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Infrared Correlation Functions in Quantum Chromodynamics Monica Marcela Peláez Arzúa

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Infrared Correlation Functions in Quantum Chromodynamics Monica Marcela Peláez Arzúa Infrared correlation functions in Quantum Chromodynamics Monica Marcela Peláez Arzúa To cite this version: Monica Marcela Peláez Arzúa. Infrared correlation functions in Quantum Chromodynamics. Quan- tum Physics [quant-ph]. Université Pierre et Marie Curie - Paris VI; Universidad de la República (Montevideo), 2015. English. NNT : 2015PA066491. tel-01298242 HAL Id: tel-01298242 https://tel.archives-ouvertes.fr/tel-01298242 Submitted on 5 Apr 2016 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Ecole doctorale Physique en Ile-de-France et PEDECIBA-UdelaR PhD thesis Physics AUTHOR: Marcela Peláez Infrared correlation functions in Quantum Chromodynamics Supervisors: Matthieu Tissier et Nicolás Wschebor Jury: Mr. Rodolfo Gambini Universidad de la República Mrs. Tereza Mendes Universidade de São Paulo Mr. Bertrand Lafforge Université Paris 6 Mr. Matthieu Tissier Université Paris 6 Mr. Nicolás Wschebor Universidad de la República Mr. Michael Reisenberger Universidad de la República Rapporteur : Mrs. Tereza Mendes Universidade de São Paulo Mr. John Gracey University of Liverpool Acknowledgements Foremost, I would like to express my gratitude to my advisors Nicolás Wschebor and Matthieu Tissier for their continuous support, for their patience and their guidance. I can not imagine writing this thesis without the confidence they gave me. I would like to thank my family Alicia, Fernando and Paula for their love, their support and attention and for always prioritizing my education. I am also grateful to my partner, Pablo Lessa, for all these beautiful years together, for the constant encouragement to continue learning physics, and also for reading this thesis and saying he found it interesting. My sincere thanks also goes to Pablo Pais, for all the interesting discussions and the intense hours shared learning physics. I also want to thank Federico Benitez for reading this thesis and for his insightful comments. I want to thank Andréas Tresmontant also for the discussions and the calculations shared during my stay in Paris. I thank Lucía Duarte and Rodrigo Eyhralde for the difficult courses we attended together. Thanks to all of them for being my friends and to the rest of my friends that supported me through this venture. I thank the Anii and CAP for the financial support. Abstract Infrared correlation functions in Quantum Chromodynamics Abstract The aim of this thesis is to investigate the infrared behaviour of Yang-Mills correlation functions. It is known that the gauge invariance of the theory brings as a consequence the necessity of a gauge fixing procedure in order to compute expectation values analyti- cally. The standard procedure for fixing the gauge is the Faddeev-Popov (FP) procedure which allows one to do perturbation theory in the ultraviolet regime. Perturbative cal- culations using the Faddeev-Popov gauge fixed action successfully reproduce Quantum Chromodynamics observables measured by experiments in the ultraviolet regime. In the infrared regime the coupling constant of the theory computed with the above procedure diverges, and standard perturbation theory does not seem to be valid. However, lattice simulations show that the coupling constant takes finite and not very large value. This suggests that some kind of perturbative calculations should be valid even in the infrared regime. The theoretical justification for the FP procedure depends on the absence of Gribov copies and hence is not valid in the infrared regime (where such copies exist). To correct this we propose to take into account the influence of the Gribov copies by adding a mass term for the gluons in the gauge-fixed Lagrangian, which is a particular case of Curci- Ferrari Lagrangian. The gluon mass term is also motivated by lattice simulations which observe that the gluon propagator behaves as it was massive in the infrared regime. We use this massive extension of the FP gauge fixed action to compute the one loop correction of the two- and three-point correlation functions in the Landau gauge for arbi- trary kinematics and dimension. We investigate the quenched ghost and gluon propagators in detail, and compare the results obtained using two different renormalization schemes. Taking into account the Renormalization Group effects we compare our results with the lattice data available. Once the parameters of our model are fixed so that the propagators match their values in simulations, the same parameters also produce very good matches for the quenched ghost-gluon and three-gluon vertices. We continue our investigation by including dynamical quarks and studying the un- quenched gluon, ghost and quark propagators. The analysis is also extended to the quark- gluon vertex. Our one-loop calculations are enough, in general, to reproduce with good accuracy the lattice data available in the literature. Keywords Quantum Chromodynamics, Gribov copies, Non-perturbative QCD. 6 Fonctions de corrélation infrarouges de la Chromodynamique Quantique Résumé Le but de cette thèse est l’étude des fonctions de corrélation des théries Yang-Mills dans le régime infrarouge. Il est connu que, à cause de l’invariance jauge, il est nécessaire de fixer la jauge pour calculer des valeurs moyennes analytiquement. La procedure de fixation gauge standard est la procedure de Faddeev-Popov (FP). Le Lagrangien de FP permet de faire des calculs perturbatifs pour la Chromodynamique Quantique dans le régime de hautes énergies dont les résultats sont comparés avec succès avec des expériences. Cependant, dans le régime de basses énergies, il se trouve que la constante de couplage, calculée avec la procedure antérieure, diverge. En conséquence, la théorie des perturbations standard n’est plus valide. D’autre part, les simulations du réseau trouvent que la constante de couplage est finie avec une valeur modérée même dans le régime infrarouge. Ceci suggère qu’il devrait exister une manière de faire des calculs perturbatifs également dans le régime infrarouge. Cette différence dans la constante de couplage peut être due au fait que la procedure de FP n’est pas bien justifiée dans ce régime parce qu’elle ignore l’existence des copies de Gribov. Afin de prendre en compte les copies de Gribov, nous proposons de modifier le Lagrangien de FP avec un terme massif pour les gluons. Ce Lagrangien est un cas particulier du Lagrangien de Curci-Ferrari. Cette modification est également justifiée par le fait que le réseau trouve un propagateur du gluon qui paraît massive aux basses énergies. Nous utilisons cette version massive pour calculer à une boucle les fonctions de corré- lations à deux et trois points pour une configuration cinématique générale et en dimension quelconque dans la jauge de Landau. En particulier, nous calculons les propagateurs du gluon et du fantôme sans la présence des quarks et on compare nos résultats avec du réseau. Une fois fixés les paramètres de la théorie, on utilise les mêmes pour comparer les vertex fantôme-gluon et trois-gluons en obtenant un très bon accord avec le réseau. Finalement, on inclut les effets des quarks dynamiques pour étudier les propagateurs du gluon, du fantôme et du quark. L’analyse est aussi faite pour le vertex quark-gluon. On trouve que les comparaisons de notre calcul à une boucle avec les résultat du réseau donnent, en géneral, un très bon accord. Mots-clefs Chromodynamique Quantique, Copies de Gribov, QCD non-perturbative. 7 Funciones de correlación en Cromodinámica Cuántica Resumen La presente tesis investiga el comportamiento de las funciones de correlación de las teorías Yang-Mills en el límite infrarrojo. Como es sabido, para poder calcular valores espera- dos en el marco de estas teorías invariantes gauge, debe realizarse algún procedimiento que permita fijar el gauge. El procedimiento estándar, ultilizado exitosamente para hacer cálculos perturbativos a grandes energías, es el procedimiento de Faddeev-Popov (FP). Los cálculos perturbativos usando el Lagrangiando de Faddeev-Popov para Cromodinámi- ca Cuántica permiten reproducir con éxito los valores obtenidos en los experimentos que involucran la fuerza fuerte a grandes energías. Sin embargo, los cálculos perturbativos usando el Lagrangiano de FP muestran una constante de acoplamiento divergente en el régimen de bajas energía. Por ende, la teoría de perturbaciones en este régimen no es válida. Por otra parte, las simulaciones Monte Carlo, que no implementan dicho procedimiento, encuentran una constante de acoplamiento que se mantiene finita tomando valores no muy grandes incluso a bajas energías. Este hecho sugiere que debe existir alguna forma de teoría de perturbaciones que pueda ser aplicada en el régimen infrarrojo. Esta diferencia encontrada en el comportamiento de la constante de acoplamiento puede deberse al hecho de que el procedimiento de FP no está completamente justificado a bajas energías. Este último ignora la presencia de copias de Gribov en este régimen. Para tener en cuenta la existencia de copias de Gribov, proponemos usar una pequeña modificación del Lagrangiano de FP. Esta consiste en agregar un término de masa para los gluones, caso particular del Lagrangiano de Curci-Ferrari. Otra motivación para considerar el término de masa para los gluones es el hecho de que las simulaciones Monte Carlo muestran que el propagador del gluon se comporta a bajas energías como un propagador masivo. Dicha extensión del Lagrangiano de FP es usada para calcular a un loop las funciones de correlación a dos y tres puntos en el gauge de Landau para una configuración cinemática genérica y en dimensión arbitraria. El primer cálculo está enfocado en el propagador del fantasma y del gluón despreciando el efecto de los quarks.
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