Three-point correlation functions in Yang-Mills theory

Peláez, Marcela; Tissier, Matthieu; Wschebor, Nicolás

doi:10.1103/physrevd.88.125003

Cited by 143 publications

(234 citation statements)

References 61 publications

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“…2 (to the left) are slightly different from the ones obtained by Peláez, Tissier and Wschebor in Ref. [18]. The difference lies in their fitting of the renormalization group improved result for the ghost dressing function to the lattice data for momenta in the directions (0, 0, 1, 1) and (1, 1, 1, 1) (red and blue data points in the online version), in the momentum regime where the breaking of rotational invariance on the lattice is visible, while we have found better overall fits by adjusting our curves to the data for momentum directions (0, 0, 0, 1) and (0, 1, 1, 1).…”

Section: Epj Web Of Conferencescontrasting

confidence: 44%

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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Section: Epj Web Of Conferencescontrasting

confidence: 44%

Callan-Symanzik equations for infrared Yang-Mills theory

Weber

Dall’Olio

2017

EPJ Web Conf.

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“…(i) The zerocrossing has been claimed to happen as a purely gluodynamical effect in refs. [40,[46][47][48][49][50], by using the SDE formalism, and then argued to shift down to deeper momenta by the presence of light quarks [72]. The study of that effect in pure gluodynamics deserves interest per se but, if the latter is true, can also provide with noteworthy qualitative information about the IR behavior of the QCD gluonic Green's functions.…”

Section: Lattice Qcd Resultsmentioning

confidence: 99%

Refining the detection of the zero crossing for the three-gluon vertex in symmetric and asymmetric momentum subtraction schemes

et al. 2017

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This article reports on the detailed study of the three-gluon vertex in four-dimensional SU (3) Yang-Mills theory employing lattice simulations with large physical volumes and high statistics. A meticulous scrutiny of the so-called symmetric and asymmetric kinematical configurations is performed and it is shown that the associated form-factor changes sign at a given range of momenta. The lattice results are compared to the model independent predictions of Schwinger-Dyson equations and a very good agreement among the two is found.

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“…Specifically, a precise nonperturbative connection between the masslessness of the ghost, the detailed shape of the gluon propagator in the deep infrared (IR), and the IR divergences observed in certain kinematic limits of the three-gluon vertex, has been put forth in [17] (see also [18][19][20] for related contributions). This detailed study led to the conjecture that any purely gluonic n-point function will display the same kind of behavior, given that ghost loops 1 appear in all of them (and, hence, the associated IR logarithmic divergence in d = 4).…”

Section: Jhep09(2014)059mentioning

confidence: 99%

Nonperturbative study of the four gluon vertex

Binosi

Ibañez

Papavassiliou

2014

J. High Energ. Phys.

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In this paper we study the nonperturbative structure of the SU(3) four-gluon vertex in the Landau gauge, concentrating on contributions quadratic in the metric. We employ an approximation scheme where "one-loop" diagrams are computed using fully dressed gluon and ghost propagators, and tree-level vertices. When a suitable kinematical configuration depending on a single momentum scale p is chosen, only two structures emerge: the tree-level four-gluon vertex, and a tensor orthogonal to it. A detailed numerical analysis reveals that the form factor associated with this latter tensor displays a change of sign (zero-crossing) in the deep infrared, and finally diverges logarithmically. The origin of this characteristic behavior is proven to be entirely due to the masslessness of the ghost propagators forming the corresponding ghost-loop diagram, in close analogy to a similar effect established for the three-gluon vertex. However, in the case at hand, and under the approximations employed, this particular divergence does not affect the form factor proportional to the tree-level tensor, which remains finite in the entire range of momenta, and deviates moderately from its naive tree-level value. It turns out that the kinematic configuration chosen is ideal for carrying out lattice simulations, because it eliminates from the connected Green's function all one-particle reducible contributions, projecting out the genuine one-particle irreducible vertex. Motivated by this possibility, we discuss in detail how a hypothetical lattice measurement of this quantity would compare to the results presented here, and the potential interference from an additional tensorial structure, allowed by Bose symmetry, but not encountered within our scheme.

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Three-point correlation functions in Yang-Mills theory

Cited by 143 publications

References 61 publications

Callan-Symanzik equations for infrared Yang-Mills theory

Callan-Symanzik equations for infrared Yang-Mills theory

Refining the detection of the zero crossing for the three-gluon vertex in symmetric and asymmetric momentum subtraction schemes

Nonperturbative study of the four gluon vertex

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