Constraints on the infrared behavior of the ghost propagator in Yang-Mills theories

Cucchieri, Attilio; Mendes, Tereza

doi:10.1103/physrevd.78.094503

Cited by 233 publications

(287 citation statements)

References 37 publications

(54 reference statements)

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“…values is indeed larger than a point, and has an infinite upper limit, experience has shown that this cannot so easily be decided without investigating the volume dependence over a much wider range [121][122][123][124]. In particular, convincing evidence has been found that at least in three and four dimensions the lower limit is necessarily finite [121,122,124], and thus the value of min b has to flatten out.…”

Section: Landau-b Gaugesmentioning

confidence: 99%

Gauge bosons at zero and finite temperature

2013

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Gauge theories of the Yang-Mills type are the single most important building block of the standard model of particle physics and beyond. They are an integral part of the strong and weak interactions, and in their Abelian version of electromagnetism. Since Yang-Mills theories are gauge theories their elementary particles, the gauge bosons, cannot be described without fixing a gauge. Therefore, to obtain their properties a quantized and gauge-fixed setting is necessary.Beyond perturbation theory, gauge-fixing in non-Abelian gauge theories is obstructed by the Gribov-Singer ambiguity, which requires the introduction of non-local constraints. The construction and implementation of a method-independent gauge-fixing prescription to resolve this ambiguity is the single most important first step to describe gauge bosons beyond perturbation theory. Proposals for such a procedure, generalizing the perturbative Landau gauge, are described here. Their implementation are discussed for two example methods, lattice gauge theory and the quantum equations of motion.After gauge-fixing, it is possible to study gauge bosons in detail. The most direct access is provided by their correlation functions. The corresponding two-and three-point correlation functions are presented at all energy scales. These give access to the properties of the gauge bosons, like their absence from the asymptotic physical state space, particle-like properties at high energies, and the running coupling. Furthermore, auxiliary degrees of freedom are introduced during gauge-fixing, and their properties are discussed as well. These results are presented for two, three, and four dimensions, and for various gauge algebras.Finally, the modifications of the properties of gauge bosons at finite temperature are presented. Evidence is provided that these reflect the phase structure of Yang-Mills theory. However, it is found that the phase transition is not deconfining the gauge bosons, although the bulk thermodynamical behavior is of a Stefan-Boltzmann type. The resolution of this apparent contradiction is also presented. In addition, this resolution provides an explicit and constructive solution to the Linde problem.Thus, the technical and conceptual framework presented here can be taken as a basis how to determine correlation functions in Yang-Mills theory, therefore opening up the avenue to investigate theories of direct practical relevance. The status of this effort will be briefly described, alongside with connections to other approaches to Yang-Mills theory beyond perturbation theory.

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Section: Landau-b Gaugesmentioning

confidence: 99%

Gauge bosons at zero and finite temperature

2013

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“…The gluon propagator has been studied intensely in the past both on the lattice, with DSEs and the FRG due to its supposed connection with confinement of the non-Abelian gauge theory, see e.g. [200,216,227,[229][230][231][232][233][234][235][236] and references therein. Due to its much more complicated structure, the nonperturbative three-gluon vertex has only been begun to be explored in numerical simulations in recent years, see e.g.…”

Section: Munczek-nemirovsky Modelmentioning

confidence: 99%

Baryons as relativistic three-quark bound states

Eichmann

Sanchis-Alepuz

Williams

et al. 2016

Progress in Particle and Nuclear Physics

406

529

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We review the spectrum and electromagnetic properties of baryons described as relativistic three-quark bound states within QCD. The composite nature of baryons results in a rich excitation spectrum, whilst leading to highly non-trivial structural properties explored by the coupling to external (electromagnetic and other) currents. Both present many unsolved problems despite decades of experimental and theoretical research. We discuss the progress in these fields from a theoretical perspective, focusing on nonperturbative QCD as encoded in the functional approach via Dyson-Schwinger and Bethe-Salpeter equations. We give a systematic overview as to how results are obtained in this framework and explain technical connections to lattice QCD. We also discuss the mutual relations to the quark model, which still serves as a reference to distinguish 'expected' from 'unexpected' physics. We confront recent results on the spectrum of non-strange and strange baryons, their form factors and the issues of two-photon processes and Compton scattering determined in the DysonSchwinger framework with those of lattice QCD and the available experimental data. The general aim is to identify the underlying physical mechanisms behind the plethora of observable phenomena in terms of the underlying quark and gluon degrees of freedom.

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“…Since the ghost propagator is actually given by 8) it is clear that the inequality (1.7), known as the no-pole condition, should be equivalent to the restriction of the functional integration to the Gribov region Ω.…”

Section: The Gribov No-pole Conditionmentioning

confidence: 99%

Ghost dissection

Dudal¹,

Vandersickel²,

Cucchieri³

et al. 2012

Proceedings of International Workshop on QCD Green's Functions, Confinement and Phenomenology — PoS(QCD-TNT-II)

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We show that a necessary condition to have a positive Landau-gauge ghost propagator in d = 2 Yang-Mills theories is a vanishing zero-momentum gluon propagator. Our proof is based on a careful scrutinizing of the ghost Dyson-Schwinger equation. Said otherwise, the Gribov no-pole condition forbids the occurrence of the "decoupling/massive" gluon propagator solution in d = 2, in sharp contrast with d = 3 and 4, but consistent with state-of-the-art lattice data.

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Constraints on the infrared behavior of the ghost propagator in Yang-Mills theories

Cited by 233 publications

References 37 publications

Gauge bosons at zero and finite temperature

Gauge bosons at zero and finite temperature

Baryons as relativistic three-quark bound states

Ghost dissection

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