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The Search for Physics Beyond the Standard Model in Connection to Electroweak Symmetry Breaking A brief Summary Article in the Context of a Cumulative Habilitation Treatise Philip Bechtlea January 23, 2014 Abstract This article is a summary of – and a commentary on – developments in the interpre- tation of data from various aspects of physics beyond the Standard Model connected to electroweak symmetry breaking. A special focus is laid on the motivation of the Higgs mechanism, the critical evaluation of its virtues, and on the best motivated theories to stabilise electroweak symmetry breaking, based on Supersymmetry. The main targets of the article are the description of aspects of the direct and indirect search for the Higgs and for Supersymmetry, and the description of two sets of tools, their experimen- tal and theoretical input, and their most important results: First, HiggsBounds and HiggsSignals, two tools for model-independent tests of limits on and measurements of Higgs boson properties against predictions from any theory with Higgs-like states. Second, Fittino, a tool to make full use of the measurements from B-physics, preci- sion electroweak measurements, other precision data, cosmology, Higgs discovery, and cosmological measurements, to constrain Supersymmetry and/or other physics beyond the Standard Model. aPhysikalisches Institut, Universit¨at Bonn, Nussallee 12, 53115 Bonn, Germany 1 Contents 1 Introduction 5 2 Theories about the Fundamental Constituents of Nature 7 2.1 The Standard Model of Particle Physics: So near... ........ 7 2.2 ... andyetsofar................................. 11 2.3 Arethereanyalternatives,afterall? . ....... 12 3 Boundary Conditions: Precision Measurements and Cosmology 15 3.1 Precision measurements at lower energies . ....... 15 The anomalous magnetic moment of the muon (g 2) ........... 15 − µ Rare decays of B mesons ............................ 15 PrecisionmeasurementsatLEPandSLD . 17 3.2 DoweunderstandtheUniversewelivein?. ..... 17 4 The Search for the Origin of Electroweak Symmetry Breaking 19 4.1 HiggsSearchesatLEP.............................. 19 4.2 HiggsSearchesandMeasurementsattheLHC . 22 4.3 Model Independent Interpretation in Arbitrary Higgs Models ........ 25 HiggsBounds ................................... 26 HiggsSignals.................................... 28 5 The Search for Supersymmetry 33 5.1 StrongProductionSearches . 33 5.2 Electroweak Production Searches and Simplified Models . .......... 37 5.3 Searches Based on Kinematic Reconstruction . ....... 38 6 Interpretations 41 6.1 InterpretationsofStatistics . ...... 41 6.2 Limits on Supersymmetry, or: How unattractive did it get yet? ....... 43 AnexampleforanMSSMfit .......................... 44 AnexampleforaCMSSMfit .......................... 46 7 Summary and Outlook 53 References 61 3 5 1 Introduction This article motivates and partly summarises the current status of the search for New Physics at high energy collider experiments. The rather general term “New Physics” denotes the theories about the fundamental constituents of matter and their interactions, which go beyond the well established Standard Model of particle physics (SM). There is an infinite number of such theories, and an almost infinite number has been proposed or, surely, will be proposed in the near future. Hence, this is a very wide field, and thus only a small selection can be presented here. The focus lies on the search for new phenomena at high energy collider experiments. But also selected precision measurements at lower energies will be introduced, if useful for constraining the selected models of New Physics. Therefore, the approach used here is also sometimes called the “Multi Messenger” approach, because the simultaneous test of many predictions of a theory against a large variety of measurements (the “messengers”) in different phenomena allows to obtain a global picture on the validity of the theory. A further emphasis in this article is placed on methods and software tools allowing tests of the SM and New Physics against the data. These tests can be done in two conceptually different ways: Either by providing model independent interfaces between measurements and predictions, which means that typically only specific sectors of measurements are treated at once. This is the case for the Higgs sector limits and measurements presented here. Or by testing very specific models and their model dependent predictions against data from all kind of measurements in parallel, as shown for Supersymmetry here. Three central questions do arise from these starting points, and will be covered in detail in the following sections: First, what are the principles from which successful theories of Nature are derived and what are their basic properties and predictions? Second, how could they be tested and potentially be falsified by precision measurements or searches for individual new phenomena, and how can these tests be used to constrain the range of validity of the theory? Third, is it possible to find a concrete hint for actually prefering a given theory of New Physics over the Standard Model in the global picture, e.g. by combining mesaurements and limits from many areas in global fits? Before looking at the current state of the search for New Physics, it is important to briefly touch the history of the theoretical foundation on which our current model of the fundamental building blocks of matter is based, the Standard Model (SM). It is remark- able because its theoretical conception was in the 1960’s and 1970’s, and its fundamental theoretical ingredients are still unchanged. Since then, the SM predictions have survived a very wide range of tests against a plethora of more and more data, over a period of radical improvement in our experimental capabilities and precision. Currently, given the expected statistical fluctuations of the measurements within their uncertainties, the SM correctly describes precision physics over a span of more than 20 orders of magnitude in energy (resp. scale), from the limit on the photon mass, over everyday electricity and magnetism, the description of fundamental properties of chemical reactions, nuclear physics and up to the highest energies per particle tested in the laboratory at the LHC. This enormous range of energy scales of 20 orders of magnitude is unparalleled in the history of science and the SM can be regarded as one of the greatest cultural achievements in the history of mankind – of course together with other milestones of science in other fields. The fact that in 2012 a Higgs boson was experimentally discovered, which was predicted 48 years earlier, shows that the degree of understanding of the ways of Nature in the form of the SM is indeed unique. Even more so, since we experimentally know that the SM is falsified – at least it cannot describe the history of the Universe and its currently measured composition. This is the fascinating state of particle physics in 2013: We seem to know exactly how to 6 Section 1 Introduction describe precision experiments, now, on earth, but the same brilliant theory which achieves this fails in describing aspects of the history of the Universe and its current state. In ad- dition, there is no hint as to how to combine the SM with gravity. This partly explains the intensity with which the theoretical and experimental particle physics community is searching for a clear deviation of the behaviour (or type) of particles from what is described by the SM. To achieve this, there are two fundamental strategies: First, finding new par- ticles not included in the SM, like a candidate for Dark Matter (DM) in the Universe, and second, measuring the properties of particles and their interaction with utmost precision and comparing to the SM prediction, hoping for deviations. Both of these approaches shall be described here, following the idea of the multi-messenger approach. Both types shall also be used in the global interpretations which are the main objective of this document. In this situation, where existing individual measurements from many different areas can be correctly described by different theories, including the SM as well as theories beyond, it is an interesting task to work on the interface between experiment and theory, providing methods and tools to link the complex measurements to the predictions of equally complex models and to provide means of the statistical evaluation of agreement or disagreement. It is the main objective of this document to describe the environment in which such methods are necessary and to give a short introduction into some of them, and discuss examples of their results. The examples given in this short summary of course can not cover the full span of the different areas of promising attempts to find New Physics – whole fields like neutrino physics, measurements of CP violation and electric dipole moments and so forth cannot be covered here. Instead, this article concentrates on the miraculous ways of electroweak symmetry breaking and its (at least for a long time) theoretically most promising explanation: Supersymmetry (SUSY). This document is organised as follows: In Section 2, a short introduction into the Standard Model of particle physics, its successes and shortcomings, and into SUSY is given. Section 3 then describes the precision measurements which set important constraints on the design and parameters of New Physics models, mostly from other experiments than those at the LHC. Section 4 then covers the search for Higgs bosons in the SM and in models such as SUSY from

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