Licentiate Thesis Phenomenology of SO(10) Grand Unified Theories Marcus Pernow Particle and Astroparticle Physics, Department of Physics, School of Engineering Sciences, KTH Royal Institute of Technology, SE-106 91 Stockholm, Sweden Stockholm, Sweden 2019 Typeset in LATEX Vetenskaplig uppsats f¨or avl¨aggande av teknologie licentiatexamen (TeknL) inom ¨amnesomr˚adetfysik. Scientific thesis for the degree of Licentiate of Engineering (Lic Eng) in the subject area of Physics. ISBN 978-91-7873-269-2 TRITA-SCI-FOU 2019:38 c Marcus Pernow, September 2019 Printed in Sweden by Universitetsservice US AB Abstract Although the Standard Model (SM) of particle physics describes observations well, there are several shortcomings of it. The most crucial of these are that the SM cannot explain the origin of neutrino masses and the existence of dark matter. Furthermore, there are several aspects of it that are seemingly ad hoc, such as the choice of gauge group and the cancellation of gauge anomalies. These shortcomings point to a theory beyond the SM. Although there are many proposed models for physics beyond the SM, in this thesis, we focus on grand unified theories based on the SO(10) gauge group. It predicts that the three gauge groups in the SM unify at a higher energy into one, which contains the SM as a subgroup. We focus on the Yukawa sector of these models and investigate the extent to which the observables such as fermion masses and mixing parameters can be accommodated into different models based on the SO(10) gauge group. Neutrino masses and leptonic mixing parameters are particularly interesting, since SO(10) models naturally embed the seesaw mechanism. The difference in energy scale between the electroweak scale and the scale of unification spans around 14 orders of magnitude. Therefore, one must relate the parameters of the SO(10) model to those of the SM through renormalization group equations. We investigate this for several different models by performing fits of SO(10) models to fermion masses and mixing parameters, taking into account thresholds at which heavy right-handed neutrinos are integrated out of the the- ory. Although the results are in general dependent on the particular model under consideration, there are some general results that appear to hold true. The observ- ables of the Yukawa sector can in general be accommodated into SO(10) models only if the neutrino masses are normally ordered and that inverted ordering is strongly disfavored. We find that the observable that provides the most tension in ` the fits is the leptonic mixing angle θ23, whose value is consistently favored to be lower in the fits than the actual value. Furthermore, we find that numerical fits to the data favor type-I seesaw over type-II seesaw for the generation of neutrino masses. Key words: Grand unified theories, renormalization group equations, neutrino masses, gauge coupling unification. iii Sammanfattning Trots att partikelfysikens standardmodell beskriver observationer v¨al s˚ahar den ett antal brister. De mest framtr¨adande av dessa ¨ar att standardmodellen inte kan beskriva ursprunget av neutrinernas massa samt existensen av m¨ork materia. Dessutom verkar ett antal av dess aspekter ad hoc, s˚asom valet av gaugegrupp och att gaugeanomalierna ov¨antat tar ut varandra Dessa brister pekar mot en teori bortom standardmodellen. Trots att det finns m˚angaf¨orslag till modeller f¨or fysik bortom standardmodellen s˚afokuserar vi p˚a storf¨orenade teorier baserade p˚agaugegruppen SO(10). Den f¨orutsp˚aratt de tre gaugegrupperna i standardmodellen f¨orenas vid en h¨og energiskala. Denna f¨orenade gaugegrupp inneh˚allerstandardmodellen som en delgrupp. Vi fokuserar s¨arskilt p˚aYukawasektorn hos dessa modeller och unders¨oker i vilken omfattning som observabler s˚asomfermionmassor och blandningsparametrar kan rymmas i olika modeller baserade p˚aSO(10)-gaugegruppen. Neutrinomassor och leptonska bland- ningsparametrar ¨ar s¨arskilt intressanta eftersom SO(10)-modeller inneh˚allergung- br¨ademekanismen. Skillnaden i energiskala mellan den elektrosvaga skalan och f¨oreningsskalan str¨acker sig ¨over 14 storleksordningar. D¨arf¨or b¨or man relatera parametrarna i SO(10)-modellen till de i standardmodellen genom renormeringsgruppsekvationer. Vi unders¨oker detta f¨or ett antal olika modeller genom att utf¨ora numeriska an- passningar av SO(10)-modeller till fermionmassor och blandningsparametrar och tar h¨ansyn till tr¨osklar vid vilka de tunga h¨ogerh¨anta neutrinerna integreras ut ur teorin. Trots att resultaten i regel beror p˚aden s¨arskilda modellen som studeras s˚afinner vi ett antal resultat som verkar g¨alla allm¨ant. Observablerna i Yukawa- sektorn kan allm¨ant sett rymmas i SO(10)-modeller endast om neutrinomassorna ¨ar normalt ordnade och inverterad ordning ¨ar starkt missgynnad. Vi finner att ` den observabel som ¨ar sv˚arastatt anpassa till ¨ar blandningsvinkeln θ23 vars v¨arde fr˚ananpassningarna konsekvent ¨ar l¨agre ¨an det faktiska v¨ardet. Dessutom finner vi att numeriska anpassningar till data gynnar typ-I-gungbr¨ademekanismen ¨over typ-II-gungbr¨ademekanismen f¨or genereringen av neutrinomassor. Nyckelord: Storf¨orenade teorier, renormeringsgruppsekvationer, neutrinomas- sor, gaugekopplingsf¨orening. iv Preface This thesis is the result of my research at the Department of Physics from August 2017 to October 2019. The first part of the thesis presents an introduction to the subjects relevant to the scientific work of this thesis. These include the Standard Model and its shortcomings, grand unification and SO(10), as well as renormaliza- tion group equations and the numerical methods used. The second part contains the three papers that my research has resulted in. List of papers The scientific papers included in this thesis are: Paper (I) [1] T. Ohlsson and M. Pernow Running of fermion observables in non-supersymmetric SO(10) models J. High Energy Phys. 11, 028 (2018) arXiv:1804.04560 Paper (II) [2] S. M. Boucenna, T. Ohlsson and M. Pernow A minimal non-supersymmetric SO(10) model with Peccei{Quinn symmetry Phys. Lett. B 792, 251 (2019) arXiv:1812.10548 Paper (III) [3] T. Ohlsson and M. Pernow Fits to non-supersymmetric SO(10) models with type I and II seesaw mecha- nisms using renormalization group evolution J. High Energy Phys. 06, 085 (2019) arXiv:1903.08241 v vi Preface The thesis author's contribution to the papers I participated in the scientific work as well as in the writing of all papers included in this thesis. I am also the corresponding author of all three papers. 1. I modified large parts of the code and ran all numerical computations. All figures were produced by me and I wrote the majority of the paper. 2. All calculations were performed by me and I wrote the code for the numerical computations. I produced all figures and wrote large parts of the paper. 3. I performed all numerical computations, produced all figures, and wrote most of the paper. Preface vii Acknowledgements My sincerest thanks go to my supervisor Tommy Ohlsson for taking me on as his PhD student and giving me the opportunity to do research in theoretical particle physics, and for suggesting that I apply to Stiftelsen Olle Engkvist Byggm¨astare for funding. Thank you for the guidance and advice that you have given as well as for the scientific collaboration that led to the papers included in this thesis. The two years of my PhD studies that culminated in this thesis were made possible by financial support from Stiftelsen Olle Engkvist Byggm¨astare.I am very grateful to that foundation for accepting my application. Thank you to the members of the theoretical particle physics group. I am especially grateful to Sofiane for all the discussions about physics and everything else. These discussions really helped me to understand the process of model building in particle physics. Thank you also to my former office mate Stefan for making the office a nice environment and for the many discussions about physics and teaching. Thank you Mattias for being such a great motivator and competitor in the gym. Many thanks are due to all the people of the former theoretical physics group for pleasant lunch discussions, fika and after-work beers. Thank you for making the corridor such a nice place to work. Now that we have moved upstairs, I thank all the members of particle and astroparticle physics group for welcoming us up here. I would like to thank my family for their support during my studies. Thank you to my parents for always supporting and encouraging me and to my brother Jonathan for always sharing his many innovative ideas with me. Thank you to my grandparents for always being supportive and especially to my grandfather for inspiring me to study physics in the first place. Last, but certainly not least, thank you Lara for all your love and support. This thesis is dedicated to you. Contents Abstract . iii Sammanfattning . iv Preface v List of papers . .v The thesis author's contribution to the papers . vi Acknowledgements . vii Contents ix I Introduction and background material 1 1 Introduction 3 1.1 Outline . .4 2 The Standard Model 5 2.1 Overview of the Standard Model . .5 2.1.1 Gauge sector . .6 2.1.2 Fermionic particle content . .6 2.1.3 The Higgs mechanism . .8 2.1.4 Fermion masses . 10 2.1.5 Parameters of the Standard Model . 12 2.2 Open questions and some proposed solutions . 12 2.2.1 Observational problems . 12 2.2.2 Aesthetic problems . 16 3 Grand unified theories and SO(10) 19 3.1 Gauge coupling unification . 20 3.2 Candidate gauge groups . 22 3.2.1 Viable gauge groups . 24 3.2.2 The SU(5) group . 24 3.2.3 The Pati{Salam group . 26 ix x Contents 3.2.4 The SO(10) group .