Добірка наукової літератури з теми "Curci-Ferrari model"

We study a dependence of Green's functions for the Curci–Ferrari model on the parameter resembling the gauge parameter in massless Yang–Mills theories. It is shown that the on-shell generating functional of vertex functions (effective action) depends on this parameter.

In the present paper, a particular form of Slavnov–Taylor identities for the Curci–Ferrari model is deduced. This model consist of Yang–Mills theory in a particular nonlinear covariant gauge, supplemented with mass terms for gluons and ghosts. It can be used as a regularization for the Yang–Mills theory preserving simple Slavnov–Taylor identities. Employing these identities, two nonrenormalization theorems are proved that reduce the number of independent renormalization factors from five to three. These new relations are verified by a comparison to the already known three-loops renormalization factors. These relations include, as a particular case, the corresponding known identities in Yang–Mills theory in Landau gauge.

At large energy quarks and gluons behave as free particles and therefore the standard perturbative analysis of QCD gives very good results. However, this is not the situation in the low energy regime of QCD which is generally treated with nonperturbative methods. In spite of this, lattice simulations observe that the expansion parameter is not large in the gluonic sector. In particular, the coupling constant do not reach a Landau pole in the infrared as it is expected by standard perturbation theory. On top of this, lattice simulations find that the gluon propagator behaves as a massive propagator in the infrared. Motivated by these observations we use a model that includes a mass for the gluon (Curci-Ferrari) that can reproduce the same kind of behaviour for the gluon propagator and also a similar expansion parameter as the one found by the lattice. In this proceeding we show some of the results of quenched correlation functions obtained by using that small parameter for computing one and two loops corrections. At the end, we compare them with lattice data obtaining very good results.

Exploiting the theoretical potential of the modified Bonora-Tonin superfield approach (MBTSA) as well as the (anti-)chiral superfield approach (ACSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism, we derive the complete set of off-shell nilpotent (anti-)BRST symmetry transformations corresponding to the classical two- 1 + 1 dimensional (2D) diffeomorphism symmetry transformations on the worldsheet (that is traced out by the motion of a model of bosonic string). Only the BRST symmetry transformations for this model have been discussed in the earlier literature. We derive the (anti-)BRST invariant Curci-Ferrari- (CF-) type restrictions (using MBTSA) which turn out to be the root cause behind the absolute anticommutativity of the above (anti-)BRST symmetry transformations. We capture the symmetry invariance of the (anti-)BRST invariant Lagrangian densities within the ambit of ACSA. The derivation of the proper anti-BRST transformations (corresponding to the already-known BRST transformations) and the (anti-)BRST invariant CF-type restrictions are the novel results in our present endeavor.

We derive the off-shell nilpotent and absolutely anti-commuting Becchi–Rouet–Stora–Tyutin (BRST) as well as anti-BRST symmetry transformations corresponding to the non-Yang–Mills (NYM) symmetry transformations of (2+1)-dimensional Jackiw–Pi (JP) model within the framework of "augmented" superfield formalism. The Curci–Ferrari (CF) restriction, which is a hallmark of non-Abelian one-form gauge theories, does not appear in this case. One of the novel features of our present investigation is the derivation of proper (anti-)BRST symmetry transformations corresponding to the auxiliary field ρ that cannot be derived by any conventional means.

Within the framework of the Becchi-Rouet-Stora-Tyutin (BRST) formalism, we discuss the full set of proper BRST and anti-BRST transformations for a 2D diffeomorphism invariant theory which is described by the Lagrangian density of a standard bosonic string. The above (anti-)BRST transformations are off-shell nilpotent and absolutely anticommuting. The latter property is valid on a submanifold of the space of quantum fields where the 2D version of the universal (anti-)BRST invariant Curci-Ferrari (CF) type of restrictions is satisfied. We derive the precise forms of the BRST and anti-BRST invariant Lagrangian densities as well as the exact expressions for the conserved (anti-)BRST and ghost charges. The lucid derivation of the proper anti-BRST symmetry transformations and the emergence of the CF-type restrictions are completely novel results for our present bosonic string which has already been discussed earlier in literature where only the BRST symmetry transformations have been pointed out. We briefly mention the derivation of the CF-type restrictions from the modified version of the Bonora-Tonin superfield approach, too.

La Chromodynamique Quantique (QCD) est une théorie de jauge bien établie qui décrit la dynamique des quarks et des gluons. Au niveau analytique, les observables physiques ne peuvent être calculées que lorsque la jauge est fixée. La méthode standard pour y parvenir est la méthode de Faddeev-Popov (FP), qui introduit comme sous-produit des champs auxiliaires non physiques, les "fantômes". D'autre part, le couplage de jauge de la QCD devient faible pour des impulsions très élevées, ce qui fait de la théorie des perturbations (TP) un outil de calcul approprié dans cette limite. L'approche perturbative dans le cadre de la méthode de FP s'est avérée extrêmement utile et a été testée expérimentalement à de nombreuses reprises. Cependant, dans la gamme opposée d'impulsions, la méthode de FP n'est plus entièrement valide en raison de la présence de copies de Gribov. Par conséquent, pour accéder à l'infrarouge de la QCD, une approche alternative est nécessaire.Cette thèse est consacrée à une de ces approches : le modèle de Curci-Ferrari (CF) dans la jauge de Landau. Elle consiste en une simple extension de la théorie de FP, à laquelle est ajouté un terme de masse pour le champ de gluons. Sa principale motivation provient des simulations numériques de fonctions de corrélation dans la jauge de Landau, qui indiquent clairement que le gluon acquiert une masse dans l'infrarouge profond. En plus de ce phénomène frappant, les simulations numériques montrent un couplage de jauge compatible avec une analyse perturbative pour toute la gamme d'impulsions, au moins pour le secteur pure jauge - ou de Yang-Mills (YM). Ainsi, afin de tester le modèle, plusieurs fonctions de corrélation à deux et trois points ont été évaluées de manière perturbative à une boucle. D'une manière générale, ces résultats montrent un bon accord avec leurs homologues numériques. Plus récemment, les fonctions à deux points de la théorie YM pure ont été évaluées à deux boucles, améliorant ainsi l'accord avec les données des simulations. L'objectif de cette thèse est d'étendre les calculs à deux boucles à d'autres fonctions de corrélation. Il s'agira ainsi de tester plus avant l'approche perturbative dans le modèle de CF, tout en clarifiant ses limites.Dans le cas de la théorie YM pure, nous évaluons le vertex fantôme-antifantôme-gluon et le vertex à trois gluons dans une configuration cinématique particulière, en quatre dimensions, pour les groupes de jauge SU(2) et SU(3). Ces deux quantités sont une pure prédiction du modèle de CF, puisque les deux paramètres libres du modèle sont déterminés à partir de l'ajustement des fonctions à deux points. De manière générale, les corrections à deux boucles améliorent l'accord avec les numériques par rapport aux corrections à une boucle. La dépendance de nos prédictions par rapport au schéma de renormalisation, diminue également une fois les corrections à deux boucles incluses, ce qui conforte l'approche perturbative. En ce qui concerne le vertex à trois gluons, le calcul nous permet notamment d'obtenir des informations sur le passage à zéro ainsi que de tester une prédiction sur le comportement dominant exact de cette quantité dans l'infrarouge.Nous concluons cette étude en calculant les fonctions à deux boucles pour le fantôme, le gluon et le quark dans le cadre de la QCD, en présence de deux saveurs dégénérées de quarks, et en les comparant aux données des simulations numériques. Les résultats à deux boucles montrent un accord au résultats numériques systématiquement meilleur par rapport aux évaluations à une boucle, à l'exception de la fonction de masse des quarks légers. Ce résultat est particulièrement pertinent pour la fonction d'habillage des quarks, puisque les calculs à une boucle est incapable de reproduire les données des simulations. Cette incohérence est levée à deux boucles tant sur le plan qualitatif que quantitatif
Quantum Chromodynamics (QCD) is a well established gauge theory which describes the dynamics of quarks and gluons. At the analytical level, physical observables can be computed only after the gauge is fixed. The textbook procedure to do so is the Faddeev-Popov (FP) method, which introduces, as a byproduct, auxiliary non-physical fields known as ghosts. Moreover, the QCD gauge coupling becomes small at very high momenta, making of perturbation theory (PT) a suitable calculation tool within that region of momenta. The combination of the FP theory and PT has turned out to be extremely useful and has been tested experimentally in many occasions. However, in the opposite momentum range, the FP method is no longer fully valid due to the presence of Gribov copies. Consequently, in order to access QCD in the infrared, new approaches are needed.This thesis is devoted to one of such approaches: the Curci-Ferrari (CF) model in Landau gauge. It consists in a simple gluon mass extension of the FP theory. Its main motivation comes from the lattice simulations for correlation functions in the Landau gauge, which clearly indicate that the gluon acquire a mass in the deep infrared. In addition to this striking phenomenon, the lattice simulations feature a gauge coupling compatible with a perturbative analysis for the whole range of momenta, at least in the pure gauge - or Yang-Mills (YM) - sector. Thus, with the purpose of testing the model, several two- and three-point correlation functions have been perturbatively evaluated at one-loop order. In general terms, the results show a very good agreement with the lattice data. More recently, the two-point functions from the pure YM theory were evaluated at two-loop order, improving the agreement to lattice data. The goal of this thesis is to extend the two-loop calculations to other correlation functions. This is a way of further testing the perturbative use of the model as well as to clarify its limits.In the case of pure YM theory, we evaluate the ghost-antighost-gluon vertex and the three-gluon vertex in a particular kinematical configuration in four dimensions, for the SU(2) and SU(3) gauge groups. Both quantities emerge as a pure prediction of the CF model, since its two free parameters are determined by fitting the two-point functions. Broadly speaking, the predicted vertices are able to improve the agreement with their numerical counterparts in comparison with the one-loop correction. We also investigate the renormalization scheme dependence of our results, which shows consistency with the perturbative approach. As for the three-gluon vertex, the calculation allows us in particular to gain insight on the zero-crossing as well as to test an exact prediction for the leading behavior in the infrared.We end this investigation by computing the ghost, gluon and quark two-point functions in QCD, with two degenerate quark flavors. We fit them to available lattice data. Our evaluation is consistent with such data in all the cases, except for the quark mass function for light quarks. The result is particularly relevant for the quark dressing function, since the CF model is unable to reproduce the lattice data at one-loop order. This discrepancy is corrected by the two-loop evaluation, which agrees with the data both at a qualitative and quantitative level