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The access to the contents of this doctoral thesis it is limited to the acceptance of the use conditions set by the following Creative Commons license: https://creativecommons.org/licenses/?lang=en Exploration of the Higgs sector after its discovery Marc Riembau Institut de Física d’Altes Energies Universitat Autònoma de Barcelona Memòria de recerca presentada per a l’obtenció del títol de Doctor en Física Juliol 2018 Exploration of the Higgs sector after its discovery Marc Riembau Director de tesi Christophe Grojean Co-Director de tesi Giuliano Panico Tutor de tesi Oriol Pujolàs ii Resum El descobriment del bosó de Higgs és la culminació d’una recerca que ha durat 40 anys, i completa un marc teòric sota el qual gairebé totes del dades obtingudes de col·lisionadors de partícules poden ser explicades con- sistentment. Simultàniament, i paradoxalment, l’aparent confirmació d’una separacó d’escales entre l’electrofeble i la que suposadament estabilitza la masa del bosó de Higgs posa el relleu el problema de la jerarquia. En la recerca d’una descripció del món que simplifiqui els patrons i simetries del Model Estàndard, l’exploració de l’escala dels TeVs i en particular l’estudi del bosó de Higgs tindran un paper central. En aquesta tesi presentem les possibilitats que el LHC i futurs col·lisionadors proveiran, amb énfasi en la determinació de l’auto-acoblament del bosó de Higgs. També considerarem l’estudi de la producció de bosons electrofebles com a eina per entendre les interaccions dels bosons de Golstone que formen part del doblet de Higgs, mostrant la seva rellevància al combinar-ho amb les dades del pol de la Z i altres cerques al LHC. Finalment, ens centrem en com el moment dipolar elèctric de l’electró posa fortes restriccions en models on el bosó de Higgs és descrit com un estat compost. Abstract The discovery of the Higgs boson culminates a 40-year long hunt and com- pletes a theoretical framework under which almost all collider data can be consistently explained. At the same time, paradoxically, the confirmation of an apparent mass gap above the electroweak scale exacerbates the problem of the electroweak hierarchy. In the search of a description of the world that simplifies the patterns and symmetries of the Standard Model, the ex- ploration of the TeV scale and in particular the study of the Higgs boson will play a central role. In this thesis we explore the possibilities that the LHC and future colliders will bring, with particular emphasis on the deter- mination of the Higgs self-coupling. We also consider the pair production of electroweak bosons as a probe of the Goldstone interactions in the Higgs doublet, and show its relevance as a way to improve the Z pole measure- ments and its interplay with other LHC searches. Finally, we focus on how the electron’s electric dipole moment can set strong constraints on models where the Higgs arises as a composite state. This thesis is based on the following publications • S. Di Vita, C. Grojean, G. Panico, M. Riembau and T. Vantalon, “A global view on the Higgs self-coupling,” JHEP 1709 (2017) 069 [arXiv:1704.01953 [hep-ph]]. • S. Di Vita, G. Durieux, C. Grojean, J. Gu, Z. Liu, G. Panico, M. Riembau and T. Vantalon, “A global view on the Higgs self-coupling at lepton colliders,” JHEP 1802 (2018) 178 [arXiv:1711.03978 [hep-ph]]. • G. Panico, M. Riembau and T. Vantalon, “Probing light top partners with CP violation,” arXiv:1712.06337 [hep-ph]. • M. Carena, Z. Liu and M. Riembau, “Probing Electroweak Phase Transition via Enhanced Di-Higgs Production,” arXiv:1801.00794 [hep-ph]. Further publications during the PhD • J. Elias-Miro, M. Montull and M. Riembau, “The renormalized Hamiltonian truncation method in the large ET expansion,” JHEP 1604 (2016) 144 [arXiv:1512.05746 [hep-th]]. • M. Chala, C. Grojean, M. Riembau and T. Vantalon, “Deciphering the CP nature of the 750GeV resonance,” Phys. Lett. B 760 (2016) 220 [arXiv:1604.02029 [hep-ph]]. • D. de Florian et al. [LHC Higgs Cross Section Working Group], “Handbook of LHC Higgs Cross Sections: 4. Deciphering the Nature of the Higgs Sector,” arXiv:1610.07922 [hep-ph]. Acknowledgements I am grateful to Christophe Grojean for his support. The environment he creates is very fruitful for research and his pursuit for the relevant question to be asked really shaped my scientific view. I am also very thankful to Giuliano Panico. His guidance over all these years has been crucial, and his dedication has been a great inspiration for me. I am thankful to La Caixa-Severo Ochoa program for providing the econom- ical support for this thesis. It has been a fantastic pleasure to work with M. Carena, M. Chala, S. Di Vita, G. Durieux, J. Elias-Miró, C. Grojean, J. Gu, Z. Liu, M. Montull, G. Panico and T. Vantalon. I have very good memories from my stay at IFAE and DESY, as well as from my visit at Fermilab and various schools and conferences. I would like to thank the many students and postdocs I met during this time. In particular, both Marc M. and Thibaud had to suffer my company both in Barcelona and Hamburg, and also to Joan, Mateo, Matteo, Sergi, Clara, Gauthier, Oleksii, Stefano, Jiayin and many others. M’agradaria agrair a la meva família pel suport incondicional, i a la Laura, per absolutament tot. “Not entirely, dear Adso," my master replied. “True, that kind of print expressed to me, if you like, the idea of ‘horse’, the verbum mentis, and would have expressed the same to me wherever I might have found it. But the print in that place and at that hour of the day told me that at least one of all possible horses had passed that way. So I found myself halfway between the perception of the concept ‘horse’ and the knowledge of an individual horse. And in any case, what I knew of the universal horse had been given me by those traces, which were singular. I could say I was caught at that moment between the singularity of the traces and my ignorance, which assumed the quite diaphanous form of a universal idea. If you see something from a distance, and you do not understand what it is, you will be content with defining it as a body of some dimension. When you come closer, you will then define it as an animal, even if you do not yet know whether it is a horse or an ass. And finally, when it is still closer, you will be able to say it is a horse even if you do not yet know whether it is Brunellus or Niger. And only when you are at the proper distance will you see that it is Brunellus (or, rather, that horse and not another, however you decide to call it). And that will be full knowledge, the learning of the singular. So an hour ago I could expect all horses, but not because of the vastness of my intellect, but because of the paucity of my deduction. And my intellect’s hunger was sated only when I saw the single horse that the monks were leading by the halter. Only then did I truly know that my previous reasoning, had brought me close to the truth. And so the ideas, which I was using earlier to imagine a horse I had not yet seen, were pure signs, as the hoofprints in the snow were signs of the idea of ‘horse’; and signs and the signs of signs are used only when we are lacking things." William of Baskerville, talking about Effective Field Theory, in ’The Name of the Rose’ by Umberto Eco vii Contents 1 Introduction2 2 Future colliders 12 3 A global view on the Higgs self-coupling 18 3.1 Introduction . 18 3.2 The effective parametrization . 20 3.2.1 Higgs primary couplings . 20 3.2.2 Additional operators contributing to Higgs observables . 23 3.2.3 Large Higgs self-interactions in a consistent EFT expansion . 26 3.3 Fit from inclusive single-Higgs measurements . 30 3.3.1 Single-Higgs rates and single-Higgs couplings . 31 3.3.2 Global fit including Higgs self-coupling . 38 3.3.3 Impact of the trilinear coupling on single-Higgs couplings . 42 3.4 Double Higgs production . 43 3.5 Differential observables . 46 3.5.1 Impact of single-Higgs differential measurements . 47 3.5.2 Robustness of the fits......................... 49 4 The Higgs self-coupling at future lepton colliders 52 4.1 Introduction . 52 4.2 Low-energy lepton machines . 53 4.2.1 Higher-order corrections to single-Higgs processes . 53 4.2.2 Global analysis . 56 4.2.2.1 Analysis of Higgs data at lepton colliders alone . 56 4.2.2.2 Synergy between measurements at the HL-LHC and lepton-colliders . 60 4.3 High-energy lepton machines . 61 4.3.1 Higgs pair production . 62 viii 4.3.2 Global analysis . 67 4.4 Summary . 69 5 Probing the Electroweak Phase Transition via Enhanced Di-Higgs Produc- tion 76 5.1 Introduction . 76 5.2 Model framework . 77 5.2.1 Stability, Unitarity and EWSB conditions .