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Scalar Fields in Particle Physics UNIVERSIDADE DE LISBOA INSTITUTO SUPERIOR TÉCNICO Scalar Fields in Particle Physics Leonardo Antunes Pedro Supervisor: Doctor Gustavo da Fonseca Castelo Branco Thesis approved in public session to obtain the PhD Degree in Physics Jury final classification: Pass With Merit Jury Chairperson: Chairman of the IST Scientific Board Members of the Committee: arXiv:1608.01928v1 [hep-ph] 5 Aug 2016 Doctor Francisco José Botella Olcina Doctor Gustavo da Fonseca Castelo Branco Doctor Jorge Manuel Rodrigues Crispim Romão Doctor Maria Margarida Nesbitt Rebelo da Silva Doctor Paulo André de Paiva Parada Doctor David Emanuel da Costa 2015 UNIVERSIDADE DE LISBOA INSTITUTO SUPERIOR TÉCNICO Scalar Fields in Particle Physics Leonardo Antunes Pedro Supervisor: Doctor Gustavo da Fonseca Castelo Branco Thesis approved in public session to obtain the PhD Degree in Physics Jury final classification: Pass With Merit Jury Chairperson: Chairman of the IST Scientific Board Members of the Committee: Doctor Francisco José Botella Olcina, Full Professor, Instituto de Física Corpuscular, Universitat de València, Spain Doctor Gustavo da Fonseca Castelo Branco, Full Professor, Instituto Superior Técnico, Universidade de Lisboa Doctor Jorge Manuel Rodrigues Crispim Romão, Full Professor, Instituto Superior Técnico, Universidade de Lisboa Doctor Maria Margarida Nesbitt Rebelo da Silva, Principal Researcher, Instituto Superior Técnico, Universidade de Lisboa Doctor Paulo André de Paiva Parada, Assistant Professor, Faculdade de Ciências, Universidade da Beira Interior Doctor David Emanuel da Costa, Assistant Researcher, Instituto Superior Técnico, Universidade de Lisboa Funding Institutions Fundação para a Ciência e a Tecnologia 2015 | Campos escalares em Física de Partículas Leonardo Antunes Pedro Doutoramento em Física Orientador Doutor Gustavo da Fonseca Castelo Branco Resumo Alargar o sector escalar ajuda a estudar o mecanismo de Higgs e alguns problemas do Modelo Padrão. Implementamos a correspondência entre os estados elementares dependentes de gauge e os estados assimptóticos não-perturbativos invariantes de gauges não-abelianas, necessários para estudar a fenomenologia não-perturbativa de dois-dubletos-Higgs. A violação de sabor e CP nos dados experimentais obedece a um padrão hierárquico, aco- modado pelo Modelo Padrão. Definimos a condição de Violação Mínima de Sabor com seis espuriões em teorias de campo efectivas, implicando violação de sabor e CP inteiramente de- pendente das matrizes de mistura dos fermiões mas independente da hierarquia das massas dos fermiões; é invariante sobre o grupo de renormalização. Estudamos a fenomenologia de modelos de dois-dubletos-Higgs, que verificam a condição definida como consequência de uma simetria; novas partículas escalares leves, mediando corren- tes neutras que violam o sabor, são permitidas pelos dados de sabor sem coeficientes de sabor extra; testámos os modelos com bibliotecas de C++ ligadas pela biblioteca simbólica GiNaC e propomos mais bibliotecas para uma procura por correntes neutras que violam o sabor. Mapeamos as representações do grupo de Poincare complexas para as reais, derivamos a equação de Dirac livre requerendo localizabilidade covariante das representações e estudamos Localização e simetrias de gauge. Palavras-chave modelo de dois-dubletos-Higgs; estados assimptóticos; mecanismo de Higgs; Violação de Sabor Mínima; Correntes Violadoras de Sabor; cálculo simbólico; representação real; grupo de Poincare; Localização; spinor de Majorana. iv | Scalar Fields in Particle Physics Abstract Extending the scalar sector helps in studying the Higgs mechanism and some Standard Model problems. We implement the correspondence between the gauge-dependent elementary states and the non-perturbative non-abelian gauge-invariant asymptotic states, necessary to study the non- perturbative phenomenology of two-Higgs-doublet models. The Flavour and CP violation in experimental data follows a hierarchical pattern, accounted by the Standard Model. We define the Minimal Flavour Violation condition with six spurions in effective field theories, implying Flavour and CP violation entirely dependent on the fermion mixing matrices but independent of the fermion masses hierarchy; it is renormalization-group invariant. We study the phenomenology of renormalizable two-Higgs-doublet models which verify the defined condition as consequence of a symmetry; new light physical scalars, mediating Flavour Changing Neutral Currents, are allowed by flavour data without flavour coefficients beyond the Standard Model; we tested the models with C++ libraries linked by the symbolic skills of the GiNaC library and we propose more libraries supporting a systematic search for Flavour Changing Neutral Currents. We also map the complex to the real Poincare group representations, derive the free Dirac equation requiring covariant localizability of the representations and study Localization and gauge symmetries in Quantum Field Theory. Keywords two-Higgs-doublet model; Asymptotic states; Higgs mechanism; Minimal Flavour Violation; Flavour Changing Neutral Currents; computer algebra system; real representation; Poincare group; localization; Majorana spinor. v | Acknowledgments Da daaa da. Daaaa da da.— Joana Pais Pedro (2014) When a person asks me to solve a problem which is time consuming and it is clear what is the purpose, sometimes I study if there is a solution to another problem which would serve the same purpose in a better way. My sister says “tu és um chato” and my friends used to say “mó, só és esperto para a escola!”, so the person usually don’t like my alternative solution (“mó” is an exclamation used in Algarve). I don’t make it easy for them but still, my family and friends, supervisor and collaborators, professors and colleagues have provided me all the necessary guidance, autonomy and support to do this thesis and related work. Without their help, I would have other concerns and I couldn’t focus in studying and solving physics problems. I am thankful to: • My family and friends; • My supervisor and collaborator Gustavo Branco; my collaborators Francisco Botella, Adrian Car- mona, Miguel Nebot, Margarida Rebelo; • Members of the CFTP Lisboa and Physics and Mathematics Departments of Técnico-Lisboa, IFIC València, ETH Zürich, CERN-TH and Institut für Physik UNI-GRAZ, where the work took place. Including Renato Fonseca, José Mourão, David Emmanuel-Costa and José Natário for their help related to the real representations of the Poincare group; Nuno Ribeiro, David Forero, Luís Lavoura and Jorge Romão for their help related to the phenomenology of the BGL models; Axel Maas, Wolfgang Schweiger, Elmar Biernat and António Figueiredo for their kind hospitality and help related to the non-perturbative phenomenology; Axel Maas also for his availability for an ongoing collaboration; • Current and former members of the LIP-Lisboa CMS group, including Pedro Martins, Pedro Silva, João Pela and Michele Gallinaro for their advices and availability for a collaboration which did not happened due to lack of time; also Joaquim Silva-Marcos from CFTP Lisboa and Palash Pal from Saha Institute of Nuclear Physics for the same reasons. I acknowledge the support—provided through the grant SFRH/BD/70688/2010 from the Fundação para a Ciência e a Tecnologia—of the Portuguese State. This thesis is based in part in the following publications and citeable papers (co)authored by the present author: • “Physical constraints on a class of two-Higgs doublet models with FCNC at tree level”, with F. J. Botella, G. C. Branco, A. Carmona, M. Nebot, and M. N. Rebelo, JHEP 7 (2014) 78; • “On the real representations of the Poincare group”, arXiv:1309.5280, 2013; • “The Majorana spinor representation of the Poincare group”, arXiv:1307.1853, 2013. The last two papers were not published yet because the author needs to discuss them further within the physics community (in particular mathematical physics), a process that requires some time and patience. This is expected, for estabilished authors in HEP the process of publishing a paper in a good journal can easily take six months, so for someone not yet estabilished it can easily go beyond one year. vi | Contents 1 Introduction 1 1.1 Particle Physics . .1 1.2 Contributions from Social and Computer Sciences, Mathematics and Quantum Foundations . .3 1.3 Beyond the Standard Model: a modular approach . .5 I Higgs mediated Flavour Violation9 2 Non-perturbative phenomenology of the two-Higgs-doublet model9 2.1 Custodial symmetry and the Higgs mechanism . 10 2.2 Asymptotic states . 11 2.3 Background symmetries . 13 2.4 two-Higgs-doublet model . 13 2.5 Photons . 16 2.6 Fermions . 18 2.7 Higgs doublets in an arbitrary Higgs basis . 20 3 Higgs mediated Flavour Violation 21 3.1 Correlations are important in data analysis . 21 3.2 Top-down and Bottom-up approaches . 24 3.3 Minimal Flavour Violation . 25 3.3.1 Minimal Flavour Violation with six spurions . 26 3.3.2 Renormalization group evolution of Minimal Flavour Violation . 27 3.3.3 Comparison of Minimal Flavour Violation definitions . 28 3.4 BGL models . 29 3.5 A contribution for a systematic search for FCNCs . 33 4 Physical constraints on the BGL models 39 4.1 Analysis details . 40 4.2 Confronting experimental results . 43 4.2.1 Generalities . 43 4.2.2 Processes mediated by charged scalars at tree level . 45 4.2.3 Processes mediated by neutral scalars at tree level . 48 4.2.4 Loop level processes . 52 4.3 Results . 58 vii II On the real representations of the Poincare group 63 5 On the real representations of the Poincare group 63 5.1 Introduction . 64 5.1.1 Motivation . 64 5.1.2 Systems on real and complex Hilbert spaces . 65 5.1.3 Finite-dimensional representations of the Lorentz group . 65 5.1.4 Unitary representations of the Poincare group . 66 5.1.5 Energy Positivity . 68 5.2 Systems on real and complex Hilbert spaces . 69 5.2.1 The map from the complex to the real systems . 70 5.2.2 Schur Systems . 71 5.2.3 Finite-dimensional representations . 72 5.2.4 Unitary representations and Systems of Imprimitivity . 73 5.2.5 Systems of Imprimitivity . 74 5.3 Finite-dimensional representations of the Lorentz group .
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