A Feynman Rules for Vectorlike Quarks 53

Phenomenology of Trinification models João Fonseca Seabra Thesis to obtain the Master of Science Degree in Engineering Physics Supervisors: Prof. Doutor Filipe Rafael Joaquim Prof. Doutor David Emanuel da Costa Examination Committee Chairperson: Prof.a Doutora Maria Teresa Haderer de la Peña Stadler Supervisor: Prof. Doutor Filipe Rafael Joaquim Member of the Committee: Doutor Joaquim Inácio da Silva Marcos November 2017 Acknowledgements Besides all the effort that I had put into this work, it surely would not be the same withoutthe help of many people. First of all, I devote a special acknowledgement to Professor Filipe Joaquim, not only for his guidance and support during the development of this work, but also for being the person who really convinced me through his lectures that Particle Physics is an amazing subject. I am also very grateful to Professor David Costa for his guidance. Even after leaving IST, he was always available to answer my doubts and questions. I would also like to thank my colleagues in IST for all the great discussions and study sessions that I had the fun and the pleasure to share with them during these years. Finally, a big ”thank you” to my family for their everlasting patience and support. i ii Resumo A compreensão do fenómeno de violação da simetria Conjugação de carga e Paridade (CP) tem-se revelado como um grande desafio em Física de Partículas. De facto, uma forte evidência dequeo Modelo Padrão (MP) precisa de ser expandido reside na sua incapacidade de dar resposta a questões estreitamente relacionadas com violação de CP, tais como a assimetria bariónica do Universo. Na presente dissertação, estudamos extensões do MP com quarks vectorlike, dando particular ênfase aos modelos de Trinificação. Nestas Teorias de Grande Unificação, o sector fermiónico encontra-se associado a representações fundamentais do grupo E6, o que leva naturalmente ao aparecimento de um quark vectorlike em cada geração de fermiões. Como consequência da mistura que pode haver entre quarks vectorlike e quarks do MP, surgem novas fontes de violação de CP. Além disso, esta mistura afecta os acoplamentos dos quarks do MP a outras partículas, o que nos leva a analisar as restrições experimentais impostas aos quarks vectorlike. Discutimos também a possibilidade de encontrar violação espontânea de CP (VECP) em modelos de Trinificação. Ao contrário do MP onde violação de CP só pode ocorrer ao nível do Lagrangiano, al- gumas teorias que prevêem a existência de um maior número de campos escalares (tal como os modelos de Trinificação) permitem que a simetria CP possa ser quebrada espontaneamente pelo vácuo. Neste contexto, verificamos que a introdução de quarks vectorlike num modelo de Trinificação com VECP leva-nos a obter uma matriz Cabibbo-Kobayashi-Maskawa complexa, compatível com os resultados experimentais. Palavras-Chave: Matriz Cabibbo-Kobayashi-Maskawa, Modelos de Trinificação, Quarks vectorlike, Teorias de Grande Unificação, Violação de CP iii iv Abstract Understanding the phenomenon of violation of the symmetry Charge conjugation and Parity (CP) reveals itself as a great challenge in Particle Physics. In fact, a strong evidence that the Standard Model (SM) needs to be extended stems from its inability to provide an answer to questions deeply connected with CP violation, such as the baryonic asymmetry of the Universe. In this thesis, we study SM extensions with vectorlike quarks, giving special attention to Trini- fication models. In these Grand Unified Theories (GUTs), fermions are assigned to fundamental representations of the group E6, leading naturally to the appearance of one vectorlike quark in each generation of fermions. As a consequence of the mixing that may occur between vectorlike quarks and SM quarks, new sources of CP violation arise. Moreover, this mixing affects the couplings of SM quarks to other particles and, for this reason, we will look at the experimental constraints imposed on vectorlike quarks. We also discuss the possibility of having spontaneous CP violation (SCPV) in Trinification models. While in the SM CP violation can only occur at the Lagrangian level, some theories that predict the existence of a bigger number of scalar fields (such as Trinification models) allow CP to be broken spontaneously by the vacuum. In this context, we verify that the introduction of vectorlike quarks in a Trinification model with SCPV leads to a complex Cabibbo-Kobayashi-Maskawa matrix, in agreement with experimental data. Keywords: Cabibbo-Kobayashi-Maskawa matrix, CP violation, Grand Unified Theories, Trinifi- cation models, Vectorlike quarks v vi Contents Acknowledgements i Resumo iii Abstract v List of Figures ix List of Tables xi List of Abbreviations xiii 1 Introduction 1 1.1 The discrete symmetries C, P, CP and T . 2 1.2 CP violation in the SM . 4 1.3 From the SM to GUTs . 5 2 The Standard Model of Particle Physics 7 2.1 Field content and Lagrangian . 7 2.2 The Higgs mechanism . 10 2.3 Charged and Neutral interactions . 11 2.4 Fermion masses and mixing . 12 2.5 Open questions in Particle Physics . 16 3 SM extensions with Vectorlike Quarks 19 3.1 Vectorlike quark representations . 20 3.2 SM extensions with SU(2)L singlets of vectorlike quarks . 20 3.2.1 Mass matrix diagonalization . 23 3.2.2 Quark mixing and suppression of FCNCs . 25 3.2.3 Complex phases of the generalized CKM matrix . 25 3.3 Mixing with third generation of SM quarks . 26 3.4 Experimental status of vectorlike B quarks . 27 3.4.1 Production at the LHC and mass constraints . 27 3.4.2 Mixing constraints . 29 4 Trinification Models 31 4.1 Trinification group and field content . 32 4.2 Scalar Lagrangian and SSB . 34 4.3 Fermion masses and mixing . 42 vii 5 Concluding Remarks 47 Bibliography 49 A Feynman rules for Vectorlike Quarks 53 B Representations of the Trinification group 55 B.1 The G333 Generators . 55 B.2 24 and 27 Representations . 56 viii List of Figures 1.1 The status of weak interactions in 1966 . 1 1.2 Parity transformation . 2 1.3 Charge conjugation . 3 1.4 CP transformation . 3 2.1 Unitarity triangle . 16 2.2 Experimental constraints on the (ρ, η) plane to the CKM parameters . 17 3.1 Vectorlike B quark production . 27 3.1(a) Pair production . 27 3.1(b) Single production involving a Z boson . 27 3.1(c) Single production involving a W boson . 27 3.2 Branching ratios of the B quark . 28 3.3 Lower limits for the B quark mass in the branching ratio plane BR(B → W t) versus BR(B → Hb) ......................................... 28 3.3(a) Observed 95% Confidence Level . 28 3.3(b) Expected 95% Confidence Level . 28 3.4 Experimental constraints on the mixing between b and B quarks . 30 ix x List of Tables 2.1 The SM Gauge fields and their representation properties. 7 2.2 Fermionic fields of the SM . 8 2.3 Fit results for the Wolfenstein parameters . 16 3.1 SM predictions and experimental results for the observables affected by changing the Zbb coupling . 29 4.1 Numerical values of the scalar potential and VEV parameters compatible with the observation of a SM Higgs boson with mass mH ∼ 125 GeV . 40 4.2 Masses of quarks computed at the electroweak scale . 44 4.3 Best fits of the effective down-quark matrix of the Trinification model totheCKM parameters and down-quark masses . 46 xi xii List of Abbreviations CC Charged Current CKM Cabibbo-Kobayashi-Maskawa CP Charge conjugation and Parity EWSB Electroweak Symmetry Breaking FCNC Flavor Changing Neutral Current GUT Grand Unified Theory NC Neutral Current QFT Quantum Field Theory SCPV Spontaneous Charge conjugation and Parity Violation SM Standard Model SSB Spontaneous Symmetry Breaking VEV Vacuum Expectation Value xiii xiv 1 Introduction While reflecting upon the status of weak interactions at the 1966 Berkeley Conference, Nicola Cabibbo used the cartoon shown in Fig. 1.1 to reinforce the idea that besides some good progresses were being made on the subject of weak interactions, there was a big problem to be solved. Fig. 1.1: The status of weak interactions in 1966 according to N. Cabibbo (image taken from [1]). The cartoon depicts pretty well how Charge-Parity (CP) violation was a big mystery of weak interactions two years after its discovery. But since then, more than half a century has passed and one may ask: Do we understand CP violation nowadays? We could start answering by saying that our knowledge on the subject has increased significantly. For many years we could only observe CP violation in the kaon system but today, we are able to observe it in the B-meson system too. Moreover, the explanation found in the Standard Model (SM) for CP violation in terms of the Cabibbo-Kobayashi-Maskawa (CKM) mechanism is in agreement with all measurements made up to date on those systems [2]. However, we should say at this point that the SM is not a complete theory and it leaves many open questions in Particle Physics, some concerned with CP violation. For example, we know that it occurs, but there is no definite explanation for its origin. On the other hand, it is well established that CP Violation is a crucial ingredient for baryogenesis [3], the process of dynamically generating the matter-antimatter asymmetry of the Universe. In the SM, the CKM mechanism fails to accommodate the observed asymmetry by several orders of magnitude [4]. We then conclude that the cartoon of Figure 1.1 is still relevant today, in spite of the discoveries we have made so far about CP violation. It also reveals the importance the subject of CP violation has. After all, if there was no matter-antimatter asymmetry in our Universe, we would not be here to 1 discuss it.

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