik equations for this theory in the IR regime in an epsilon expansion around the upper critical space-time dimension [7]. This analysis also shows that a

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Introduction: The Many Paths to QCD

Reinosa

2022

Perturbative Aspects of the Deconfinement Transition

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Infrared propagators of Yang-Mills theory from perturbation theory

Cited by 220 publications

References 31 publications

Lifting the Gribov ambiguity in Yang-Mills theories

Lifting the Gribov ambiguity in Yang-Mills theories

Callan-Symanzik equations for infrared Yang-Mills theory

Introduction: The Many Paths to QCD

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