Dissertation submitted to the Combined Faculties of the Natural Sciences and Mathematics of the Ruperto-Carola-University of Heidelberg. Germany for the degree of Doctor of Natural Sciences Put forward by Jamil Hetzel born in: Rheden, the Netherlands Oral examination: February 4th, 2015 Phenomenology of a left-right-symmetric model inspired by the trinification model Referees: Prof.dr.TilmanPlehn Prof. dr. Arthur Hebecker Ph¨anomenologie eines links-rechts-symmetrisches Modells basierend auf dem Trinifikationsmodell Das Trinifikationsmodell ist eine interessante Erweiterung des Standardmodells, die auf der Eichgruppe SU(3)C SU(3)L SU(3)R basiert. Das Modell beschreibt die Parit¨atsverletzung durch die spontane Brechung× × der Eichsymmetrie, und die gemessenen Fermionenmassen und -mischungswinkel k¨onnen mit wenigen Parametern reproduziert werden. Wir untersuchen die Ph¨anomenologie des Trinifikationsmodells bei niedrigen Energien, um seine Voraussa- gungen mit Experimenten vergleichen zu k¨onnen. Zu diesem Zweck konstruieren wir eine effektive Feldtheorie die es erlaubt, mit einer geringeren Anzahl von Teilchen und freien Parametern auszukommen. Die Modellparameter werden mittels den bereits vorliegenden Pr¨azisionsmessungen und experimentellen Grenzen eingeschr¨ankt. Der Skalarsektor des Mo- dells erm¨oglicht verschiedene ph¨anomenologische Szenarien, zum Beispiel ein leichtes fermio- phobisches Skalarteilchen zus¨atzlich zu einem standardmodellartigen Higgs, oder die Exi- stenz eines entarteten (Zwillings-)Higgsbosons bei 126 GeV. Wir zeigen wie die Messung der Higgskopplungen es erlaubt, zwischen solchen Szenarien und dem Standardmodell zu unterscheiden. Es stellt sich heraus, dass das Trinifikationsmodell mehrere neue Skalarteil- chen mit Massen im (100 GeV)-Bereich vorhersagt. Außerdem werden in großen Teilen des Parameterraums messbareO Abweichungen der Higgskopplungskonstanten von den Stan- dardmodellwerten erwartet. Das Trinifikationsmodell erwartet daher in den n¨achsten Jahren entscheidende Tests am Large Hadron Collider. Phenomenology of a left-right-symmetric model inspired by the trinification model The trinification model is an interesting extension of the Standard Model based on the gauge group SU(3)C SU(3)L SU(3)R. It naturally explains parity violation as a result of spon- taneous symmetry× breaking,× and the observed fermion masses and mixings can be reproduced using only a few parameters. We study the low-energy phenomenology of the trinification model in order to compare its predictions to experiment. To this end, we construct a low- energy effective field theory, thereby reducing the number of particles and free parameters that need to be studied. We constrain the model parameters using limits from new-particle searches as well as precision measurements. The scalar sector of the model allows for various phenomenological scenarios, such as the presence of a light fermiophobic scalar in addition to a Standard-Model-like Higgs, or a degenerate (twin) Higgs state at 126 GeV. We show how a measurement of the Higgs couplings can be used to distinguish such scenarios from the Standard Model. We find that the trinification model predicts that several new scalar particles have masses in the (100 GeV) range. Moreover, large regions of the parameter space lead to measurable deviationsO from Standard-Model predictions of the Higgs couplings. Hence the trinification model awaits crucial tests at the Large Hadron Collider in the coming years. to Sabine Acknowledgements I am indebted to my supervisor Tilman Plehn for providing me the opportunity to perform my doctoral study in Heidelberg. This work would not have been possible without him providing a wonderful research group, financial support, help with both time management and physics, and guidance of the project towards its completion. I am also grateful to Berthold Stech for a wonderful collaboration. This thesis would not have existed without all his suggestions and insights that have steered our project to its completion, his endless patience while discussing physics, and his tireless proofreading during the final stage of this work. Furthermore, I thank Torben Schell, Jamie Tattersall and Johann Brehmer for proofread- ing parts of this thesis and suggesting numerous improvements. I also thank my second referee Arthur Hebecker as well as my examiners Ulrich Uwer and Bernd J¨ahne for reading my thesis and being part of my examination committee. I thank everyone from the phe- nomenology group at the ITP for providing a great environment that has resulted in three fruitful years filled with plenty of cakes, nuts, and scenic walks on Philosophenweg. Last but certainly not least, I thank Sabine Keller with all my heart for her unlimited personal support. I would not have gotten this far without her neverending encouragement, love, and care. CONTENTS I Contents 1 Introduction 1 2 The trinification model 3 2.1 Gaugesector .................................... 4 2.2 Scalarsector .................................... 4 2.3 Fermionsector ................................... 7 2.4 Fromtrinificationtoelectromagnetism . ........ 9 3 The low-energy trinification model 11 3.1 Gaugebosonsector................................ 11 3.2 Scalarsector .................................... 13 3.3 Fermionsector ................................... 16 4 ComparisontosimilarmodelsbeyondtheSM 18 4.1 Thetwo-Higgs-doubletmodel . 18 4.2 Mappingthe simplified LETmodelonto the2HDM . 20 4.3 2HDMvs.simplifiedLETmodel . 23 4.4 Left-right-symmetricmodels. ...... 24 4.5 Left-right-symmetric models vs. simplified LET model . ........... 26 5 Constraints from heavy vector boson searches 28 5.1 Directsearches .................................. 28 5.2 Electroweakprecisiondata. ..... 30 5.3 High-precisionmeasurements . ..... 32 5.4 Parameterconstraints . 33 6 CouplingsoftheStandard-Model-likeHiggs 36 6.1 Standard-ModelHiggscouplings . ..... 36 6.2 Higgs-couplingmodifications . ..... 38 6.3 Higgs-coupling modifications of the simplified LET model ........... 39 6.4 TheStandard-Modellimit . 42 6.5 Coupling-modificationpatterns . ...... 43 6.6 Benchmarkpoints ................................. 46 6.7 Parameter constraints from coupling modifications . ........... 49 7 Bounds on new scalars 52 7.1 CouplingstotheSMfields. 52 7.2 LightfermiophobicHiggsparticles . ....... 53 7.2.1 Experimentalbounds ........................... 54 7.2.2 Simplified-LET-modellimits . 55 7.3 ChargedHiggses .................................. 58 7.3.1 Experimentalbounds ........................... 59 7.3.2 Simplified-LET-modellimits . 60 II CONTENTS 8 The complete LET model 63 8.1 Thesecondbidoublet.............................. 63 8.2 Gauge-bosonmixing ............................... 65 8.3 Benchmarkpoints ................................. 66 8.4 Higgs-couplingmodifications . ..... 71 9 Conclusions 73 A Gauge-boson mass eigenstates 75 A.1 Chargedgaugebosons .............................. 75 A.2 Neutralgaugebosons.............................. 77 A.3 GaugebosonsinthecompleteLETmodel . 79 B Scalar spectrum 80 B.1 Scalarpotential................................. 80 B.2 Vacuumstability ................................. 81 B.3 UnitarityoftheS-matrix . 82 B.4 Scalarmassesandmasseigenstates . ...... 86 B.5 ThecompleteLETmodel ............................. 89 C Systematic derivation of scalar invariants 95 C.1 ThesimplifiedLETmodel. 95 C.2 ThefullLETmodel ................................ 99 D Yukawa sector 101 D.1 Yukawa interactions in the trinification model . .......... 101 D.2 YukawainteractionsintheLETmodel . 102 D.3 Masseigenstatebasis. 103 D.4 Fermion mixing in charged current interactions . .......... 105 E Gauge currents 106 F Photon coupling modification 109 G Feynman rules 112 G.1 Triple-vector-bosoncouplings . ....... 112 G.2 Couplings of SM-like Higgs components to a heavy vector boson . 112 G.3 H± CouplingstoSMbosons ........................... 113 G.4 H± Couplings to a W andaneutralscalar . 113 G.5 Couplings of neutral scalars to pairs of vector bosons . ............ 114 G.6 Scalarcouplingstofermions . 114 H Charged-scalar couplings of the 2HDM 116 H.1 Couplingstobosons ............................... 116 H.2 Couplingstofermions ............................. 116 References 117 1 1 Introduction The discovery of the Higgs boson [1, 2] marks the establishment of the Standard Model (SM) of particle physics as the model that correctly describes physics at energies available at particle colliders to date. All particles of the SM have been found experimentally, and the experimental data gathered at particle colliders match the predictions of the SM to good precision [3]. Yet, the Standard Model is not regarded to be a complete theory of nature. Firstly, it does not describe correctly all observations made outside particle colliders. The Standard Model lacks a description of gravity: as a quantum field theory, it is incompatible with the theory of General Relativity. Also, the SM does not include any particles that could be viable dark matter candidates, and it is incompatible with the observation of non-zero neutrino masses (for a review, see e.g. [4]). Secondly, the Standard Model is unsatisfactory from a theoretician’s perspective: the fermion masses and mixings are free parameters that display hierarchical patterns, parity violation has to be introduced by hand, and the Higgs mass is much smaller than the Planck scale despite quadratically divergent loop corrections. Therefore our quest towards a better theory of nature requires us to extend the Standard Model. Several