Licentiate Thesis Astrophysical and Collider Signatures of Extra Dimensions Henrik Melb´eus Theoretical Particle Physics, Department of Theoretical Physics, School of Engineering Sciences Royal Institute of Technology, SE-106 91 Stockholm, Sweden Stockholm, Sweden 2010 Typeset in LATEX Akademisk avhandling f¨or avl¨aggande av teknologie licentiatexamen (TeknL) inom ¨amnesomr˚adet teoretisk fysik. Scientific thesis for the degree of Licentiate of Engineering (Lic Eng) in the subject area of Theoretical physics. Cover illustration: A Feynman diagram contributing to the three leptons and large missing energy signal, in a model where right-handed neutrinos propagate in an extra dimension. Taken from Ref. [3]. ISBN 978-91-7415-556-3 TRITA-FYS-2010:05 ISSN 0280-316X ISRN KTH/FYS/--10:05--SE c Henrik Melb´eus, January 2010 Printed in Sweden by Universitetsservice US AB, Stockholm January 2010 Abstract In recent years, there has been a large interest in the subject of extra dimensions in particle physics. In particular, a number of models have been suggested which pro- vide solutions to some of the problems with the current Standard Model of particle physics, and which could be tested in the next generation of high-energy experi- ments. Among the most important of these models are the large extra dimensions model by Arkani-Hamed, Dimopoulos, and Dvali, the universal extra dimensions model, and models allowing right-handed neutrinos to propagate in the extra di- mensions. In this thesis, we study phenomenological aspects of these three models, or simple modifications of them. The Arkani-Hamed–Dimopoulos–Dvali model attempts to solve the gauge hier- archy problem through a volume suppression of Newton’s gravitational constant, lowering the fundamental Planck scale down to the electroweak scale. However, this solution is unsatisfactory in the sense that it introduces a new scale through the radius of the extra dimensions, which is unnaturally large compared to the electroweak scale. It has been suggested that a similar model, with a hyperbolic internal space, could provide a more satisfactory solution to the problem, and we consider the hadron collider phenomenology of such a model. One of the main features of the universal extra dimensions model is the existence of a potential dark matter candidate, the lightest Kaluza–Klein particle. In the so- called minimal universal extra dimensions model, the identity of this particle is well defined, but in more general models, it could change. We consider the indirect neutrino detection signals for a number of different such dark matter candidates, in a five- as well as a six-dimensional model. Finally, right-handed neutrinos propagating in extra dimensions could provide an alternative scenario to the seesaw mechanism for generating small masses for the left-handed neutrinos. Since extra-dimensional models are non-renormalizable, the Kaluza–Klein tower is expected to be cut off at some high-energy scale. We study a model where a Majorana neutrino at this cutoff scale is responsible for the generation of the light neutrino masses, while the lower modes of the tower could possibly be observed in the Large Hadron Collider. We investigate the bounds on the model from non-unitarity effects, as well as collider signatures of the model. Key words: Extra dimensional quantum field theories, universal extra dimen- sions, Kaluza–Klein dark matter, Arkani-Hamed–Dimopoulos–Dvali model, hier- archy problem, neutrino mass, seesaw mechanism, Large Hadron Collider phe- nomenology. iii iv Preface This thesis is the result of my research at the Department of Theoretical Physics during the time period June 2007 to January 2010. The thesis is divided into two parts. The first part is an introduction to the subjects that form the basis for the scientific papers. These subjects include extra dimensional field theories, dark matter, and models of neutrino masses. The second part consists of the three scientific papers listed below. List of papers [1] Henrik Melb´eus and Tommy Ohlsson Searches for hyperbolic extra dimensions at the LHC Journal of High Energy Physics 08, 077 (2008) arXiv:0806.1841 [hep-ph] [2] Mattias Blennow, Henrik Melb´eus, and Tommy Ohlsson Neutrinos from Kaluza–Klein dark matter in the Sun Journal of Cosmology and Astroparticle Physics 01, 018 (2010) arXiv:0910.1588 [hep-ph] [3] Mattias Blennow, Henrik Melb´eus, Tommy Ohlsson, and He Zhang Non-unitary neutrino mixing from an extra-dimensional seesaw model To be submitted. The thesis author’s contribution to the papers [1] I performed the analytical and numerical calculations. I also produced the figures and did most of the writing. [2] I performed most of the analytical and numerical calculations. I also produced the figures and did most of the writing. [3] I performed the calculations of collider signatures in Sec. IV and did part of the writing. v vi Preface Notation and conventions Throughout this thesis, we use the Einstein summation convention, i.e., we im- plicitly sum over repeated spacetime indices (one covariant and one contravariant), unless otherwise stated. Ordinary four-dimensional spacetime indices are denoted by lower-case Greek letters, extra-dimensional spacetime indices by lower-case Roman letters, and gen- eral spacetime indices of the higher-dimensional spacetime by upper-case Roman letter. The sign convention for the Minkowski metric and its generalization is given by (gµν ) = diag(1, 1, 1, 1). We use natural− − units,− setting c = ~ = 1. However, we do not set G = 1, as the only context where this constant is relevant is the Arkani-Hamed–Dimopoulos– Dvali model, and in that model, G is not a fundamental constant, but only an effective low-energy parameter. Acknowledgments First of all, I would like to thank my supervisor Tommy Ohlsson, for giving me the opportunity to do research in theoretical particle physics, and for the collaboration that has resulted in the three papers in this thesis. And, although it has not worked very well, for his efforts to educate his PhD students in some Swedish history. Thanks also for the careful proof-reading of the thesis. Special thanks are due to He Zhang, for the collaboration that has resulted in Paper III in this thesis, and for providing the cover illustration; Michal Malinsk´y, who is always willing to share his knowledge, and who has welcomed me to his home in Sweden as well as in the Czech Republic on several occasions; Mats Wallin, for proof-reading of the thesis; the people mentioned above, as well as other people at the Department of Theoretical physics, including Johannes Bergstr¨om, Martin Heinze, Sofia Sivertsson, and Jonas de Woul, for providing great company and a nice working atmosphere. Special thanks are also due to Mattias Blennow, for the collaboration that has resulted in Papers II and III, and for teaching me how best to prepare the uploading of a paper to the arXiv in order for it to end up at the top of the mailing list. Thanks also to Tomas H¨allgren, who introduced me to the subject of extra dimensions. Moving outside the world of physics, I want to thank my friends—you know who you are. Very special thanks to my family: my soon-to-be parents-in-law Sven and Tinna and sisters-in-law Malin and Jenny; my dog Yoshi, who is a constant source of love and laughter; my sister Johanna, who has always been a great friend; my parents, Ronny and Ulla, who have always supported me and encouraged me to do what I want with my life. Finally, I have saved the best for last: my girlfriend Camilla, whom I will be proud to call my wife at the time when I next write a thesis. Your support is invaluable. I love you. Henrik Melb´eus Stockholm, January 2010 vii viii Contents Abstract.................................... iii Preface v Acknowledgments vii Contents ix I Introduction and background material 1 1 Introduction 3 1.1 Overviewofthethesis ......................... 6 2 Physics in extra dimensions 7 2.1 TheStandardModelofparticlephysics . 7 2.1.1 Particleinteractions . 8 2.1.2 ProblemswiththeStandardModel. 11 2.2 Higher-dimensional quantum field theories . ... 12 2.2.1 Kaluza–Kleindecomposition . 13 2.2.2 Non-renormalizability . 16 2.3 Universalextradimensions . 17 2.3.1 Fivedimensions......................... 18 2.3.2 Sixdimensions ......................... 22 2.3.3 Massspectrum ......................... 25 2.3.4 Constraintsandrangeofvalidity . 26 2.4 The Arkani-Hamed–Dimopoulos–Dvali model . 26 2.4.1 Geometry ............................ 27 2.4.2 Generalrelativity. 27 2.4.3 Generalization to higher dimensions . 29 2.4.4 Solution to the hierarchy problem . 29 2.4.5 Constraints, problems, and range of validity . .. 30 ix x Contents 3 Dark matter 33 3.1 Thedarkmatterproblem . .. .. .. .. .. .. .. .. .. 33 3.2 Detectionofdarkmatter. 35 3.2.1 Directdetection ........................ 35 3.2.2 Indirectdetection. 36 3.3 Kaluza–Kleindarkmatter . 38 3.3.1 ThelightestKaluza–Kleinparticle . 38 3.3.2 Observationalprospects . 39 4 Neutrino physics 41 4.1 Neutrinooscillations .......................... 41 4.2 Neutrinomassmodels ......................... 43 4.3 Neutrino masses in extra-dimensional models . ... 45 5 Collidersignaturesofextradimensions 47 5.1 Colliderphenomenology . 47 5.2 Universalextradimensions . 51 5.3 The Arkani-Hamed–Dimopoulos–Dvali model . 51 5.4 Neutrinosinthebulk.......................... 54 6 Summary and conclusions 55 Bibliography 56 II Scientific papers 67 Part I Introduction and background material 1 2 Chapter 1 Introduction The subject of physics arose as a result of mankind’s curiosity about how Nature works. Generally speaking, the aim of physics is to obtain a description of Nature under different circumstances, ranging from the evolution of the Universe as a whole down to the very smallest distance scales. Such a description is obtained by making experiments and observations of different phenomena, finding patterns in the experimental data, and using these patterns to formulate mathematical models. These models must be able to make well-defined predictions, so that they can be tested against the results of other experiments in order to assess the validity of the models in different contexts.