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UNIVERSIDADE ESTADUAL DE CAMPINAS Instituto De F´Isica Gleb Wataghin UNIVERSIDADE ESTADUAL DE CAMPINAS Instituto de F´ısica Gleb Wataghin CLARA TEIXEIRA FIGUEIREDO ASPECTS OF DYNAMICAL MASS GENERATION WITHIN THE FORMALISM OF SCHWINGER-DYSON EQUATIONS Aspectos da gera¸c~ao de massa din^amica dentro do formalismo das equa¸c~oesde Schwinger-Dyson CAMPINAS 2020 Clara Teixeira Figueiredo Aspects of dynamical mass generation within the formalism of Schwinger-Dyson equations Aspectos da gera¸c~ao de massa din^amica dentro do formalismo das equa¸c~oes de Schwinger-Dyson Tese apresentada ao Instituto de F´ısica \Gleb Wataghin" da Universidade Estadual de Campinas como parte dos requisitos exigidos para a obten¸c~ao do t´ıtulo de Doutora em Ci^encias, na ´area de F´ısica. Thesis presented to the \Gleb Wataghin" Institute of Physics of the University of Campinas in par- tial fulfillment of the requirements for the degree of Doctor of Science, in the area of Physics. Orientador: Arlene Cristina Aguilar Este exemplar corresponde a` versao~ fi- nal da tese defendida pela aluna Clara Teixeira Figueiredo e orientada pela Profa. Dra. Arlene Cristina Aguilar. Campinas 2020 Ficha catalográfica Universidade Estadual de Campinas Biblioteca do Instituto de Física Gleb Wataghin Lucimeire de Oliveira Silva da Rocha - CRB 8/9174 Figueiredo, Clara Teixeira, 1991- F469a FigAspects of dynamical mass generation within the formalism of Schwinger- Dyson equations / Clara Teixeira Figueiredo. – Campinas, SP : [s.n.], 2020. FigOrientador: Arlene Cristina Aguilar. FigTese (doutorado) – Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin. Fig1. QCD não perturbativa. 2. Schwinger-Dyson, Equações de. 3. Geração de massa dinâmica. I. Aguilar, Arlene Cristina, 1977-. II. Universidade Estadual de Campinas. Instituto de Física Gleb Wataghin. III. Título. Informações para Biblioteca Digital Título em outro idioma: Aspectos da geração de massa dinâmica dentro do formalismo das equações de Schwinger-Dyson Palavras-chave em inglês: Non-perturbative QCD Schwinger-Dyson Equations Dynamical mass generation Área de concentração: Física Titulação: Doutora em Ciências Banca examinadora: Arlene Cristina Aguilar [Orientador] Adriano Antonio Natale Attilio Cucchieri Márcio José Menon Jun Takahashi Data de defesa: 20-08-2020 Programa de Pós-Graduação: Física Identificação e informações acadêmicas do(a) aluno(a) - ORCID do autor: https://orcid.org/0000-0002-3995-5934 - Currículo Lattes do autor: http://lattes.cnpq.br/6035273307680376 Powered by TCPDF (www.tcpdf.org) MEMBROS DA COMISSÃO JULGADORA DA TESE DE DOUTORADO DE CLARA TEIXEIRA FIGUEIREDO – RA 123161 APRESENTADA E APROVADA AO INSTITUTO DE FÍSICA “GLEB WATAGHIN”, DA UNIVERSIDADE ESTADUAL DE CAMPINAS, EM 20 / 08 / 2020. COMISSÃO JULGADORA: - Profa. Dra. Arlene Cristina Aguilar– Orientador – IFGW/UNICAMP - Prof. Dr. Adriano Antonio Natale – IFT/USP - Prof. Dr. Attilio Cucchieri – IF/USP - Prof. Dr. Marcio José Menon – IFGW/UNICAMP - Prof. Dr. Jun Takahashi – IFGW/UNICAMP OBS.: Ata da defesa com as respectivas assinaturas dos membros encontra-se no SIGA/Sistema de Fluxo de Dissertação/Tese e na Secretaria do Programa da Unidade. CAMPINAS 2020 Acknowledgements Firstly, I would like to express my deepest gratitude to my supervisor Professor Cristina Aguilar for the several years of dedicated guidance and for the advice provided throughout my time as her student. I have been extremely blessed to have her as my supervisor. I would also like to extend my sincere gratitude to Professor Joannis Papavassiliou for welcoming me in Valencia, supervising my work there, and teaching me so much. I also wish to thank my colleague Mauricio N. Ferreira for the discussions and assis- tance provided during the research process. Special thanks to the IFGW Professors Jun Takahashi, Marcelo M. Guzzo, Marcio J. Menon, Orlando L. Goulart, and Pedro C. de Holanda for participating in the evaluation committees and contributing with suggestions and questionings. I would also like to thank Professors Adriano A. Natale and Attilio Cucchieri for their disposition to evaluate and contribute to this work as members of the thesis examination committee. I would like to acknowledge the financial support from S~aoPaulo Research Foundation (FAPESP) through the Grants No. 2016/11894-0 and No. 2018/09684-3. I also wish to acknowledge the support provided by the Brazilian National Council for Scientific and Technological Development (CNPq) under Grant No. 142228/2016-8. I would also like to acknowledge that this study was financed in part by the Coordena¸c~aode Aperfei¸coamento de Pessoal de N´ıvel Superior - Brasil (CAPES) - Finance Code 001. I would also like to thank the staff of the\Gleb Wataghin"Institute of Physics (IFGW), the University of Campinas (UNICAMP), and the University of Valencia (UV) for offering the structure and resources needed for the realization of this research project. Thanks should also go to my family and friends who have supported me during these years. In particular, I am sincerely grateful to my husband, Paulo Henrique, for the love and support in any circumstance. I am also deeply indebted to my parents, M´arcia and Ricardo, for their constant care and encouragement. In addition, I would also like to thank my brother, Pedro, for his fellowship and assistance whenever needed. Many thanks to my friend Ren´efor our conversations and his constant disposition to aid in both personal and academic matters. I would also like to extend my thanks to my friends at the University of Valencia for making my time there so pleasant and at the University of Campinas for all the conversations and encouragement during these years. Finally, I praise God for his grace, sustaining me every day, and for placing all of these people in my life. Resumo Neste trabalho estudamos a gera¸c~ao de uma massa din^amica para o gluon na regi~ao n~ao-perturbativa de QCD usando o formalismo de equa¸c~oesde Schwinger-Dyson. Apre- sentamos uma an´alise geral que preserva a transversalidade da autoenergia do gluon, exigida pela simetria de gauge n~ao-Abeliana da teoria, e resulta em um propagador de gluon finito na regi~ao infravermelha, corroborando os resultados de v´arias simula¸c~oes de QCD na rede. Esse estudo ´erealizado dentro do formalismo conhecido como Pinch Tech- nique e sua correspond^encia com Background Field Method, e faz uso das identidades de Ward satisfeitas pelos v´ertices n~ao-perturbativos e de uma identidade especial, chamada identidade de seagull. O resultado dessas considera¸c~oes ´eque o gluon pode adquirir uma massa din^amica somente quando polos longitudinalmente acoplados s~ao incorporados aos v´ertices da teoria. Tais polos representam excita¸c~oes de estado ligado n~ao-massivas, que podem ser estudadas dentro do contexto de equa¸c~oes de Bethe-Salpeter. Trabalhos ante- riores sobre a din^amica desses estados ligados consideram a possibilidade de polo somente no v´ertice de tr^es-gluons, negligenciando efeitos de poss´ıveis polos nos demais v´ertices. Aqui, estudamos o impacto do setor de ghost na equa¸c~ao din^amica que descreve a cria¸c~ao desses polos. Essa an´alise revela que a contribui¸c~ao do polo associado ao v´ertice ghost- gluon ´esuprimida na gera¸c~ao din^amica de massa do gluon. Adicionalmente, estudamos a equa¸c~aoda massa do gluon no gauge de Landau, levando em conta a sua estrutura n~ao- linear completa, diferentemente de trabalhos pr´evios, nos quais essa equa¸c~ao´elinearizada ao considerar o propagador de gluon como uma fun¸c~ao externa. Com isso, a indeter- mina¸c~aona escala da massa glu^onica encontrada nas an´alises anteriores ´eeliminada. A renormaliza¸c~aomultiplicativa da equa¸c~aoda massa ´erealizada de acordo com um m´e- todo aproximado, inspirado no tratamento dado `amassa din^amica dos quarks. A massa glu^onica resultante ´epositiva-definida e monotonicamente decrescente e o propagador de gluon, constru´ıdo a partir dessa massa, est´ade acordo com os dados de simula¸c~oes de redes de grande volume. Palavras-chave: QCD n~ao-perturbativa. Equa¸c~oes de Schwinger-Dyson. Gera¸c~ao de massa din^amica. Abstract In this work, we study the generation of a dynamical mass for the gluon in the nonper- turbative region of QCD using the formalism of Schwinger-Dyson equations. We present a general analysis that preserves the transversality of the gluon self-energy, required from the non-Abelian gauge symmetry of the theory, and results in the infrared finiteness of the gluon propagator observed in several lattice simulations. This study is done within the Pinch Technique formalism, and its correspondence with the Background Field Method, and relies on the Ward identities satisfied by the nonperturbative vertices and a special identity named seagull identity. The result of these considerations is that the gluon can only acquire a dynamical mass when longitudinally coupled massless poles are incorpo- rated into the vertices of the theory. These poles act as colored massless bound state excitations and can be studied under the context of Bethe-Salpeter equations. Previous works on the dynamics of such bound states considered only the possibility of a pole in the three-gluon vertex, neglecting effects from possible poles in the remaining vertices. Here, we study the impact that the ghost sector may have on the dynamical equation that describes the creation of such poles. This analysis reveals that the contribution of the pole associated with the ghost-gluon vertex is suppressed. We also study the gluon mass equation in the Landau gauge, taking into account its full nonlinear structure, con- trary to what has been done in previous works, in which this equation was linearized by considering the gluon propagator as an external input. This eliminates the indeterminacy in the scale of the mass found in these previous analyses. In addition, our treatment of the multiplicative renormalization of the mass equation is carried out according to an approximate method inspired in several works about the quark gap equation.
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