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 interpretation 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 experimental 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, precision 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

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

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 remarkable 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 addition, 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 particles 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 the LEP to the LHC era, and it is shown how tools can be built to apply these results in a model independent way, such that every model with Higgs-bosons can be tested against the measurements. In Section 5 the desperate attempt to find the most elegant known cure to the miracle of electroweak symmetry breaking, SUSY, are briefly sketched. Section 6 deals with statistical considerations in model testing and with the interpretation of all the measurements discussed before in constrained SUSY models. A combined summary and outlook is given in Section 7. Due to its role as a summary, this article does not aim to give a complete overview over the whole field, but only to touch on the most important aspects relevant in the context of the cumulative Habilitation treatise of the author and his previous work. Also, no part of this text will provide a fundamental introduction into the basis of the theories or experimental techniques used here. The reader is encouraged to refer to the cited material and/or the articles forming the basis of this cumulative Habilitation. 7

2 Theories about the Fundamental Constituents of Nature

This section covers the current status of the SM, and why it is desirable to go beyond it. Supersymmetry (SUSY), one of the theories which could show the way towards a more complete theory of Nature, will be brieﬂy discussed in the second part. It is discussed why SUSY is still of interest, despite a complete lack of experimental evidence at the LHC so far. In order to focus on the open questions and the interesting developments in the last years, the remainder of this text will assume that the reader has a fundamental knowledge on how the SM and SUSY are constructed mathematically.

2.1 The Standard Model of Particle Physics: So near . . .

The SM [1] together with general relativity (GR) [2] is the most detailed description of Nature obtained so far. An overview of the SM can be found e.g. in [3]. A particularly interesting pedagogical overview over the history of the discoveries and theoretical ideas which led to its invention and completion can be found in [4]. The SM is based on the notion of the three gauge symmetries SU(3) SU(2) U(1) C × L × Y describing the strong interaction with its colour charge C, and the unbroken electroweak interaction based on chirality L and hypercharge Y . These interactions are mediated by µ massless gauge bosons, the eight gluon gauge fields Ga for the strong interactions, the µ µ three gauge fields Wi for the SU(2) symmetry and the gauge field B for the hypercharge symmetry. While the massless gluons can be directly identified with the strong interaction, the situation is more involved for the electroweak sector. The photon, transmitting the electromagnetic force, is massless and one could attempt to identify it with the Bµ and test whether its couplings would be correctly predicted. This does not work out. However, the failure of the unbroken theory to describe Nature is even more apparent for the massless µ Wi , which obviously cannot be identified with the massive mediators of the weak force, the W ± and the Z0. Before curing the interactions by hand, it is essential to tackle the more fundamental problem of the missing gauge boson mass first. This can be achieved by the Higgs mechanism [5]. Here, the SU(2) U(1) symmetry is broken spontaneously by the vacuum L × Y expectation value (vev) of a scalar field, the Higgs field, which is added to the theory. The details of how this vev arises will be discussed later. A more thorough recent review of the theoretical and experimental status of the Higgs mechanism can be found e.g. in [6]. At first glance, this idea sounds extremely elegant: The Higgs field is coupled dynamically to the gauge bosons through gauge interactions, and the mass of the gauge bosons is only determined by the vev of the Higgs field as well as the values of the original gauge couplings. The gauge bosons acquire mass by incorporating the Goldstone degrees of freedom, such that no physical massless Goldstone boson remains [7], but there is one massive scalar degree of freedom: The Higgs boson. The largest part of this article evolves around the search for the Higgs boson and for the theories used to add stability to its properties and to add predictivity, because they can dynamically predict the Higgs potential and they can put constraints on its allowed mass range. However, before the properties of the Higgs boson are discussed, the consequences of the Higgs mechanism for the other SM particles shall be mentioned: The SU(2)L U(1)Y µ × is broken to U(1)EM with the massless gauge boson A , which successfully can be identified with the photon. It has no coupling to the neutrinos and it couples with the same strength to left- and right-handed fermions. To achieve that in parallel is already not completely trivial. Further, a neutral massive gauge boson Z0 is obtained, which can be successfully iden- 8 Section2 TheoriesabouttheFundamentalConstituentsofNature tified with the mediator of the neutral current of the weak force. Not only does it couple to neutrinos and charged fermions, it also does so with exactly the correct and different couplings for both left- and right handed states, as it will be described in Section 3.1. The last two degrees of freedom of the Higgs field are left for the mass of the charged massive gauge bosons W ±. The Higgs mechanism predicts exactly the correct relation between 2 the mixing angle sin θW,eff (given solely by the couplings of SU(2)L and U(1)Y ) and the ± masses, mZ = mW / cos θW,eff , and allows the W to couple only to left-handed fermions. In addition, the theory allows the physical gauge bosons W ±,Z0 and γ to acquire a self- interaction from their non-abelian self-energy terms, with no added degree of freedom. Also this sector can be experimentally tested (see Section 3.1). This part is maybe one of the most interesting ones: At the invention of the theory neither any motivation for these terms nor any experimental hint for their existence was known. Still, the prediction of their self-interactions, without any possibility to tune them in the theory using additional free parameters, matches the data perfectly. Thus, with respect to the physical gauge bosons there is no need for changing the interactions of the gauge bosons: After fixing their mass using the Higgs mechanism, all interactions agree with the precision data. As presented above, the Higgs mechanism appears to be inevitable, and as an extremely elegant part of the SM and its 3 gauge interactions. However, there are a few problems. First, up to now there was no discussion of the details of how the Higgs boson acquires its vev, and as a byproduct also its mass. The origin lies in the form of the Higgs potential, added in an ad-hoc way to the theory: V (Φ) = µ2 Φ 2 + λ Φ 4/2, which for µ2 > 0 and − | | | | λ> 0 has a non-trivial minimum at Φ = v = µ/√λ = 246GeV. This dynamically breaks | | the SU(2) U(1) symmetry. Why is this an ingenious idea and unsatisfactory at the L × Y same time? On the one hand, it is the only explicit scalar potential which can be added to the SM which preserves the gauge symmetries. On the other hand, within the theory there is no reason to add the Higgs field and the Higgs potential at all, and no explanation for it, apart from the fact that it fulfills its purpose. At the same time this potential lies at the very heart of the construction of the SM. This is one of the most attractive reasons for the introduction of a theory which dynamically generates such a potential, such as Supersymmetry, as briefly discussed in Section 2.3. Tightly connected with the potential there is a second problem. The SM is motivated very clearly by the 3 gauge groups introduced above, leading to 3 gauge interactions. Thus, most particle physicists would agree that the SM contains three forces. However, this is not correct, because the Higgs potential V (Φ) contains the term λ Φ 4, which obviously | | is a four-point interaction. It is not a gauge interaction, and thus easily overlooked. The fact that this interaction is not directly motivated by the gauge groups can be regarded as a mere aesthetic argument, but the resulting consequence of large loop corrections to the Higgs parameters due to Higgs self interactions and Yukawa interactions will lead to stability problems, as outlined below. In addition, there is a third problem. Up to now, only the masses of the gauge bosons were discussed. However, the SM fermions f also cannot acquire mass, since every mass term in the theory has the form mf¯ f . This is not obeying the SU(2) U(1) symmetry, L R L × Y since fR is a singlet under SU(2)L, while fL is not. Thus, also the fermion masses need to be generated dynamically. Since the Higgs field has been introduced already, it is tempting to use the Higgs field also here and write the mass as λ Φf¯ f , which obeys SU(2) U(1) . f L R L × Y That is very elegant, but without notice a fifth force is now introduced into the SM, the Yukawa interaction with one free coupling λf for each fermion. Also, this force leads to problems in several places, see below. Take note here that the neutrino masses might be generated in another way (for a recent review see e.g. [8]), and that the unknown details of the neutrino sector might point at yet another set of problems in the construction of the 9

m = 152 GeV 6 March 2012 Limit Theory uncertainty 182 ∆α(5) had = 180 EW vacuum 5 ± 0.02750 0.00033 instable 0.02749±0.00010 178 2 4 incl. low Q data 176 95%CL

2 174 3 meta–

∆χ stable pole t 172 m 2 170 168 stable ILC 1 166 LHC LEP LHC Tevatron excluded excluded 164 0 120 122 124 126 128 130 40100 200 MH [GeV] [ ] mH GeV (a) (b)

Figure 1: In (a) the agreement between the indirect constraints on the SM Higgs boson mass, indicated 2 by the χ function, and the direct Higgs mass constraint around mH = 125 GeV shown [9]. (b) shows the current and possible future constraints on the stability of the SM vacuum as a function of the top quark and Higgs boson mass, strongly motivating a much more precise measurement [10].

SM. Still, it is not obvious how these challenges in the neutrino sector would be connected to the issues with the breaking of the fundamental gauge groups of the SM, and hence they are not discussed further here. Before the experimental discovery of the candidate for the SM Higgs boson in 2012 by ATLAS and CMS, the only new unknown parameters in the Higgs sector were µ and λ. ± Since v = µ/√λ can be measured from the W boson mass mW and the Fermi coupling GF , only one degree of freedom is left in the Higgs potential, which can be identified with the Higgs boson mass. However, there was already indirect knowledge on the Higgs sector before the Higgs boson discovery, because of its impact in quantum loops. The measurements at LEP and SLD discussed in Section 3.1 are sensitive to corrections which the Higgs boson inflicts upon the W ± and Z0 propagator. From a global fit to this precision data [9], the Higgs boson mass can be inferred indirectly, as shown in Fig. 1(a). It can be seen from the comparison of the blue band, showing the indirect constraints, with the white vertical line around the mass of the discovered Higgs particle, that there is agreement at the 1 σ level. This very nice agreement alone can be regarded as a highly non-trivial achievement of the description of Nature by the SM. In Sections 4.2 and 4.3 more stringent tests of the properties of the discovered particle will be discussed, showing that at the present precision it indeed fulfils all requirements for the SM Higgs boson. In addition to the great possibility to test the Higgs mechanism in the gauge sector independently and indirectly, loops have another important role for the Higgs, which is not so positive. Fermion loops, most importantly from the top quark, which due to its high mass by far has the strongest coupling λt to the Higgs of all SM particles, lead to quadratic divergences of the loop-corrected Higgs boson mass. Therefore, the question appears whether the scale of the electroweak symmetry breaking is the only relevant high- energy scale in the SM, or whether there is another, higher scale which needs to be taken into account (see e.g. the introduction in [11]). There indeed is such a scale, namely where gravity becomes strong at the Planck mass scale of around M 1019 GeV. Thus, one P ≈ would expect that the quadratic loop effects to the Higgs boson mass mH are of the order of the scale Q M , and thus that the natural scale of m is M . This is in obvious ≈ P H P 10 Section2 TheoriesabouttheFundamentalConstituentsofNature contrast to the observation, both indirect [9] and direct, which require m 125 GeV. H ≈ This is called the hierarchy problem of the SM. Therefore, a mechanism to stabilise mH is highly desired, another reason to contemplate Supersymmetry in Section 2.3. Considering the two loop-induced effects discussed here, the part of the Higgs sector which is only concerned with the 2 gauge interactions of the electroweak force works flaw- lessly and beautifully, while it runs into difficulties as soon as the two ad-hoc interactions, the Higgs self-interaction and the Yukawa interaction are concerned. However, not everything is bad in the Yukawa sector. Not only does the Higgs allow to give the experimentally required mass to the fermions (albeit with many free parameters), it also allows to introduce complex physics in the form of flavour mixing, which arises from the fact that the Yukawa interactions are not required to be formulated in the same basis as the gauge interaction of the fermions. The mixing between these two bases is encoded in the CKM matrix [12]. It not only allows for a rich flavour phenomenology (see Section 3.1 for a short summary and [13] for a more detailed overview) which in hundreds of measurements almost perfectly matches the ad-hoc flavour sector description made possible by the application of the Higgs field to the fermions, but also for stringent tests of extensions of the SM which are connected to the Higgs. The question arises whether the non-trivial vacuum of the SM is stable up to highest energies. Not only is mH subject to loop-induced corrections, but thus also λ in the Higgs potential. If mH is too low with respect to the strongest loop correction from the top quark, then at high energy scales Q the top quark loops drive λ < 0 (see e.g. [10]). In this case, there is no minimum in V (Φ), and the SM could fall into another, yet unknown vacuum once in a tunnelling process a high potential wall is overcome, which corresponds to the energy scale Q v at which λ(Q) < 0 is reached. The tunnelling probability for this ≫ process determines the lifetime of the known ground state of the Universe. This is shown in Fig. 1(b) [10]. Interestingly, the SM seems to live near the boundary to a meta stable state. A more precise measurement of mt and mH in the future would strongly help to clarify this issue. The discovery of New Physics of course could alter the behaviour of λ(Q), maybe rendering the known physics fully stable. This makes it even more interesting to find a direct sign of New Physics soon. The question remains whether all predictions of the Higgs mechanism have already been tested experimentally, now that a Higgs boson has been observed at ATLAS and CMS. Interestingly, this is not the case. While mass, spin, couplings to bosons and to a certain extent to fermions are beginning to be constrained, the Higgs CP state is not yet known at the level of potentially small CP admixtures. More importantly, the Higgs boson contribution to the scattering of the longitudinal components of the W ±, W W W W L L → L L is of high interest, because this process violates the unitarity bound without the contribution of the Higgs in the s-channel at centre-of-mass energies of about √s 1TeV. The Higgs self- ≥ interaction λ can be measured in the future in h hh processes. These three measurements → are prime examples of precision physics for which a e+e− linear collider with √s = 250 to 1000 GeV is highly desirable [14]. In summary, the rather ad-hoc addition of the Higgs sector to the SM is at the centre of making the SM describe the data so incredibly well – both on the gauge interaction side as on the fermion and Yukawa interaction side. While it works in an historically unparalleled way in describing the data from precision experiments of all sorts, it also causes many theoretical challenges, as mentioned above. The question remains for the next section: If the SM is the greatest theory of the fundamental constituents of Nature conceived so far, does it describe all of known physics, or not? 11

2.2 ... and yet so far

After summarising the virtues of the SM, the question at the end of the last section was: Does the SM plus GR fundamentally describe all known physics? The answer is clearly “no”. All the problems discussed in Section 2.1 are of theoretical nature and can be ignored as long as the SM (plus gravity in the form of general relativity (GR)) is regarded as an effective theory. There is a clear indication in the construction of the SM that it is only an effective theory: The strong force, based on SU(3)C , is completely independent of the electroweak force in the SU(2) U(1) gauge groups. Thus, one would expect that L × Y one could vary their parameters, like the number of colours NC and the electromagnetic charges qe,qu,qd of the leptons and quarks independently without destroying the theoretical consistency of the SM. However, this is not the case due to triangular anomalies [15], which require q = N (q q ). If this condition is not fulfilled, the SM is meaningless. However, e − C u − d NC has theoretically no connection to the other parameters. Thus, one would expect some theoretical connection, in the form of a yet unknown Grand Unified Theory (GUT). The SM then would be the effective theory of that GUT, and any precision measurement with clear deviations from the SM will help to narrow down the successful set of hypotheses for that GUT. That aside, even being an effective theory, unfortunately the SM is not the complete effective theory of all known physics, which is most evident in the form of the composition and history of the Universe [16]. The first problem is that of the composition of the Universe. This problem is already apparent at the – cosmologically – rather small scale of a galaxy. This argument works as follows: General relativity (GR) works perfectly within our solar system. Hence, in a daring move it is assumed that GR also is the theory of gravity at the scale of a galaxy, which is about a factor of 108 larger than our solar system. It is further assumed that the baryonic matter can be inferred from the visible matter alone. Then, the rotation curves of stars in nearby galaxies, measured using their redshift, is compared to the assumption that the visible matter is the only matter in the galaxy. This assumption fails miserably (for a small overview of the experimental status see e.g. [17] and references therein), leaving the conclusion that either GR is not the theory of gravity at those scales (see e.g. [18]), or that there is an unknown component in the galaxies which only interacts gravitationally and maybe weakly. This is called Dark Matter (DM). In order to settle this issue, the observation of a colliding pair of galaxies (using weak lensing [19]) can be used, where the non-interacting dark matter can be separated from the visible gaseous matter, which scatters inelastically. This hints towards the existence of DM and against the obvious failure of GR, because in this case the visible gaseous matter would still inflict the largest part of the gravitational force, and not an invisible component like DM, scattering elastically. This is all very fascinating, even more so since the SM does not contain any candidate particle for DM. Neutrinos are not heavy enough, leading to too low DM densities and too wide distributions, since they move too fast at any given temperature, and all other SM particles couple too strongly. Thus, if the astrophysical interpretation including the existence of DM is accepted (which is a direction also supported by additional hints, see [20]), there is a firm falsification of the SM as an effective theory of Nature. There are more indications towards New Physics in cosmology, most notably the flatness of the Universe [16] and the apparent acceleration of distant objects, making Dark Energy necessary, which is not provided by the SM plus GR in the right order of magnitude. Fur- ther, structure formation, i.e. the observed densities of galaxies now and earlier in the observations of the cosmic microwave background, require Dark Energy and DM. Finally, there is almost only matter left in the visible Universe, and hardly any antimatter. Interest- 12 Section2 TheoriesabouttheFundamentalConstituentsofNature ingly, the only mechanism in the SM to create a violation of the CP symmetry, a necessary ingredient to create a matter-antimatter asymmetry, is the CKM mechanism. It is closely connected to the Higgs mechanism. Unfortunately, the matter-antimatter asymmetry con- ceivable by the SM is about 9 orders of magnitude too small for what is cosmologically required [21]. While the above mentioned observations are obvious, undeniable and statistically significant deviations from the prediction of the SM, there are also more specific particle physics measurements which show deviations from the SM, however at a level which is still marginally in agreement with the expectations. It should be kept in mind that with thousands of precise measurements in particle physics, it is expected that a small number of them deviates from the expectation by more than three standard deviations, even if the expectation happens to be the correct theory. Examples for such deviations currently can be found at B factories, e.g. the branching ratio of B D∗τν by BaBar [22] which deviates → from the SM by 3.4 σ. This could also be interpreted in terms of type III Higgs Doublet Models (see e.g. [23]). Another current candidate for a potentially significant signal of New Physics is the measurement of complex kinematic observables in B K∗ℓℓ decays by → LHCb [24]. For the discrepancy between SM prediction and measurement of the anomalous magnetic moment (g 2) of the muon see Section 3.1. − µ Another interesting phenomenon is the forward-backward asymmetry in pp¯ tt¯ events → observed at CDF and D0 [25], which would hint towards a heavy spin-1 particle like a very massive partner of the gluon. However, no sign of that is visible at the LHC [26], which due to its much higher centre-of-mass energy should be much more sensitive to heavy states. However, it is running on symmetric pp collisions, which somewhat lowers its sensitivity. For an assessment of the compatibility of these phenomena, see e.g. [27].

2.3 Are there any alternatives, after all?

As already stated in the introduction, theoretically there is an infinite number of extensions of and alternatives to the SM. However, in the last 20 years one of these extensions was significantly more prevalent and more present on many different fields of measurements than any other alternative or extension: Supersymmetry (SUSY), a new symmetry between fermions and bosons, thus doubling the particle content of the SM. For a much deeper and wider introduction into its ideas, merits, and features see e.g. [11]. SUSY itself was developed in the 1970’s [28] as a tool to allow for the description of physics at the scale of grand unified theories. It was soon discovered that when breaking SUSY appropriately [29], it could be a realistic theory of physics at or slightly above the electroweak scale. In this case the experimentally undiscovered superpartners of the SM particles (sparticles), stemming from the symmetry between bosons and fermions and differing from their partners only by a half-integer unit in their spin, can be moved to higher, yet untested mass scales. In addition to the nice features discussed below, it allows to couple the SM gauge symmetries to gravity in the form of the minimal supergravity implementation [30] (mSUGRA). Also, phenomenological descriptions of its minimal implementation were developed, the minimal supersymmetric standard model MSSM [31]. What makes SUSY so attractive? First, on a purely theoretical level, it completes the SM symmetries by the only non-trivial external extension of the Poincarégroup [32], which is interesting because it follows the empirical construction principle of successful theories: if something can be added to the theory to make it more complete, it should be added. Also, it achieves unification of the strengths of the three SM forces at the so-called GUT scale [11] at around M 1016 GeV , which makes it easier to combine the three independent SM GUT ≈ forces into one Grand Unified Theory (GUT). This by itself is not really a very compelling 13 reason for SUSY, because any unknown New Physics could appear between the currently tested scale at the LHC of up to (1TeV) and M 1016 GeV and spoil that relation O GUT ≈ again. A more concrete and very welcome advantage of SUSY is the stabilisation of the SM Higgs sector. As described in Section 2.1, the fermion coupling of the top quark destabilises the Higgs boson mass. The addition of the superpartner of the top, the stop, adds a particle with the same couplings but different spin-statistics, such that it cancels the quadratic divergences inflicted by the top, and only logarithmic divergencies remain. If the two stop mass states are not much heavier than (√m˜ m˜ ) 1TeV, then the correction to the O t1 t2 ≈ remaining divergency remains small enough to avoid finetuning issues (cf. Section 6.2). Not only is mH much better behaved in SUSY, it also motivates the form of the Higgs potential V (Φ), which was ad-hoc in the SM. In SUSY, two Higgs doublets are required to avoid triangular anomalies [11]. For these two doublets, individual mass scale parameters can be chosen at the GUT scale. Through renormalisation group equation (RGE) running [11], one of these two parameters is driven negative automatically in the presence of a large top Yukawa coupling λt, and thus the conditions for the generation of the Higgs potential, with µ2 as the factor in front of the quadratic term, is naturally generated [33]. − This also means that SUSY (at least if realised at or around the TeV scale), despite the large number of parameters, is actually a very predictive theory, because in contrast to the SM it couples the parameters of the Higgs potential, the Yukawa sector and the gauge sector. Further, the presence of the second Higgs doublet leads to at least 5 degrees of freedom in the Higgs sector, corresponding to two additional neutral Higgs bosons and one additional charged Higgs boson. It has been noted that SUSY cannot be an exact symmetry of Nature, since otherwise e.g. a spin-0 partner of the electron with the same charge, coupling and mass would exist. This is ruled out by experiment. Several ways of implementing the breaking have been conceived. First, a generic description of SUSY breaking at a phenomenological mass scale, typically around Q 1TeV can be used. The minimal formulation of the model, the MSSM, at such ≈ a scale with a soft SUSY breaking Lagrangian [31] has 105 free parameters in addition to the 19 SM parameters. This version already includes the notion of a conserved quantity called R-Parity, which is introduced to ensure that SUSY particles can only be pair-produced or -annihilated. This decouples SUSY more strongly from the SM, because no single SUSY particles can show up in loop corrections to vertices and propagators, and ensures the existence of a stable lightest SUSY particle, which can serve as a DM candidate if neutral. However, such a model with arbitrary parameter choice typically still violates constraints from flavour changing neutral currents (FCNC), electric dipole moments (for results on those see e.g. [34]) and other CP-violation measurements, the proton lifetime is radically reduced below existing limits, and so forth. Therefore, in practical applications the model is often, but not exclusively, constrained by generic assumptions: All terms generating FCNCs on tree level are set to 0 and CP-violating phases are mostly set to 0. Second, considerations about SUSY breaking mechanisms at the GUT scale can be added. Examples for these models are gravity mediation (mSUGRA or CMSSM), gauge mediation (GMSB) and anomaly mediation. Using these, together with explicit assumption on the unification not only of the forces, but also of the parameters at the GUT scale, it is possible to bring the number of additional free parameters down to 5. Anyhow, compared to other extensions of the SM, SUSY has the advantage that it is fully renormalisable and largely decouples from the propagators of the SM gauge bosons, thus having minimal effect on the SM precision measurements at LEP and SLD. This is an experimental difficulty, because it makes it harder to constrain SUSY indirectly. Still, it is 14 Section2 TheoriesabouttheFundamentalConstituentsofNature good for SUSY, because most alternative theories as extensions to the SM fail immediately because they break the great agreement of the SM with precision measurements as described in Section 3. To summarise, if broken SUSY with R-parity conservation on the TeV scale is realised in Nature, the following central predictions can be expected and searched for:

A Higgs boson with m < 135GeV (see e.g. [35] or [36]). If it is the lightest SUSY • H Higgs, then the heavier, the more SM like in its couplings.

A neutral stable candidate particle for DM, which is the lightest superpartner state. • Additional Higgs bosons, most easily realised at masses signiﬁcantly above the ob- • served Higgs state at m 125 GeV. H ≈ A spectrum of superpartners of the SM particles with higher masses than their SM • partners and spin diﬀering by 1/2, but identical couplings. The higher mH , the higher the sparticle mass scale. In the collider detector, if produced they would leave a missing energy signature due to their decay to the invisible dark matter candidate.

Possible corrections to precision observables in the ﬂavour sector and anomalous mag- • netic moments, most strongly in processes forbidden at tree level in the SM, or if helicity suppressed in the SM. On average, the higher mH , the higher the superpartner mass scale, and hence the smaller the expected corrections.

Very little impact on the SM precision measurements at LEP and SLD. • It can easily be observed that in the presence of no direct sign of SUSY at the LHC or elsewhere, the observation of a Higgs boson in the upper range of the mass range predicted by SUSY is actually in perfect agreement with the expectations, because that correlates with heavy superpartners and thus no direct sign of SUSY. Of course, despite such comforting arguments, the non-observation of SUSY so far should not be mistaken as an encouragement. Still, the search for physics beyond the SM, and more specifically for SUSY, in all of the above areas in a global picture is the focus of the remaining sections of this article. Of course there is no reason why SUSY must be realised in Nature. Or even if it was, it could be at such a high scale that it is currently inaccessible. There are many other ideas on how the electroweak symmetry breaking could be realised and how the hierarchy problem could be evaded or reduced. Among them are strong interactions in the gauge sector in Technicolor theories (see e.g. [37] and references therein for an overview of the current status), so-called little Higgs models (e.g. [38]) and extra dimensions (see e.g. [39]). Still, non of these possibilities covers such a wide range of physics as SUSY, and allows precision predictions at the loop level for so many measurements, which is another practical reason why SUSY is studied in more detail in the following sections. Instead of looking at complete models of New Physics, there is also the possibility to phenomenologically parametrise the effective impact of any arbitrary high-scale theory, in which all new states are highly virtual and can be integrated out, in the Higgs sector [40]. Then, effective operators in the Lagrangian at dimension [E6] in energy E appear, and their Wilson-coefficients can be constrained by precision measurements, triple gauge couplings, and the Higgs measurements. In this case, one would leave other objective challenges, like the dark matter problem, to other physics, e.g. axions [41], the search for which is another fascinating field of the quest for New Physics, but also rather unrelated to the questions arising around electroweak symmetry breaking discussed here. 15

3 Boundary Conditions: Precision Measurements and Cosmology

In Section 2, the basic motivation, virtues and drawbacks of the SM and its possible extensions were discussed. A lot of emphasis was laid on electroweak symmetry breaking, the mechanism in the SM, which gives mass to the gauge bosons. It is responsible for forming their physical states W ±, Z0 and γ, which are not there in the unbroken symmetry, and therefore the Higgs mechanism also impacts the couplings of the physical gauge boson states. It was also seen that flavour physics relies on the Yukawa couplings, and that therefore it is expected that New Physics also affects flavour precision observables. Finally, there is the role of New Physics with heavy particles showing up indirectly in loops, and there is cosmology. In this section, a short overview of only a few of these aspects will be given, whith special emphasis on the relevance for the New Physics studied here.

3.1 Precision measurements at lower energies This section discusses precision measurements in the electroweak sector. In this context, “lower energies” range from the muon mass mµ = 105MeV (this and all further measured mass scales are from [42]), over the mass scale of the B meson mB = 5.28GeV to the mass of 0 the Z gauge boson mZ = 91.2GeV. These are high energies when compared to the physics of everyday life, but low compared to the centre-of-mass energy of LHC at √s = 8 TeV.

The anomalous magnetic moment of the muon (g 2) − µ The anomalous magnetic moment of the electron is measured more than two hundred times more precisely than that of the muon, (g 2) = 2a . All the same, the sensitivity of a to − µ µ µ New Physics can be enhanced by a factor of (m /m )2 43000, and thus represents a much µ e ∼ more powerful constraint on the SUSY parameter space. The magnetic moment Gµ can be measured from the spin precession of muons stored in a low energy storage ring. Their spin direction at decay is inferred from the angular distribution of their visible decay products, the electrons, by detectors completely surrounding the storage ring. While the measurement of aµ [43] is undisputed, there is an ongoing debate about the accuracy of the input into its Standard Model prediction [44]. In particular, the non-perturbative contribution to aµ from the hadronic vacuum polarisation has to be extracted from experiment, via data from e+e− annihilation to hadrons or from τ-lepton decays. For the studies presented in SM + − Section 6.2 the value of aµ based on e e data has been chosen, which has been argued to be theoretically cleaner than that based on τ decays [44]. As expected in constrained models, note that in the CMSSM studied in Section 6 there is a strong correlation between (B µµ), discussed below, and a [45]. B s → µ Rare decays of B mesons Strong constraints on New Physics models can be obtained from flavour observables, including, in particular, B-meson decays. The precise measurement of branching fractions of rare decays which are helicity suppressed or which in the SM are mediated only at the loop level by heavy particles, places important restrictions on New Physics. Significant constraints come from B oscillations, the branching fraction of B τν and the inclusive branching s → fraction of b sγ, which is covered here in slightly more detail. → Since flavour changing neutral currents (FCNC) are forbidden in the SM at tree level, the radiative process b sγ or b dγ can occur only at the one loop level at lowest order. → → This sounds like a disadvantage, because the branching fraction is expected to be small, due to the two heavy particles, a top quark (or with a lower amplitude also a charm or up 16 Section 3 Boundary Conditions: Precision Measurements and Cosmology

1500 BB Continuum control control

1000

500 Events/0.1 GeV 0

1.5 2 2.5 3 3.5 Eγ* (GeV)

(a) (b)

Figure 2: In (a) the experimentally observed energy spectrum of the photon in inclusive b sγ decay → candidates in the BaBar experiment is shown in the experimentally directly accessible Υ(4S) frame. This result can be theoretically translated into the B rest frame and compared with the expectations. (b) shows the same result interpreted as a limit on the two-Higgs-doublet-model (THDM) type II parameter space [47]. quark) and a W ± boson, required in the leading order radiative penguin loop. However, this is really advantageous for the search for new contributions to that loop, because New Physics can enter at the same order as the SM physics, at 1-loop, and not only at a higher order, as typical for R-Parity conserving SUSY. Examples for contributions of New Physics comprise charged Higgs bosons instead of the W ± in SUSY or two-Higgs-doublet-models (THDM) [46], or stops, the superpartners of the SM top, and charginos, the mass eigenstates of the superpartners of the W ± and H±. The experimental search for these radiative penguin decays can be carried out in several different ways. Historically, the first measurement was the exclusive decay B K∗γ at → CLEO [48]. It is experimentally attractive, since the final state of the B decay can be fully reconstructed, making use of the constraint of the known B meson mass and the fact that it carries half the centre-of-mass energy. However, due to uncertainties connected to the strong interaction of the hadronic components in the mesons, the calculation of the associated branching fraction into the K∗, and not into any other strange final state, is not very precise, not in the SM and hence also not in any New Physics model [49]. Therefore, one attempts to experimentally determine the fully inclusive branching fraction, at the cost of experimental precision, but at the gain of precision in the prediction and in statistics. Also here there are two possibilities: Either a fully hadronic B decay is reconstructed on the spectator side [50], making it possible to directly reconstruct the momentum frame of the B decaying in a radiative penguin. This is theoretically advantageous, but comes at a strong loss of statistics due to the tagging efficiency of the spectator B. Or, as done by the BaBar collaboration in [47],1 one does not reconstruct the spectator B, but instead translates the observed γ energy distribution from the Υ(4S) frame into the lab frame using theoretical models of the kinematics of the b sγ decay, which are mostly independent → of New Physics. The resulting photon energy spectrum, after multivariate background suppression, continuum subtraction by the use of off-resonance data, and after a control of

1 For the full details of this analysis see the article “Precision Measurement of the B Xsγ Photon → Energy Spectrum, Branching Fraction, and Direct CP Asymmetry ACP (B Xs+dγ)”, Phys.Rev.Lett. → 109, 191801 (2012), which is contained in the full Habilitation treatise. 17 the background from π0 decays, is shown in Fig. 2(a). The shape of this distribution, at least after the transfer into the B rest frame, is very sensitive to theoretical schemes of the calculation of quark dynamics in mesons, and thus interesting for SM precision calculations 2 2 in the field of QCD with αs(Q ) at lower Q [51]. The magnitude of the branching fraction above a certain cut in the photon energy (below which neither experiment nor calculation are very precise) is sensitive to contributions from New Physics. The result of this measurement is (b s/dγ)=(3.21 0.33) 10−4 for E > 1.8GeV B → ± × γ where the energy cut is applied in the B rest frame. In addition, the direct CP asymmetry in the decay between B and B¯ mesons can be measured by applying a lepton charge tag on the opposite B. This is also sensitive to New Physics, this time with an emphasis on models with additional CP violation. The result is (b sγ) = 0.057 0.063 [47]. The ACP → ± current world average of all sensitive measurements on the branching fraction is (B B → sγ) = 3.43 0.21 0.07 10−4, for E > 1.6GeV [52]. This agrees very well with the SM ± ± × γ expectation [49]. Similar measurements exist from the Belle experiment [53]. Fig. 2(b) shows an interpretation of the constraint of the measurement on the tree-level Higgs parameters in the THDM type II. It can be seen that mass scales of more than 300GeV can be tested using the precision measurement of 5.28GeV particles. There are also other interesting channels beyond b sγ. Recently there has been a → substantial improvement in the measurement of the branching ratio of the decay B µµ. s → The best measurement is now the average of measurements from LHCb, CMS and ATLAS at (B µµ)=(3.2 1.0) 10−9 [52]. The SM rate of (B µµ) = (3.2 0.2) 10−9 [54] B s → ± × BSM s → ± × agrees perfectly with the measurements. This is unfortunate for finding New Physics, but it does not not cause a significant problem for constraint SUSY models as studied in Section 6. There, it was expected that (B µµ) agrees perfectly with the SM already before the B s → (B µµ) (see e.g. [55]), because the superpartners and the heavy Higgs bosons are forced B s → to higher mass values by the direct bounds from SUSY searches at LHC (cf. Section 5).

Precision measurements at LEP and SLD As outlined in Section 2.1, the agreement of the SM prediction with precision measurements of the gauge interactions is remarkable, as outlined in Fig. 3 [9,56]. See these references also for a description of the experimental definition of the observables and the analyses. For many models of New Physics, such as most Technicolor models, the precision data cannot be explained. However, this is not a problem for every model. In many Constraint SUSY models [57], the SM precision observables are automatically preserved. Indeed, despite their high precision and the absence of any ambiguity in the interpretation of the measurement, the contributions of these observables to the fits in [57] have been found to be negligible. 2 Relevant constraints only come from the effective weak mixing angle sin θeff and the W- 2 boson mass. The former is a remarkable feat, because SUSY can actually predict sin θeff . This works by turning the argument of unification around: Instead of observing that SUSY achieves unification of the gauge couplings given their measured values, one can assume gauge unification at the scale MGUT and then predict the ratio of the gauge couplings in 2 sin θeff at the scale mZ . This fit matches almost perfectly [55].

3.2 Do we understand the Universe we live in? The obvious and simple answer to the question in this section title is “No”. This was already outlined in Section 2.2. If the standard model of cosmology is correct at all, the Universe seems to be made of Dark Energy at about 70% of its energy content, and DM at about 25 % of its energy content, about none of which anything is known in detail. The matter we know in the SM makes up only about 5% of the energy content of the visible 18 Section 3 Boundary Conditions: Precision Measurements and Cosmology

30 L3 LEP 10 4 (pb)

− + − e+e →e e–qq − − WW e+e →qq(γ) 3 σ 10 + − + − e e →µ µ (γ) 20

10 2

10 10 Cross section (pb)

− + − e+e →W W YFSWW/RacoonWW + − no ZWW vertex (Gentle) 1 e e →ZZ − + − only ν exchange (Gentle) e+e →W W γ e − e+e →γγ -1 − 10 e+e →HZ 0 m = 115 GeV H 160 180 200 80 100 120 140 160 180 200 √s (GeV) √s (GeV) (a) (b)

Figure 3: In (a) an overview of the cross-section measurements of different processes compared to the SM prediction at LEP I and LEP II is shown for the L3 experiment [9]. Results of similar precision are obtained from the 3 other LEP experiments. This exemplifies the extraordinary precision at which the SM describes the data, and which makes it so difficult to find alternative theories. A specific example of the power of the LEP data is shown in form of the threshold scan of the W ±W ∓ production in (b), which shows that the gauge interactions also work for the non-abelian direct 3-point and 4-point interactions made possible by the theory, which were not motivated in any way by the measurements known at the time of invention of the SM [56].

Universe. Alternatively, one could say “If it isn’t dark it doesn’t matter” [58]. However, the fact that one does not know what Dark Energy and DM is, does not mean that its properties are completely unknown. The most obvious observable which is measured quite precisely by a combination of the data from the WMAP and PLANCK satellites, distant Supernova observations, baryon acoustic oscillations and rotation curves of the galaxies [16] is the contribution of DM to the total energy content in the Universe, which is estimated to be Ω h2 = 0.1187 0.0017. DM ± Weakly interacting massive particles (WIMPs), if neutral and stable on cosmological time scales, are very good candidates for the cosmological dark matter – the prime example being the lightest neutralino [59]. Thermally produced in the early Universe, the WIMP relic density is set by the (co-)annihilation rate (see e.g. [60]) requiring that all dark matter is constituted by thermally produced neutralinos. This makes the relic density one of the most constraining observables for the CMSSM parameter space. Another possibility to learn about DM is the so-called direct detection, where it is assumed that the relic DM collides with the detector material and leaves a recoil signal. To add to the already existing confusion concerning the composition of the Universe, controver- sial results have been reported from diﬀerent direct detection experiments. While some of the collaborations, DAMA/LIBRA [61], CoGeNT [62] and CRESST [63] show a signal, others, primarily XENON100 [64] and LUX [65], have shown upper limits nominally excluding the regions of signal detection by the other experiments. Reconciling these on the basis of diﬀering experimental conditions is possible, but challenging, and possible not in the models studied here. Thus, for the interpretations shown in Section 6 it is generally assumed that there is no positive signal of direct detection and that the limits set by XENON100 and LUX apply. 19

4 The Search for the Origin of Electroweak Symmetry Breaking

The search for the Higgs boson and the measurement of its properties, both in the context of the SM and of extended models or alternatives, is the central attempt on closing in on understanding electroweak symmetry breaking. The summary of this quest in this article starts with the searches carried out with the full LEP2 data set, since these essentially dominated the understanding of the limits on the Higgs boson in the SM from around 2000 till around 2010, and in certain cases they are still very important constraints on extended Higgs sectors in many models. For an overview of the theoretical and experimental status of Higgs studies before the LEP era, see e.g. [66], and for a summary of the situation after the first precision measurements and Higgs searches on the Z0 pole, see e.g. [67]. After LEP, it was the task of the Tevatron experiments CDF and D0 to narrow the allowed range of Higgs boson masses [68]. The mass range of 147 m 180GeV was exclusioned mainly ≤ H ≤ using the H WW ∗ channel, but on the lower end of the allowed SM Higgs masses after → LEP2, which are most interesting due to the preference of a low Higgs mass scale by the precision data (cf. Fig. 1(a)), no significant progress over LEP2 was achieved before the LHC experiments ATLAS and CMS started to become significant. Finally, the very smooth start of the LHC machine and detector operation at centre-of-mass energies of √s = 7 and 8 TeV in 2011 and 2012 allowed to close in on the SM-like Higgs much more quickly than anticipated, and on July 4th 2012 ATLAS and CMS jointly announced the discovery of a candidate for the SM Higgs [69,70]. Therefore, in this section, the first focus lies on the Higgs searches at LEP and their model dependent and model-independent interpretation in Section 4.1. The successful Higgs searches for a SM-like Higgs boson at the LHC is covered in Section 4.2. Section 4.3 then introduces two tools, HiggsBounds and HiggsSignals, which aim to make the results from LEP, the Tevatron, and the LHC accessible in the test of arbitrary models containing any number of Higgs-like particles.

4.1 Higgs Searches at LEP

One of the main objectives of the LEP experiments was the search for the Higgs boson, both in the context of the SM [71] as well as in SUSY [36] and in many other possibilities (see e.g. [72]). Compared to high-background environments with unknown initial parton momenta, such as at hadron colliders, LEP was an ideal environment for the search for the Higgs, but of course only if it was kinematically accessible: Beam-related backgrounds were low, in-time background basically non-existent, the event could be completely and precisely reconstructed and was kinematically completely constrained, since the incoming beam energy and momentum was known and completely transferred onto the final state. In addition, the SM physics which contributed the strongest backgrounds was very well under- stood and could be measured independently. Most importantly, the main production modes and the decay modes could be reconstructed precisely and with minimal overlap, making the search very sensitive in all models due to the possibility of the statistical combination of all individual, clean channels. This led to a situation where backgrounds and systematics were low and thus sensitivity was guaranteed up to the kinematic limit. The statistical tools developed and used in the searches for the Higgs boson at LEP can be regarded as a breakthrough in particle physics analyses. The first application of multivariate selection techniques in particle searches at colliders in the form of one-dimensional likelihood analyses was carried out in the search for the Higgs at LEP [73], saving significant amounts of luminosity with respect to cut-based analyses because of a reduction of backgrounds by about 30% for the same signal efficiency. 20 Section4 TheSearchfortheOriginofElectroweakSymmetry Breaking

Another milestone is the improvement in the techniques used for the statistical analysis of the search outcome. Instead of using only counting experiments as before, frequentist multi-bin calculations of confidence levels were introduced to particle physics. Most importantly, the CLs technique was invented [74,75]. It addresses a fundamental issue in the interpretation of confidence intervals, which in principle also appears in any other application of statistical confidence intervals in any other field of research: In a hypothesis test, how shall a situation be treated in which a statistical downward fluctuation of the data with respect to the background could yield an exclusion of a signal to which there is no sensitivity? There are two ways of dealing with that: First, changing the meaning of the measurement, or changing the statistical coverage. The seemingly straightforward solution [76], developed in the context of the ATLAS experiment, is to generally use the confidence limit of the signal plus background hypothesis CLs+b to exclude the alternative hypothesis s + b in favour of the null hypothesis (or background hypothesis) b if CLs+b < 0.05, i.e. if the probability for excluding the s+b hypothesis, if true, on the basis of a statistical fluctuation is 5%. However, as already indicated, in the limit of s + b = b and a downward fluctuation of the data d with respect to the background expectation b by 2 standard deviations, in this approach s + b will be excluded although there cannot be sensitivity to the hypothesis obs exp s = 0. Therefore, in this approach, if CLs+b < CLs+b( 1σ), the observed confidence limit obs − CLs+b is replaced by the expected 1σ fluctuation of the confidence limit of the s + b exp − hypothesis CL ( 1σ). This approach looks simple and attractive, because it maintains s+b − the statistical coverage of the hypothesis test. But it has one fundamental drawback: It changes the definition of the measurement depending on the outcome of the measurement. Therefore, the previous solution from LEP prevailed: In [74] the definition of the measurement remains independent of the outcome of the measurement, but instead the statistical coverage of the limit is sacrificed by defining a quantity CLs = CLs+b/CLb which does not follow the frequentist properties of a confidence limit anymore. On average, if CLs < 0.05 is used to exclude the s + b hypothesis, the probability to exclude a true signal s grows to 10%. On the positive side, there is no possibility to exclude too small s anymore, since in this case CL CL and hence CL 1, and most importantly the definition of s+b ≈ b s ≈ the measurement is unambiguous. Interestingly, there seems to be a third way of dealing with the question of what to do about potentially excluding hypotheses to which there is no sensitivity, which is to ignore this problem. This seems to be the adopted solution outside high energy physics. It was already indicated that CLs is not strictly a well behaved frequentist quantity. Also, while the limit setting at LEP [74,75] was still defined in a statistically frequentist way, there is a Bayesian element in the form of the treatment of systematic uncertainties. Signif- icant improvements in that regard were made in the context of the LHC experiments (see Section 4.2). For a general discussion of frequentist and Bayesian treatments of statistics, see Section 6.1. LEP2 took data from 1996 to 2000 at √s = 161 209GeV and with integrated lu- − minosities of around int 200 pb−1 per step in the centre-of-mass energy. The main L ≈ search channels in the SM [71] are all combinations of the three production mechanisms Higgsstrahlung e+e− Z0h0, WW fusion e+e− ννh0 and ZZ fusion e+e− e+e−h0 → → → with all Z0 decays into e+e−,µ+µ−,τ +τ −,νν,q¯ q,¯ b¯b and the most relevant Higgs decays in the SM, h0 b¯b, τ +τ −. For New Physics scenarios, many alternative channels were added → to the SM-like ones [36]2: Yukawa production e+e− b¯b b¯bh and associated produc- → → 2For the full details of this analysis see the article “Search for neutral MSSM Higgs bosons at LEP”, Eur.Phys.J. C47, 547 (2006), which is contained in the full Habilitation treatise. 21 95 β 1 LEP (b)

(b) tan m -max √s = 91-209 GeV h - H→bb 10

-1 Excluded 10 by LEP

1 Theoretically Inaccessible

S -2 10 20 40 60 80 100 120 0 20 40 60 80 100 120 140 2 2 mH1 (GeV/c ) mh (GeV/c ) (a) (b)

Figure 4: In (a) a model independent interpretation of the LEP Higgs searches from all 4 experiments is shown. The data is tested against the presence of a Higgs boson with variable mass and with (H b¯b)=1. B → The excluded scaling factor with respect to the SM σ at the same mass is shown which yields a 95% ×B CL exclusion. This number can be tested in almost any model producing Higgs bosons with any branching fraction of H b¯b. The full black line denotes the observed limit, while the expectation is given by the → dotted line. The green (yellow) band shows the 1σ (2σ) uncertainty around the expectation. In (b) the interpretation of the same data in a specific benchmark model of the MSSM is shown. A more stringent limit is achieved by combining different search channels, but the resulting exclusion cannot be interpreted in any model [36]. Here, the yellow area is theoretically inaccessible (at the side of higher mh this area depends on the value of mt. Different choices from mt = 165 GeV to 180 GeV are shown in the form of the near parallel lines around the upper yellow area), the light (dark) green areas are excluded at the 95% CL (99% CL), and the dashed line gives the expectation for the 95% CL. tion of two Higgs states e+e− h h , and including additional decays like h invisible, → 1 2 → h anything, h h h and h gg. For all four experiments, more than 160 search → 2 → 1 1 → channels were analysed in parallel. Generally the overlap is small, and where an overlap exists, like between e+e− h h b¯bb¯b and e+e− Z0h0 b¯bb¯b, in most channels it is → 1 2 → → → analysed and subtracted. Finally, where an overlap could exist but has not been numerically analysed, the search channel with the higher expected significance is used and the other one is discarded. Using the approach described above, a large number of limits in the SM, in alternative theories and in model-independent analyses are derived. The first set of model independent results to be discussed here are the model independent limits. An example can be found in Fig. 4(a). Here, all Higgs searches at LEP, independent of what they were aimed for, where interpreted for the presence of a signal of e+e− Z0h0, WW fusion e+e− ννh0 and ZZ → → fusion e+e− e+e−h0, with a SM mixture of Z0 decays, fixed SM-like ratio between the → three production modes, and a branching fraction (h0 b¯b) = 1. This is the prototype B → of a simplified model search (SMS) as introduced for LHC much later (cf. Section 5.2). In the absence of a significant signal, the limit is guaranteed to be conservative, because the signal in the single channel h0 b¯b can consume the full available statistical space left in → the statistical analysis between the background expectation and the data, instead of sharing that space with other channels. The result can be interpreted in every physics model, which within statistical precision obeys the conditions assumed during calculation of the limit, in this case the relative rates of the three production channels. Luckily, this is a rather general assumption, since basically all models which break the above conditions also completely 22 Section4 TheSearchfortheOriginofElectroweakSymmetry Breaking destroy electroweak symmetry breaking or at least violate the precision data. The plot in Fig. 4(a) then for each Higgs mass mh gives the maximal scaling factor S with respect to the SM cross-section at the same mass, which is still allowed at the 95% CL. For a more detailed description, see [36]. Similar results exist for all major search channels. These results form the basis of the HiggsBounds input described in Section 4.3. As already outlined, the model independent results can be applied in almost every model, but they have the drawback that they are conservative in terms of the significance of the limit. Therefore, an attempt is made to maximise the sensitivity to specific cases of New Physics by defining so called benchmark models, in the case discussed here for SUSY in the rather general form of the MSSM [77]. The idea is to adjust the parameters of the general MSSM in such a way that for every given choice of two “visible” parameters, in this case the tree-level parameters of the MSSM Higgs sector tan β and mA or mH± , a given phenomenon is maximised. An example for that is given in the “mh-max” scenario in Fig. 4(b). There, for every point in (tan β, mH± ), mh is maximised, moving the theoretically allowed space of the plot in Fig. 4(b) as much to the right as possible. Thus, the minimal exclusion of tan β around tan β 1 in the plot is realised, because the maximal excluded area of course ≈ does not increase over the SM equivalent limit of m 114.4GeV. The plot also shows the h ≥ dependence of the upper limit on mh on the top quark mass mt, which dominates the loop contributions to m , which at tree level is constraint to m m . h h ≤ Z Today, these LEP Higgs benchmarks not only still provide exclusions in the parameter space where no other experiment can contribute (see e.g. [78]), but serve as an ideal calibra- tion of re-interpretations of the model independent search results. Thus the legacy of LEP is still important today: As a milestone in the way selections and statistical analyses were performed, and still as a source of the most significant exclusions on significant parameter ranges in interesting models, even more than 13 years after the shutdown of LEP.

4.2 Higgs Searches and Measurements at the LHC

In a multi-messenger approach, it is obvious that it is advantageous to search for a new particle not only in a small set of exclusively reconstructable production modes based entirely on the electroweak interaction, as at LEP, but to use different probes. Hadron colliders can probe the Higgs sector in both the SM and New Physics in a partly orthogonal and complementary way. While LEP reached very high sensitivity where the Higgs was expected to be kinematically accessible, it had no sensitivity above a hard kinematical cut-off, evident in the near vertical slope of the curves in Fig. 4(a) at around mh = 114 GeV. At a hadron collider, the situation is different. While the backgrounds are much higher than at an e+e− machine, and while the control of the initial state and production mode is very much reduced, the accessible centre-of-mass energy can be significantly increased due to the absence of synchrotron radiation. However, a high luminosity is needed to acquire enough collisions at high momenta of the colliding partons. In addition, new production modes such as gluon- gluon fusion with a top-quark loop and associated production with top quarks open. For 10 years, the Tevatron experiments [68] pushed the limits on the production cross-section down towards the SM over a very wide mass range, but were not ultimately able to gather enough luminosity to claim a discovery. Despite the great methodological improvements in the Tevatron era it is therefore obvious that the next breakthrough discussed here is the Higgs discovery at LHC by ATLAS and CMS [69,70], using int = 4.9fb−1 of data taken L each at √s = 7TeV and int = 5.9fb−1 of data taken each at √s = 8TeV in the first part L of the LHC Run1 in 2011 and the beginning of 2012. The experimental results at LHC are interpreted on the basis of an improved frequentist calculation of sensitivities, uncertainties, discovery significance and exclusions [79]. This 23 approach is called profile likelihood limit setting (PLL). On the outside, it works just as at LEP, with a multi-bin input and the calculation of CLb,CLs+b and CLs. But on the inside, it is improved in three important aspects. First, it can be used in an almost entirely frequentist way, since the Bayesian treatment of the systematics can be avoided. This is achieved by including the data in the systematics control analyses into the limit machinery and to fit a nuisance parameter θ for each systematic uncertainty, simultaneously in the control region and the signal region. Such, any Bayesian assumption on the probability density function of the systematic variations can be avoided. Second, there is a set of changes in the test statistics q used for the hypothesis test. There are now different test statistics for discovery (q0) and exclusion or parameter measurement (qµ). For the former, that reduces the dependence of the meaning of a discovery on the signal hypothesis, which is aimed for because a statement of whether the data agrees with the background hypothesis or not should not depend strongly on the signal hypothesis, which unfortunately could happen in the LEP setup. For the latter, this is interesting because a limit is now treated completely analogously to a fit, with a free parameter µ to control the signal strength, and consisting of a comparison of the signal hypothesis to the best fit parameter point, and not to original null hypothesis. This changes the meaning of the limit, though, from “how well can signal plus background and background hypotheses be separated” to “How well can the signal plus background hypothesis be separated from the best fit configuration”. As a practical side effect, this setup allows the faster calculation of asymptotic approximations of the limit and of the look-elsewhere-effect [80]. Third, the re-definition of the test statistics allows to seamlessly transform the calculation of exclusions on models with a given signal strength µ into measurements of model properties, once a signal is significant. Then, one can fit µ instead of testing a given µ, and determine the best-fit signal strengthµ ˆ and its uncertainties. Further, almost arbitrary combinations of parameters can be fitted, once the measurements are significant enough to constrain more and more parameters simultaneously. Such, e.g. a mass m and a signal strength µ can be fitted simultaneously, or several signal strength modifiers of different final states. In terms of dominant search channels, the situation is also different compared to LEP: First, the mass range of the searches is moved to higher values, allowing WW and ZZ final state to become dominant for the SM Higgs above m 135GeV. Second, the limitations h ≈ of the trigger play an important role: Higgs decays into hadronic final states, such as the dominant b¯b, cannot be recorded unless the rest of the event (e.g. the part recoiling against the H) produces a usable trigger. This limits the production mode significantly for a mode with high hadronic branching fraction, to e.g. tth¯ or Zh with Z ℓℓ. On the → other hand, the luminosity is enormous, reaching inst = 8 1033 cm−2s−1 [81], effectively L × producing a Higgs boson every 3 seconds on average, at the price of about 20 overlaid hadronic interactions per individual bunch crossing and with 20 Million bunch crossings per second. Hence, also low branching fraction modes can be used if the trigger efficiency is high and the reconstruction is clean. Therefore, modes with branching fractions of around −4 ∗ + ′− ∗ 10 like h γγ, h WW ℓ ν ℓ ν¯ ′ and h ZZ 4ℓ become the most important → → → ℓ ℓ → → search channels at mh < 150GeV. If the final state of the Higgs boson can be triggered directly, no restriction on the production mode exists and all modes, gluon fusion ggF , vector boson fusion V BF , Higgsstrahlung VH and associated production ttH can contribute. Fig. 5 gives an impression of the results for the LHC Run1 data set at √s = 7 and 8TeV, taken in 2011 and 2012 with the ATLAS and CMS detectors. In Fig. 5(a) as an example of the experimental results the reconstructed mass distribution of the H γγ search for the → full Run1 data set from ATLAS is shown, which exemplifies the unquestionable significance 24 Section4 TheSearchfortheOriginofElectroweakSymmetry Breaking

10000 m = 125.5 GeV ATLAS ATLAS Preliminary H → 8000 Data 2011+2012 W,Z H bb SM Higgs boson m =126.8 GeV (fit) s = 7 TeV: ∫Ldt = 4.7 fb-1 H ∫ -1 Bkg (4th order polynomial) s = 8 TeV: Ldt = 13 fb H → ττ 6000 s = 7 TeV: ∫Ldt = 4.6 fb-1 -1 Events / 2 GeV H γγ→ s = 8 TeV: ∫Ldt = 13 fb (*) H → WW → lνlν 4000 s = 7 TeV: ∫Ldt = 4.6 fb-1 -1 -1 s = 8 TeV: ∫Ldt = 20.7 fb s = 7 TeV ∫Ldt = 4.8 fb H → γγ 2000 -1 -1 s = 7 TeV: ∫Ldt = 4.8 fb s = 8 TeV ∫Ldt = 20.7 fb s = 8 TeV: ∫Ldt = 20.7 fb-1 (*) H → ZZ → 4l 500100 110 120 130 140 150 160 s = 7 TeV: ∫Ldt = 4.6 fb-1 400 s = 8 TeV: ∫Ldt = 20.7 fb-1 300 200 Combined µ = 1.30 ± 0.20 ∫ -1 100 s = 7 TeV: Ldt = 4.6 - 4.8 fb s = 8 TeV: ∫Ldt = 13 - 20.7 fb-1 0 -100 -200 -1 0 +1 100 110 120 130 140 150 160 Events - Fitted bkg Signal strength (µ) m γγ [GeV]

(a) (b)

Figure 5: In (a) the distribution of data events after the selection of photon pairs in the ATLAS Run1 data of 2011 and 2012 is shown [82]. The background is subtracted in the lower inlet, showing the compelling signiﬁcance of the peak at the Higgs mass of around 126 GeV. (b) shows the measurement of the strength of the signals in the most relevant SM Higgs search channels relative to the SM expectation [83]. A slight excess over the SM is observed, and a very clear separation from the null hypothesis. Similar results from the CMS collaboration are shown in (c), which shows the H ZZ∗ 4ℓ channel [84], and (d), which shows → → the CMS Higgs signal rate measurements [85].

of the discovery. Since the final state can be triggered and reconstructed independently of the initial state, all production modes can contribute and the significance is high due to the good mass resolution. Additionally, the search can be decomposed into many different subcategories. This allows to increase the significance by separating low-background and high-background configurations. The mass measurement can be improved by separating low resolution and high mass resolution configurations. In addition, this separation can be used to tag different production modes with reasonable purity and efficiency, such as ggF and V BF , which in turn allows to measure the contribution from the different production modes separately and thus acquire a significance of more than 3 σ for the V BF process [86]. These subchannels are also important for the techniques employed by HiggsSignals described 25 in Section 4.3. The other Higgs decay channel allowing a precise mass measurement is H ZZ∗ 4ℓ, shown in Fig. 5(c) from the CMS experiment [84]. → → The summary of most of the present signal strength measurements from ATLAS is given in Fig. 5(b) [83,86]. The measurements are consistent with each other and with a SM signal strength of µ = 1. An important update is the first measurement of a direct decay mode into fermions above a significance of 4 σ in the form of H ττ by the ATLAS collaboration [87]. → While ATLAS seems to prefer a signal strength slightly larger than the SM prediction for most channels, CMS interestingly seems to stay on the opposite side [70,85]. This can also be observed in Fig. 5(d), which shows the corresponding CMS Higgs deacy rate measurements. No systematic reason for that phenomenon is known, and it is not yet significant, such that it can be expected that the two experiments will converge, whether at the SM strength or somewhere else. In addition to the compelling measurements of the Higgs signal strengths in agreement with the SM, many other measurements have already been published or are ongoing. More decay channels (e.g. µµ, Zγ) can be tested, the spin is already measured convincingly to be 0 [88], and if the particle is a pure CP state then indications are strong that it is + as required for the SM Higgs boson. Also, the first unfolded differential distributions of the Higgs production kinematics are already public [89]. One particularly interesting approach is to look for invisible decays of the Higgs boson [90] in the recoil from the leptonic Z decay in ZH or in the recoil from the jets in VBF. These searches can be used to constrain the total width of the Higgs boson under the assumption that it has no other non-SM decays. For an overview over the growing list of results from ATLAS and CMS, see [91]. Not only was the Higgs discovery at LHC quicker than anticipated before the start of data taking, but also is the depth of experimental knowledge about the new particle already much greater than expected. The observables at the LHC are already excluding every candidate for the observed Higgs boson in New Physics models which does not at least roughly behave as the SM Higgs boson (this of course does not mean that there cannot be other Higgs bosons in New Physics models which would not yet be detected). An example would e.g. be the SM with 4 generations, which can be easily constrained strongly [92]. However, as it will be discussed in Section 4.3, there are not yet many truly model independent measurements of the Higgs boson which holds under any assumption. Thus, many more refinements of measurements can be done at the LHC with higher centre- of-mass energy and luminosity, and there is a lot of room for truly model-independent measurements3 of the Higgs at a precision machine like the ILC.

4.3 Model Independent Interpretation in Arbitrary Higgs Models The negative Higgs search results at LEP, the partially negative results at Tevatron, and also the many other searches for very low-mass Higgs bosons at other colliders (see e.g. [94]) form one of the most important constraints on New Physics, of course in close conjunction with the SM precision data (cf. Section 3.1). Now, in addition, a Higgs boson has been discovered by ATLAS and CMS, and also the results from the Tevatron can be used to help to understand this particle. But is important to stress that the discovery of this Higgs boson does by no means render the Higgs searches with negative outcome unimportant, because they still constrain models with extended Higgs sectors with respect to the SM as much as they did before. And it is also obvious that there is an inﬁnite number of interesting models with SM-like as well as with extended Higgs sectors which remains to be tested against the data with as much precision as possible. Especially in a situation like the present one, where it is clear that particle physics has to leave the SM and move on, but where it is completely

3For a discussion of what “model independent” means in this context see e.g. [93]. 26 Section4 TheSearchfortheOriginofElectroweakSymmetry Breaking unclear where to go. Finding a ﬁrst concrete hint of where exactly to go beyond the SM is one of the most interesting opportunities in particle physics. Unfortunately, there is a practical diﬃculty for this important task, on which hundreds or thousands of particle physicists are working, though: First, it is very tedious to implement results from a very large number of papers from many collaborations. And second, for the theory community it proved to be not straightforward to reliably do so with full statistical consistency. Therefore, this section describes a set of tools which allows one to interpret any model with any number of scalars against the negative Higgs search data and against the Tevatron and LHC Higgs rate and mass measurements.

HiggsBounds HiggsBounds [95,96,97]4 is a public Fortran computer code which allows to test SM-like or extended Higgs sectors against the published negative search data. For a full list of the experimental input, consisting of 150 individual limits, see the extensive list of references in [95,96,97]. As input, the code requires information about the number of charged and neutral Higgs mass states, their masses and their production and decay. The information about the couplings can be given in the form of branching fractions and hadronic or partonic cross-sections, or simply in the form of effective couplings, if the model under study allows one to do so. Computer codes for calculating predictions of New Physics models such as SUSY can calculate the required input (see e.g. [98]), which for SUSY for simplicity can also be given in the SLHA interface [99]. The public code HiggsBounds has been used in a very large number of phenomenological studies, as evident from the about 250 citations for the first two papers alone. The main motivation for the creation of such a code was the observation that many phenomenological studies of Higgs-like sectors against the data were done with just a subset of the available sensitive experimental results , and often with questionable statistical techniques. One common misconception is to test a given prediction for observables in different channels or experiments against more than one observed limit. That sounds intuitive, but unfortunately the limits are typically 95% CL, implying that hypothetically there is an up-to 5% chance to exclude the signal hypothesis despite the “fact” that it is true. The exact number of this error rate is unknown and different for each search. That itself is not a problem, since it is known to be 5% or less. However, when testing several observed limits in parallel, the chance to wrongfully exclude a true signal is up to 5% at each test, which means that after n tests the true confidence level might be as low as 1 0.95n, where n can be of − (100). This of course is not intended, and mostly not realised in these studies. Therefore, O if a true statistical combination cannot be done precisely enough, e.g. because of missing information on channel systematics correlations or simply because of missing computing resources, it is necessary to test the data against only the most significant observed limit. This is implemented in HiggsBounds in such a way that of all applicable channels, the expected limit is compared first with the prediction. Only for the single channel with the highest ratio of expected signal against expected limit, the observed limit is compared with the prediction. Compared with a full combination, this is conservative, but always correct. A second challenge arises from the applicability of a given limit on a prediction. A typical example concerns the assumptions made in the published limit on the composition of

4For the full details of this analysis see the articles “HiggsBounds: Confronting Arbitrary Higgs Sectors with Exclusion Bounds from LEP and the Tevatron”, Comput.Phys.Commun. 181, 138 (2010), “Higgs- Bounds 2.0.0: Confronting Neutral and Charged Higgs Sector Predictions with Exclusion Bounds from LEP and the Tevatron”, Comput.Phys.Commun. 182, 2605 (2011), and “HiggsBounds-4: Improved Tests of Extended Higgs Sectors against Exclusion Bounds from LEP, the Tevatron and the LHC”, arxiv:1311.0055 [hep-ph], accepted by EPJC, which are contained in the full Habilitation treatise. 27

60 LEP e+e- → HZ 100 f=1.00 f=0.50 10 f=0.25

10 1 ) s+b tan β 0.1 ( CL 2 χ 0.01

1 0.001 max mh scenario (mt = 174.3 GeV) 0.0001 0.4 110 112 114 116 118 120 0 20 40 60 80 100 120 140 mH [GeV] Mh[GeV] (a) (b)

Figure 6: In (a) a reproduction of the model-dependent limit in Fig. 4(b) is made with the program HiggsBounds, using only the model independent limits in the spirit of Fig. 4(a). This is guaranteed to deliver a conservative approach to the true combination and matches the true combination almost everywhere [95]. In (b) another information is shown which can be extracted from the LEP Higgs data and is provided by HiggsBounds: A translation of the observed CLs+b for every combination of Higgs masses and most importantly for every signal strength into a χ2 (under Gaussian assumptions) [97]. production modes and decay branching fractions. A weak form of this would be the mixture of production modes in the LEP model independent interpretations of the single Higgs production from HVV vertices (cf. Section 4.1). There, a SM-like mixture of Higgsstrahlung and vector boson fusion is assumed. This is a weak assumption because it is very difficult for a model to break this SM prediction without violating the SM precision measurements. Still it is a model assumption whose validity needs to be confirmed. A strong assumption e.g. would be assumption on SM-like Higgs branching fractions in a LEP or Tevatron SM search combination. In order to test whether a model is applicable, HiggsBounds checks whether the ratios of the relevant channels in the tested model point, weighted with their absolute size, are within a very small (user configurable) band around the assumption used for the limit generation [97]. Testing the applicability, as described above, is an important step in ensuring that the reported limit is truly exact or conservative. Given the two important restrictions on the fact that there is only one applicable channel, as discussed above, might sound destructive for the power of the test. In practice, the limitations are mostly small. This is shown in Fig. 6(a) [95]. It is a test of HiggsBounds against the LEP results shown in Fig. 4. Using only the model independent results (as e.g. in 4(a)) as input, the limit in the “mh-max” scenario is almost perfectly reproduced (cf. Fig. 4(b)). In blue, there is the additional contribution of the Tevatron at the time of publication of this plot, which is of course not in Fig. 4(b). Only above the little nose, in the area around mh = 90GeV, tan β = 6, there is a small difference, where the HiggsBounds result is conservative. The reason is that in that area the largest amount of channels contributes at the same time (e.g. e+e− hA b¯bb¯b → → or b¯bτ +τ − and the same final state for e+e− Zh). In the official analysis, a combination → under application of the full information on correlations of systematics and partially of overlap is done, while in the HiggsBounds analysis only the strongest channel at each point is shown. Therefore, as intended in the construction of the HiggsBounds algorithm, one can see that the general agreement with full combinations can be regarded as excellent, and 28 Section4 TheSearchfortheOriginofElectroweakSymmetry Breaking that where differences are expected they are conservative. Up to now HiggsBounds was discussed in terms of the purely digital question of whether a channel is excluded at the 95% CL or not. HiggsBounds 4.1 [97] brings the addition of an approximation of a likelihood for the LEP exclusions, which are still dominant contributions to the exclusion in significant areas of parameter spaces of New Physics models (see e.g. [97,100] for examples from SUSY). This is provided in the form of χ2 contributions from the limit for every mass point and for every signal strength parameter µ = [0.001, 1], for which the CLs+b value has been retained in the LEP model independent limits. From 2 CLs+b for every given set of Higgs mass(es) and µ, an approximation to the χ is calculated under the assumption that the CLs+b is Gaussian. An example for this is shown in Fig. 6(b) [97], for the LEP HZ channel and H b¯b. For different signal strength (labelled → f in the plot) different χ2 are obtained. The χ2 goes to 0 at the point where both the limit of sensitivity is reached and where the expected signal plus background agrees exactly with the data. This point moves to smaller mH with smaller f. Such information is very valuable in fits, and it would be useful for many more information if likelihoods like that, for all relevant parametrising dimensions, and not only for e.g. masses, would be available also from the LHC and the Tevatron routinely. In addition to the LEP and Tevatron limits, negative search results from the LHC on Higgs bosons beyond the SM or at m 125GeV are also included in HiggsBounds, and H ≫ also limits from non-classical Higgs searches like t H+b searches [101], but these are not → further discussed here. In summary, HiggsBounds is a tool which allows to test a very wide set of negative search results on Higgs bosons. This is still very relevant today – many models of New Physics, for example SUSY, predict extended Higgs sectors, and the limits on those additional Higgs bosons should not be forgotten in the presence of one discovered Higgs.

HiggsSignals In the presence of the recent discovery of a new particle, a 125 GeV Higgs boson, and given the very important role it could play in understanding electroweak symmetry breaking (cf. Sections 2 and 4.2), it is obvious that there is enormous interest to test the properties of this particle against all possible models with at least one scalar in the right mass range. Of course there is a large amount of already very sensitive interpretations published by AT- LAS and CMS [91]. However, these are interpretations, under given assumptions. Not every model can be mapped onto, e.g., pure variations of the effective ggH cross-sections and the effective H γγ branching fraction. Therefore, the aim of HiggsSignals [100,102]5 is to → use the fundamental experimental results, the mass peak and signal strength µ measurements in each individual search channel (currently 67 individual channels with 4 precise mass measurements), or preferentially even the µ-band plots, where available. From this fundamental experimental input, also from Tevatron where available [68], the interpretation in every model can be attempted using a χ2 calculated in HiggsSignals. It uses a complex procedure to try to treat the experimental results as closely as possible to what is available within the collaborations, by carefully decomposing the uncertainties on the published rate measurements into all theoretical sources of systematic errors and all known correlated experimental errors, and a rest which contains the statistics and the remaining publicly inseparable experimental systematics. Another scarce piece of information is the sub-channel composition, which depends on the relative efficiency of the different Higgs

5For the full details of this analysis see the article “HiggsSignals: Confronting arbitrary Higgs sectors with measurements at the Tevatron and the LHC”, arxiv:1305.1933 [hep-ph], accepted by EPJC, which is contained in the full Habilitation treatise. 29

HiggsSignals-1.1.0 10 using ATLAS Moriond 2013 results H -> WW H -> ZZ 8 H -> γγ

4 qqH+VH µ

-2 0 1 2 3 µ ggF+ttH (a) (b)

Figure 7: In (a) the reproduction of the fit from the ATLAS collaboration of the signal strength modifiers for Higgs couplings to gauge bosons µV BF +VH and for Higgs couplings to fermions µggFttH by HiggsSignals for different Higgs decays is shown [83]. HiggsSignals reproduces the results very closely [100], including the lower cut-off of the h ZZ∗ channel, where the predicted rate turns negative. This serves as a validation → of the HiggsSignals approach. For the HiggsSignals results, the full (dotted) lines denote the 1σ (2σ) uncertainty. In (b) at simultaneous fit of the modifiers κ of the Higgs to vector-boson partial widths and cross-sections (κV ) and of the Higgs to fermion couplings (κF ) using the ATLAS, CMS and Tevatron results is made in HiggsSignals. The full line gives the 1σ uncertainty around the measurement (green star). Agreement with the SM (yellow diamond) at the 1 σ level is observed [100]. production modes into all (sub)channels of the analysis. If public information on these efficiencies is available, it is used by default in HiggsSignals. The interpretations done by the experimental collaborations cannot always be reproduced exactly, first, because the exact likelihood of all individual searches which enter the PLL calculation are not public, and second because there is missing information in the form of correlations on experimental systematics or on the exact way of how the theory systematics was implemented. The first challenge is of course fundamental. In HiggsSignals, a χ2 is constructed under the assumption of Gaussian errors with linear correlations. In practice, this seems to work reasonably well, but of course not fully exactly. The second problem could in principle be circumvented if more information was publicly available [103]. Despite these limitations, there is the advantage that HiggsSignals allows to treat every model with scalars in a phenomenological study, which would not be possible without large efforts (similar to HiggsSignals) otherwise. It is of course advisable that very interesting models, which look very attractive based on evaluations using e.g. HiggsSignals, are tested directly by ATLAS and CMS. Given the substantial differences between the full knowledge of all correlations, the nuisance parameter treatment of the systematics, and the Poissonian probability density functions for the statistics employed in the PLL calculation of the results from ATLAS and CMS, it is an obvious question to ask how well the approach in HiggsSignals with all its sophistication, but also inevitable simplification, fares in a direct comparison. The most straight-forward sensitive comparison is shown in Fig 7(a) for the comparison with ATLAS (similar results available for CMS) [100]. Here, the signal strength modifiers µggF +ttH and µV BF +VH are fitted in parallel against the data of three different final states at fixed mass and keeping the SM Higgs branching fractions fixed, which makes it both sensitive (due to the dependence on the production kinematics) and simple (due to only two physical 30 Section4 TheSearchfortheOriginofElectroweakSymmetry Breaking

2σ BR(H → NP) 1σ 0.0 0.2 0.4 0.6 0.8 1.0

2σ 2σ κV κV 1σ 1σ

2σ 2σ κu κu 1σ 1σ

2σ 2σ κd κd 1σ 1σ

2 2σ σ κℓ κℓ 1 1σ σ

2 2σ σ κg κg 1 1σ σ

2 2σ σ κγ κγ 1 1σ σ

0 1 2 3 4 0 0.5 1 1.5 2 2.5

(a) (b)

Figure 8: An example for the capabilities of HiggsSignals [105]. (a) shows a validation of the HiggsSignals approach using a 6 dimensional fit of κ parameters. The blue line is the official CMS result, which is approached quite closely by the HiggsSignals result. (b) adds data from ATLAS and the Tevatron to the fit, and at the same time adds one important parameter: The branching fraction of the Higgs into invisible parameters. parameters). It can be seen that for the best-fit points and for the 1 σ environments an excellent agreement is reached. For H ZZ∗ it is even possible to reconstruct the line below → which the signal prediction turns unphysical, i.e. negative. The slope of this line critically depends on the sub-channel efficiency assumptions. The only area of visible disagreement is the upper 2 σ in H ZZ∗, which, due to the low statistics in the relevant VBF enhanced → categories, can be expected to be most strongly subject to remaining differences between the Gaussian and Poissonian probability density functions. After this and many other generally successful tests against results of ATLAS and CMS [100], simple “combinations” of the experimental results, also including the Tevatron, which is still sensitively contributing for H b¯b final states, can be attempted. An example → for this is shown in Fig. 7(b). It shows the result of a fit in the plane of κV and κF [104], strength modifiers not for the bare couplings, but directly for the relevant partial widths and cross-sections. In this case, the Hff channels with a direct contribution from Higgs- to-fermion couplings (such as Γ(H b¯b) or also Γ(H γγ) through the top loop) are → → scaled independently from the vector boson channels (such as σV BF in the production or Γ(H ZZ∗) in the decay). Such a result is up to now not available from the collaboration, → since no true combination exists. Here, we can see that the data from all experiments is in agreement with the SM at the 1 σ level, and that loop-induced processes and their interferences help to reduce the allowed region to the (κV , κF ) = (1, 1) point and disallow the ( 1, 1) point, albeit only at the > 2σ level. For a much more extensive list of available − − cross-checks of and results from HiggsSignals, see [100]. In Fig. 8, there is a glimpse of more complex results obtained with HiggsSignals. As already outlined, the Higgs measurements from the LHC (and partially still the Tevatron) are starting to become extremely sensitive to deviations from the SM, albeit only under certain assumptions. For example, at the LHC the total Higgs width cannot be experimentally 31 constrained. Therefore, if one assumes that basically arbitrary branching fractions into any state, triggerable, untriggerable, and invisible are allowed, then one can allow any coupling to any fermion or vector boson. The simple reason is that in the calculation of =Γ /Γ Bi i tot each measured branching fraction can be fixed to the observed value by simultaneously Bi increasing Γi and Γtot. As long as no independent constraint on the total cross-section exists, such as at an e+e− machine [14], this problem cannot be solved at the LHC. However, while it is uninteresting to plot a measurement with no constraint, it is possible to make more constraining assumptions, which are still relevant in a large set of models and which allow the LHC to make reasonable measurements. In this case, the assumption is that there is no significant amount of an untriggerable component (such as H cc¯ or worse). In this → case, the only unknown is H invisible, which can be made visible in analyses looking for → recoil structures [90]. Before making complex fits including a freedom in the production of H invisible be- → yond the results from the experimental collaborations, one can aim to reproduce official results, such as for CMS [85] in Fig. 8(a) [105], which again works not perfectly, but surpris- ingly well. There is a small trend of HiggsSignals to be very slightly more aggressive than the experimental interpretation, which probably mostly is due to missing public information on correlations in the systematic uncertainties. Once this is accepted as being in very good agreement, results from ATLAS and the Tevatron can be added as well as one additional fit parameter, (H inv). Amongst the most important results are of course the direct B → limits on (H inv) from [90]. If one accepts the theoretical assumptions behind this B → simple κ model [104], which are not generally transferable to all models, this is a rather general representation of the knowledge of the Higgs couplings at the end of 2013. And a pleasantly surprising precise picture, that is. Despite these obvious successes of the HiggsSignals approach, there is still ample room for improvement. As already stated, the input on the sub-channel efficiencies and on the composition and correlation of the experimental and theoretical systematics could be much more precise [103]. Another challenge is the fact that many experimental results omit the µ band result, which allows one to interpret each channel at each mass. This would be particularly interesting for models like SUSY, where there is still a substantial uncertainty on the mass prediction. At least the µ measurements, if no band is given, could be given at the same mass, which is also not always the case and which makes comparisons difficult, because the measured µ of course depends on the assumption on mH . Another interesting feature of HiggsSignals is the possibility to modify the (sub)channel efficiencies for each tested point. This is interesting for models which go beyond simple scalings of rates. An example is [40]. Here, the effective operators contain derivative couplings, which change the Lorentz structure of the vertices and hence angular distributions. In such a case, HiggsSignals allows to include the result of studies of the acceptance change for a given New Physics model point with respect to the SM, such that the efficiencies in all sub-channels can be corrected for changing kinematics. In the future, this could be coupled to an input also incorporating differential distributions of production and decay kinematics. These possibilities set HiggsSignals clearly apart from other implementations. These are not based on public codes, such that their applicability beyond the result shown in the relevant publications cannot be tested, and they do typically neither provide a very large set of validations nor a very wide customisability, such as HiggsSignals. Still, very interesting other results on the interpretation of the Higgs measurements are also available from a large amount of other studies. For the LHC, the ones closest in approach to HiggsSignals are [106] and [107], for the latter of which also interesting ILC projections [108] are available. In summary, it is clear that the studies of the Higgs sector truly have only begun. Up 32 Section4 TheSearchfortheOriginofElectroweakSymmetry Breaking to now, the SM prevails, but the hope for a deeper understanding of electroweak symmetry breaking grows with each new result and each improved uncertainty. At the same time, the possibility to discover small deviations from the SM grows with increasing precision. Tools like HiggsBounds and HiggsSignals can play an important, but of course not definite, role in such a vibrant and dynamic environment, enabling quick and rather precise tests of any model with any number of scalars and any kinematics against the results from the experimental collaborations. 33

5 The Search for Supersymmetry

The quest for understanding electroweak symmetry breaking does not end with the experimental conﬁrmation of the completion of the SM particle content, in the form of the discovery of a Higgs boson. As discussed in Section 2.2, the SM remains theoretically fragile and fails to comply with important questions about the history and content of the Universe. Most of its theoretical challenges originate in the way how electroweak symmetry breaking is realised. As discussed in Section 2.3, SUSY would be an attractive extension of the SM, not only because it could provide DM, but also because it would stabilise electroweak symmetry breaking. Therefore, this section covers the search for SUSY particles at the LHC. The discussion is grouped into an example for a search for sparticle production in the strong interaction in Section 5.1, electroweak production in Section 5.2, and a special case where the ﬁnal state kinematics is the focus in Section 5.3.

5.1 Strong Production Searches

This section covers a rather general search for SUSY. That might sound simple, but it actually is not entirely simply to apply. The reason is that if a search for a certain new phenomenon including the appearance of new particles is done, it is typically not a very sensitive solution to simply measure everything, which is already known and then to state whether there is a discrepancy from the known physics, the SM, or not. The reason why this is not very sensitive is simple: There is a huge rate of SM particle production. But at the LHC it is expected that SUSY production, depending on the mass scale, is about a factor of 1010 lower than the total inelastic SM rate. Therefore, it is typically not a sensitive solution to search for “anything new”, despite the fact that in some cases there are interesting approaches on doing that (see e.g. [109] for an earlier example, which still by far cannot reach the sensitivity of dedicated searches). Also keep in mind that this situation is different than the approach described in Section: 3.1. There, the SM process was loop- suppressed, with the potential New Physics appearing at the same loop level at potentially similar mass scales. Hence, there it is a very sensitive strategy to measure the SM precisely, and then declare every significant deviation as a generic sign of New Physics. It has the disadvantage that not too much can be said about the nature of the New Physics. In this section, the approach has the opposite advantage: The direct appearance of SUSY particles cannot be found by simply looking at general deviations from the overall SM predictions, but it can be used to make very significant statements about the nature of New Physics, if found. See Section 5.3 for an example. Thus, in the direct search for SUSY it is most sensitive to look for a specific signature and try to isolate that signature in the selection and suppress all background which does not belong to the specific signal signature. This in turn poses the problem how such an approach could be generic, and of course such a search can never be entirely generic. However, some of the features of rather attractive variants of SUSY, as listed in Section 2.3, can be used to derive some ideas for a more or less generic behaviour of SUSY: First, it should explain dark matter, and the most easy solution (but not the only one, see e.g. [110]) to achieve this is to have a neutral stable DM particle ensured by R-parity, which is the lightest supersymmetric particle (LSP) that interacts only weakly. Thus, it would leave the detector unseen and create a missing transverse energy signature. Second, the SUSY particles should be heavy, otherwise they would have been discovered already at LEP or the Tevatron or seen indirectly in precision experiments, e.g. in flavour observables. Third, the couplings of the sparticle interaction eigenstates must be exactly the same as for the SM particles. Such, the squarks and gluinos, the partners of the quarks and gluons of the SM, must couple strongly and 34 Section 5 The Search for Supersymmetry thus should be copiously produced at the LHC if kinematically accessible. These conditions can be used to set up searches [111,112] for large missing transverse energy and a varying number of hard jets. The exact experimental techniques may differ, but the general strategy and outcome is similar. A trigger on large missing transverse energy and/or a combination with high-pT jets is applied. Sensitive variables for the background discrimination are e.g. HT = i pT,jeti and meff = HT + ET,miss. Typically, a lepton veto is applied to allow more straightforwardP combinations of the results with searches for final states with leptons (see e.g. [113,114]). The search itself is rather straight-forward and interpreted only in single, partially overlapping bins, optimised separately according to the number of jets (to account for possibly different lengths of SUSY production and decay cascades) and different energy scale of the final state objects and the missing transverse energy, to account for different SUSY mass scales and mass differences. For the final interpretation, only the most significant bin for each signal model point is chosen. The challenge in the analysis lies mostly in the data-driven background determination in the tails of the SM backgrounds. For each signal bin, several control regions, which use cuts orthogonal to those in the signal regions and which are expected to be mostly signal-free, are designed to account for the SM backgrounds separately, like Z νν+jets, W ℓν+jets, → → multi-jet QCD background with mostly fake missing transverse energy, and events with top quarks. The differences found between data and simulation in the control regions are then transferred into the signal regions using scale factors derived from the simulation. In order to test this procedure, a third set of statistically independent bins in so called validation regions are defined, where data and simulation are compared after applying the scaling, but before analysing the signal regions. All analyses are designed “blindly”, i.e. without looking into the signal region data until the selection, the data-driven background estimate and the main systematic uncertainties on the background estimate are finalised. Unfortunately, in all of those searches, no significant sign of SUSY or a similar signature of New Physics is observed. Hence, model dependent and model independent limits are set from the results, which lay in the order of magnitude of M1/2 > 450 GeV for all M0 in the CMSSM scenario, or mg˜ > 1200 GeV and mu˜ > 2000GeV in the same scenario [111]. The interpretation in a model independent way is less straight forward, but generally similar scales are obtained using weak assumptions on other masses. Unfortunately, this type of very generic search also has significant disadvantages. Most importantly, it is not very sensitive to the sparticles of the third generation, simply because their SM partners are not abundantly available in the proton and hence their cross-section is much lower than the one for sparticles of the first generation, due to the missing t-channel process. Also, they decay in a more complicated way and hence a specific search for e.g. top quarks in SUSY decays is more attractive (see e.g. [115] for recent examples). For an overview of the current experimental status of stop or sbottom searches in ATLAS, see Fig. 9, which shows that the limits on the vital third generation are much weaker in terms of mass limits than the limits on the first generation. Keep in mind that, as the plot shows, the direct limits on third generation particles can almost vanish if the kinematic configuration is compressed (very small mass differences between different sparticles in the decay cascade), thus generating very soft final state particles. Thus, in addition to these very generic searches, there is the possibility to make stronger guesses on the possible attractive signs of New Physics. One possibility is the following: What is really needed for the most attractive features of SUSY are the lightest gauginos, for dark matter, and the partners of the third generation, to stabilise the Higgs boson mass and avoid the SM hierarchy problem (cf. Section 2). The rest of the SUSY spectrum is not really needed phenomenologically and can be realised at much higher mass scales. For the top quarks, though, it would be aesthetically attractive if they were not significantly heavier 35

Figure 9: A summary of the status of the search for sbottoms or stops in ATLAS. For references, see the labels in the plot. It can be observed that even the strongest the limits on stops are still signiﬁcantly below mt˜1 2 700 GeV, signiﬁcantly below the bound of √mt˜1 mt˜2 < 1 TeV suggested by naturalness. Thus, there , ≈ still is enough space to breath for SUSY in general models [116].

than √m˜ m˜ 1TeV on average, in order to keep the Higgs sector free of significant t1 t2 ≈ finetuning (cf. also Section 6.2). Such a situation would naturally also keep the lighter mass eigenstate of the staus, theτ ˜1, light, potentially much lighter than any other SUSY particle apart from the LSP. In such a situation theτ ˜1 is the next-to-lightest SUSY particle (NLSP), and many SUSY decays would progress through cascades involvingτ ˜1, and thus by lepton number conservation also 2 to 4 τ leptons in the final state, depending on the exact decay chain. An example for such a search with a requirement on third generation particles in the form of τ leptons [117,119]6 is shown in Fig. 10(a), using 20.3fb−1 of luminosity taken at √s = 8TeV with the ATLAS experiment in 2012. It is still based on the assumption of production via the strong interaction, and still generic in the sense that it tries to make as little as possible of additional kinematic assumptions or requirements on other particles or reconstructed objects other than jets (due to strong production) and τ leptons. It follows a similar search strategy as outlined above for the pure strong production search. It is separated in 1τ hadrons, 2τ hadrons, and 2τ ℓ+hadron final states, to account → → → for a variable number of reconstructed τ leptons in either the hadronic decay mode or a combination of hadronic and leptonic decay modes. The search for more reconstructed τ leptons is not attractive, despite the typically higher number of τ leptons in the expected final states, due to the reconstruction efficiency which does not exceed 60% even in ≈ the configuration with the largest misidentification rate of hadronic jets as reconstructed hadronic τ decays [120]. Depending on the final state, either a trigger on jets and missing energy for the purely hadronic τ decays, or on a single electron or muon for the partially

6For the full details of this analysis see the article “Search for Supersymmetry in Events with Large Missing Transverse Momentum, Jets, and at Least One Tau Lepton in 7 TeV Proton-Proton Collision Data with the ATLAS Detector”, Eur.Phys.J. C72, 2215 (2012), which is contained in the full Habilitation treatise. 36 Section 5 The Search for Supersymmetry

400 ATLAS Preliminary [GeV]

0 1 350 SR OS-m -nobjet ∼ χ T2

m -1 ∼ ∼ mτ,ν ∫ L dt = 20.7 fb , s=8 TeV = 0.5 300 m∼± ∼0 + m∼0 ± σSUSY χ ,χ χ Observed limit ( 1 ) 1 2 1 theory ∼±∼0 ∼ ∼ ∼ ∼ ∼0 ∼0 χ χ → τ ν (τν) τ τ( νν ) → ντ χ ττ ( νν )χ Expected limit (±1 σ ) 1 2 L L 1 1 250 exp 6.38 0.90 All limits at 95% CL ∼0 χ 10.63 200 1 < m 1.51 ∼± 19.43 m χ 1 0.30 0.13 25.65 0.29 0.12 0.06 150 1.18 3.40 0.29 0.14 0.06 0.04 1.31 123.23 0.32 0.16 0.06 0.04 100 0.92 83.45 0.30 0.15 0.06 0.04 0.03 12.56 1.00 50 0.53 0.410.31 0.19 0.09 0.05 0.04 8.27 0.48 0.19 0.09 0.06 0.04 0.51 00.63 0.11 0.07 0.04 0.03 100 150 200 250 300 350 400 450 500

m∼± ∼0 [GeV] χ ,χ 1 2 (a) (b)

Figure 10: In (a) the interpretation of the search for SUSY with strong production modes and one or more tau leptons in the final state interpreted in the GMSB model are shown [117]. (b) shows a search for electroweak direct production of gauginos with a decay into tau leptons, this time not interpreted in a model like GMSB, but in so called “simplified model”, assuming a certain mass ratio given in the plot. The numbers in the plot can then be interpreted as 95% CL upper limits of the visible cross-section in pb at the given mass configuration in the plot. This number can be applied to every model fulfilling the mass requirements [118]. leptonic decay mode are chosen. This is a helpful approach to reduce the dependency on the mass scale of the strong production process, since the rather high trigger thresholds of jet and ET,miss triggers of pT > 80GeV for the hardest jet and ET,miss > 100 GeV. Such, in the hadronic decay modes an unwanted significant dependence on the kinematics of the beginning of the production chain is introduced. This can be avoided in the partially leptonic decay mode. There, the branching fraction of (τ e,µ) = 35% is lower than the B → corresponding branching fraction to hadrons of the remaining 65%, but the reconstruction is more clean than for hadrons and the dependence on the kinematics of the production process can be weakened by relying on a trigger on the final state particle from the τ lepton decay, the electron or muon. After the trigger, the object identification, and the event cleaning, there are similar strategies applied as discussed above for the fully generic search for strong production. The number of jets, m , H , E and, as a separation against W τν backgrounds, the eff T T,miss → transverse mass mτ = 2Eτ E (1 cos ∆Φ ) are employed in different signal T q T T,miss − τ,ET,miss regions to search for SUSY in the CMSSM, in gauge mediated SUSY breaking (GMSB) [121], a generalisation of the GMSB called general gauge mediation GGM [122] and a so-called natural Gauge Mediation model (nGM) [117], where the GGM parameters are adjusted such that the finetuning on the Higgs sector is reduced, and thus naturally τ leptons play a large role. In all these cases, the gravitino G˜ is the LSP and thus each decay chain is expected to end withτ ˜ τG˜, where the G˜ escapes the detector undetected and creates 1 → the ET,miss signature. Again, the biggest challenge is the description of the backgrounds into the farthest tails of the kinematics of the SM processes. The additional challenge is the τ reconstruction, which is generally well modelled [120], but where certain deviations between the signal region and control processes are inevitable. The reason is that the performance of the reconstruction of hadronic τ lepton decays does not only depend on uniquely observable kinematic quantities such as pT or the pseudo-rapidity η, but also on quantities which can be only measured statistically, if at all, and which differ between control processes and the 37 signal region. An example for this would be the statistical mixture of quarks and gluons causing the background jets, or even more complicatedly the colour flow between the jet causing the misinterpreted reconstructed τ and the remainder of the event. Thus, e.g. the misidentification rate does not agree between reconstructed τ’s originating directly from hadronically decaying W bosons on the one side, and reconstructed τ’s from jets recoiling against the W . A complex design of control and validation regions for W τν events, → W qq′ events, and tt¯ events is used and a very good agreement between data and MC is → observed in the validation regions after scalings based on the control region are applied. Also here, despite the excellent motivation, no significant excess of the data over the expected SM background is found and hence limits are set, which reach Λ 70 TeV [117,121] ≥ in the GMSB, corresponding to mass scales of m 1500GeV. In the nGM model, a limit u,d˜ ≥ of m 1150GeV can be set independently of m . g˜ ≥ τ˜1 Of course, there are many more possibilities to search for SUSY in strong production, e.g. with same-sign leptons, many leptons, photons, b-quarks, or any combination of the above, and many more possibilities beyond strong production. See [123] for a continuously updated list of interesting results from the LHC collaborations. Two selected examples for other types of searches are introduced in the following Sections.

5.2 Electroweak Production Searches and Simpliﬁed Models

Only one example [118] for a search based on electroweak production is discussed here, namely the search corresponding to the strong production search for SUSY events with τ leptons discussed in the previous section. In electroweak production searches, one can reach sensitivity to model points complementary to those in strong production. The strong production searches enjoy large signal cross-sections as long as squarks and gluinos are kinematically accessible, but are suppressed strongly for heavy squarks and gluinos. The electroweak production, based on the exchange of γ/Z0 or W ± in the beginning of the production chain, is penalised roughly by a factor of (g /g )2 100, but it is not O ew s ≈ hampered by the rather strong limits on generic production of strongly coupling sparticles, as quoted in Section 5.1. Thus, for sufficiently high luminosity, their sensitivities can exceed those of the corresponding strong production searches in individual model points. However, it should be kept in mind that such comparisons are always model-dependent. Thus, it is attractive to devise a way of interpreting the limits (or potential discoveries in the SUSY sector, of which there are none as of today) in a model independent way. To do that, a method similar to that explained for the LEP Higgs searches (cf. Section 4.1) has been proposed [124]. This way is commonly called “simplified model search” (SMS), despite the fact that what is used is not a model, but just a single production and decay chain combination. Then, instead of testing the experimental search result against a simulation of the complete SUSY spectrum with all production modes and all decay chains, resulting in thousands of different possibilities (as in Section 5.1), only one individual combination of production and decay is tested against the data for different kinematic configurations, and a limit on the visible cross-section, i.e. the cross-section inside the kinematic acceptance of the analysis, is quoted. There is obviously one strong advantage: The limit thus obtained can be interpreted in every SUSY model which contains the tested decay chain within the tested range of masses of the sparticles, just as explained for the Higgs in Section 4.1. In a situation where the future of SUSY is unclear, and an exceedingly large number of models is proposed by theorists, this advantage is enormous, because one experimental result can be tested against thousands of models. However, there is a number of significant disadvantages, also compared to the Higgs 38 Section 5 The Search for Supersymmetry case in Section 4.1. In case of the Higgs the combinations of Higgs production and decay can be almost fully isolated from each other experimentally at LEP (and at least partly at the LHC). Therefore, by construction, each limit in an individual channel for an individual Higgs production and decay will be of the same strength as the limit of an interpretation of a complete model in that same channel. Still, the combination of channels improves the limit for a model, but not for an individual Higgs production and decay. For the SMS in SUSY, the situation is radically different. There, due to the complexity of the decay chains and the incapability of a full kinematic reconstruction of the final state, each search is necessarily sensitive to a very large combinatorical number of different sparticle productions and decay chains. Thus, if in such a situation a single combination of production and decay is compared against the experimental result, its upper limit on that production and decay chain can be higher by orders of magnitude than the corresponding number of allowed events from the same production and decay chain, but within a full model where hundreds or thousands of combinations of production and decay can be picked up in parallel by the same search. While this problem is inevitable, there are other challenges which can be overcome, like the dependence on the kinematics of the production, which is caused by the typically different angular distributions in s- and t-channel production. There, e.g. different limits can be set. Also, this approach is difficult for chains containing more than 2 sparticles, due to the necessary high dimensionality of the model space. An example for such an interpretation can be found in Fig. 10(b) [118]. There, gaugino production with decays intoτ ˜’s and directτ ˜ production is searched using 20.3fb−1 of luminosity taken at √s = 8TeV with the ATLAS experiment in 2012. Events are triggered using a 2τ or ET,miss trigger. For the event selection, opposite sign hadronic or leptonic τ decays and the stransverse mass variable mT 2 [125] are used. The background estimation is based on an ABCD method in the orthogonal dimensions of the τ identification and mT 2. Also here, no signal is observed, thus limits are set. The example in Fig. 10(b) shows the production and decay chain χ±χ0 3τ1ν2χ0 or 1τ3ν2χ0. Since there are four sparticles 1 2 → 1 1 involved, specific assumptions on the mass relations are made to reduce the dimensionality to m ± = m 0 and m 0 , which unfortunately further reduces the generality. Still, the result χ1 χ2 χ1 is applicable to a large set of models, which is not yet possible using the inclusive results from the SUSY with τ search in Section 5.1.

5.3 Searches Based on Kinematic Reconstruction

The searches presented in the two Sections before are the most sensitive for large parts of the parameter spaces of many models. However, they have a few shortcomings. First, they depend very heavily on the combination of a missing energy signature with relatively hard jets and leptons, something which in certain kinematic configurations is not necessarily the case: e.g. in case of a so-called compressed spectrum, where all SUSY masses are relatively close together, most of the final state particles are soft, and thus might already fail in the trigger step. This is already one good reason to try other attempts on triggering and finding SUSY in parallel to the above mentioned searches. In addition, there is one even stronger argument: In case there would be a signal in the inclusive searches for strong or electroweak, it would not be easy to measure the exact kinematic configuration of the signal. Only a rough estimate of the mass scale could be extracted e.g. from the meff spectrum. Hence, it is attractive to think about observables which allow to directly reconstruct quantities which are directly correlated to the masses of all involved sparticles, from production to the LSP. Since the LSP escapes undetected, it is necessary to do this with longer chains, because for each element in the chain one kinematic constraint, the mass of the intermediate sparticle, is added. As long as the SM 39 particles emitted along the chain are visible in the detector (in contrast to e.g. neutrinos), a chain length of 4 is thus sufficient to reconstruct the full kinematics up to quadratic ambiguities [126].

The most straightforward variable of that type is mℓℓ, where ℓ stands for electrons or muons in most cases (it is also possible to pursue this approach using τ leptons, but much harder due to the missing kinematic information stemming from the neutrinos in the τ decay [127]). mℓℓ is the invariant mass of opposite sign same flavour (OSSF) leptons. They typically could occur at the end of a longer decay chain, e.g. q˜ qχ0 qℓ−ℓ˜+ qℓ−ℓ+χ0. → 2 → → 1 Since m is not the invariant mass of a resonance, in contrast to e.g. m 0 , it does not ℓℓ ℓℓχ1 form a Breit-Wigner peak, but a broad shape. Due to the kinematics of spin-0 particles such as the ℓ˜, the shape is triangular with a sharp drop-off at the maximum value of max 2 2 2 2 mℓℓ = mχ0 (1 m˜/m 0 )(1 m 0 /m˜). This drop can be searched for kinematically. 2 q − ℓ χ2 − χ1 ℓ If it would be observed, one of course would not be able to reconstruct 4 sparticle masses (m , m 0 , m , m 0 ) from one observable, but then many more combinations of invariant q˜ χ1 ℓ˜ χ1 masses of final state particles could be formed (see [126]) and the sparticle masses could be inferred from all of them together. However, one problem remains: It is kinematically impossible to assign each visible final state particle unambiguously to one of the two decay chains. Therefore, subtraction techniques have to be used. E.g. for mℓℓ all OSSF combinations can be formed, also containing combinations across decay chains, which do not contain sensible mass information. These can be subtracted in-situ bu forming all opposite sign different flavour (OSDF) combinations, which contains only combinatorics and not mass information, since the two ℓ in one chain are always of the same flavour. Then, the distribution of OSSF-OSDF in mℓℓ will contain the pure kinematic information from single chains only. Not only would such a technique allow one to reconstruct the sparticle masses, it could also contribute to a discrimination between SUSY and other interesting theories on New Physics, such as Universal Extra Dimensions UED (see e.g. [128]). There, a similar spectrum of new particles with partners for each SM particle could occur from so-call Kaluza-Klein towers, where the SM particle would be the ground state and the new particles would form the excited state with the same spin as the SM particle. Thus, the corresponding partners of SM particles in SUSY and UED would differ in spin. Hence, the kinematic distributions of the decays in the decay chain would differ, and thus the shape of mℓℓ would not be exactly triangular anymore, and such SUSY could be discriminated from UED [129]. An example for an implementation of a search – and forestalled measurement – based on the kinematics of the decay particles is the search for opposite sign dilepton events [130].7 It is based on single lepton triggers of either electrons or muons, which allows for straight forward flavour subtraction. 3 signal regions with different requirements on ET,miss and additional jets are defined. The control sample is mostly included automatically into the analysis, since the flavour subtraction allows for a straight-forward subtraction of all flavour symmetric backgrounds, such as tt¯. In contrast to that background, or to SUSY, the electroweak SM backgrounds, such as W +jets and Z+jets, is unfortunately not flavour symmetric (due to different fake rates or intrinsically, respectively). Thus, the need for additional control regions remains. The final discriminant is built on the excess of OSSF over OSDF S events, after reweighting for differences in the reconstruction and trigger efficiencies. Also those efficiencies are determined from data in control studies using tag- and probe techniques. Also here, no significant deviation from the SM is observed, and limits are set in

7For the full details of this analysis see the article “Searches for supersymmetry with the ATLAS detector using final states with two leptons and missing transverse momentum in √s = 7 TeV proton-proton collisions”, Phys.Lett. B709, 137 (2012), which is contained in the full Habilitation treatise. 40 Section 5 The Search for Supersymmetry simplified models and model-independently on . S A similar and even more detailed analysis of this type is available from CMS [131]. There, instead of calculating globally in the full range of m , the m distribution is S ℓℓ ℓℓ fitted with a rather model independent parametrisation of the triangular shape of the signal max distribution, and model independent limits are published as a function of mℓℓ . These searches represent an interesting alternative to the standard single-bin counting experiment from most LHC SUSY analyses, and they are kinematically interesting due to the softer selection criteria which can be applied due to the kinematical reconstruction of final state particles. However, they have too high SM background and too low signal cross- sections to compete with the generic searches in terms of pure significance, and thus are of use only in specific models, until SUSY is maybe found. Then, these analyses would be amongst the most important to be conducted at the LHC. 41

6 Interpretations

As stated numerous times before, the scope of this article is to connect different attempts on understanding electroweak symmetry breaking with each other. It was observed that the SM contains electroweak symmetry breaking generated by the Higgs mechanism, but it was explained that this mechanism was added to the model in a way which both leaves room for deeper explanations and which causes significant challenges, most significantly the hierarchy problem. Further, it was observed that a deeper understanding of electroweak 2 symmetry breaking, a prediction of the electroweak mixing angle sin θW , a cure of the hierarchy problem, and a solution for the DM suggested by astrophysics could be achieved by SUSY (cf. Section 2.3). After visiting precision measurements in the electroweak and flavour sector, cosmological measurements, Higgs searches and measurements, and SUSY searches and limits in the previous sections, it is the aim of this Section to bring it all together: Make maximum use of the multi messenger approach in the form of global fits of SUSY models against the data. This remaining program may sound straight-forward, but there is one remaining choice to discuss: What is the meaning of the outcome of the fit? This depends on the approach taken on the fundamental meaning of the statistical quantities. Only a few selected aspects of this debate between Bayesian and frequentist interpretations of statistics are discussed in Section 6.1. After settling this issue, at least for this article, Section 6.2 uses all the results discussed before and interprets it in SUSY models, tries to measure the parameters of selected models, with the main question being: SUSY was not found, but limits are set. So is it still alive, and if yes, in which form?

6.1 Interpretations of Statistics

Statistics deals with random numbers, such as the outcome of the experiments in particle physics or astrophysics. They are undeniably subject to statistical fluctuations, within their measurement uncertainties. These uncertainties themselves might have different reasons: pure statistical fluctuations of a counting experiment, or systematic uncertainties such as unknown miscalibrations of a measurement device, which does not cause a scatter, but an offset, which is unknown but which hopefully can be quantified somehow by a control study. This is all unavoidable and fine, but the question is how to deal with it: Since the observables have uncertainties, surely also the allowed parameter space in every model in which the observables are interpreted will have uncertainties. Or rather large allowed areas, in most cases in this Article. Thus the question arises: Is there a unique way in how we interpret the uncertainties of the observables and the model parameters, or is there a choice? Indeed there is a choice, and an important one. As often when applying mathematics to natural sciences, the mathematical foundation is undisputed. The challenge lies in how to apply the mathematical formalism to get a physically meaningful result. This question lies at the heart of the debate between the Bayesian and frequentist interpretation. The motivation for the Bayesian stance is simple: If there is a measurement, what everybody wants to know is p(theory measurement), the conditional probability that theory is true if measurement | has been measured (see e.g. [132]). Undeniably, this is just how statistical questions are dealt with in everyday life. However, there is a problem. In order to calculate the desired conditional probability, Bayes theorem is used: P (H D)= P (D|H) P (H). Here, the following | P (D) nomenclature is introduced: H = H(P~ ) is the hypothesis, consisting of a theory and a set of parameters P~ . It is the aim of the effort to determine “how true” H is and what the allowed range of measured parameters P~ = P~meas ∆P~ is. D denotes the data, which can be one ± i

SUSY searches). This is Bayesian by design, since P (Hθi ), the probability density function of the unknown nuisance parameter θi has been chosen. While this is mathematically Bayesian, it does not have the catastrophic philosophical implications discussed above: this probability density function itself can be tested in experiments and does not make a direct fundamental statement about a priori properties of Nature, even before a single experiment is done.

6.2 Limits on Supersymmetry, or: How unattractive did it get yet?

Having settled the fundamental issues on the statistical interpretation, the frequentist interpretation can be used to interpret the results in the previous sections in SUSY. Optimally, a maximum likelihood fit of all data, using the likelihoods P (D H) of all individual mea- | surements would be used, under one common hypothesis. In the studies discussed here, the 44 Section 6 Interpretations common hypotheses are different SUSY models. However, typically a full likelihood is not available for all measurements, or to be more precise: typically the likelihood is not available at all in the published data, barring some exceptions. Therefore, in a global interpretation, there have to be some approximations, as already seen in the HiggsSignals case. In the studies shown here, it is mostly assumed that the likelihood is Gaussian and that there are only linear correlations amongst the measurements and amongst the predictions. These assumptions cannot be circumvented simply due to the lack of more general information on the individual measurements. For the construction of the fit, there is another assumption which can be lifted later on (as described in the outlook of this Section), namely that there is a linear dependence of all observables on the parameters. This is obviously not true for SUSY, which shows strong dependence of the observables on the parameters at light enough mass scales, and complete decoupling at high mass scales. This obviously cannot be a linear dependence, therefore a solution for this problem will be envisaged below. However, it can be a reasonable enough approximation locally around a measurement, if the observables are constraining enough. Under the above assumptions, the likelihood = P (D H) can be written as = L | L exp( χ2/2), where χ2 =(M~ O~ (P~ ))T C−1(M~ O~ (P~ )), and where M~ are the measurements, − − − O~ (P~ ) is the prediction of the observables measured in M by the theory under study, and C is the covariance matrix of all measurements (see e.g. [132] for a general introduction). Take note that in this approach no hypothesis test is done as in the limit setting machinery described before, but that this approach is only useful for a direct measurement of or constraints on parameters, independent of any other hypothesis. In the profile likelihood approach, it can be shown that under the assumptions above, the 68% CL allowed area of the 2 2 individual parameters around the best fit point (characterised by the minimal χ = χmin) is comprised of all points within χ2 χ2 + 1, and that the 95% CL area is within ≤ min χ2 χ2 + 4. All following interpretations operate with these techniques. ≤ min An example for an MSSM fit Before looking at a global interpretation of a constraint SUSY model in the later parts of this Section, a more specific fit of the Higgs measurements (cf. Section 4.2) and a few selected low energy and precision observables (cf. Section 3.1) shall be discussed [134].8 The concrete question posed for this work is: A Higgs boson has been discovered, but which one? Is the SM the only good explanation, or are there others, and if yes, are they unique? Already in a rather well motivated version of the minimal implementation of SUSY, the CP - conserving MSSM, there are 3 choices for particles which can be assigned to the discovered Higgs boson: The lighter h or the heavier H of the two CP -even neutral states, or the CP - odd A. The A can be excluded based on the fact that the discovered Higgs couples directly to vector bosons, which still leaves the h and the H. The study of this problem has to be done in a rather general framework of the MSSM, because more constraint models, such as the CMSSM, couple the mass scale of the H and A to the spin-0 sparticle mass scale. Since the SUSY searches at ATLAS push the squarks to large masses, the discovered Higgs cannot be interpreted as the H in constraint SUSY models. The MSSM though allows to ± decouple the mass scale of H, A and H , controlled by he parameter mA, from the squark and slepton mass scales. The CP -conserving minimal flavour violating MSSM has 24 parameters in addition to those of the SM. In order to concentrate on the Higgs sector and maintain a situation where a large enough sampling density in the parameter space can be reached, further simplifications

8For the full details of this analysis see the article “MSSM Interpretations of the LHC Discovery: Light or Heavy Higgs?”, Eur.Phys.J. C73, 2354 (2013), which is contained in the full Habilitation treatise. 45 are made by unifying parameters. The tree-level parameters of the MSSM (cf. [11] for general introductions) Higgs sector tan β and mA are scanned. Further parameters with direct impact on the Higgs sector are the Higgsino mass parameter µ, the SU(2) gaugino mass parameter M2 and the trilinear coupling A. Here the effects on the Higgs sector are dominated by the trilinear coupling to the stop At, and thus all trilinear couplings are set to the same value. M1 is coupled to M2 using a relation at the GUT scale. Similarly, only one mass parameter is used in the fit for the third generation squarks and one for the third generation lepton. The other parameters, with negligible impact on the Higgs sector, like the first two generation sparticle mass parameters and the gluino mass parameter, are fixed to high enough values to evade the direct bounds from LHC. Thus, a fit with 7 parameters is obtained, which can be controlled in a parameter scan much better compared to the full MSSM. Using a simplified predecessor of HiggsSignals, the results from ATLAS and CMS are used in a χ2 fit using the observed Higgs masses in the γγ and ZZ∗ channels, the Higgs rates in all channels including Tevatron measurements, and a set of low energy precision observables. The latter is comprised of (b sγ), (B µµ), (B± τ ±ν), (g 2) B → B s → B → − µ and MW . The remaining obvious candidate, the DM relic density, is not fitted because for every choice of the parameters fitted here, the fixed parameters could be adjusted such as to fix the DM relic density prediction, without further influencing the Higgs sector or the constraints from LHC. To a lesser extend this is also true for the flavour observables used here. It is observed that the MSSM indeed fits the data very well, however just slightly better than the SM. A subset of the predicted observables, compared with the measurements and their precision, is shown in Fig. 11. Most importantly, the predictions fit the data well, but it can be observed that not only can the MSSM not be experimentally distinguished from the SM, and that the two interpretations of the discovered Higgs particle as h and H also cannot be distinguished using the data set used in [134]. Keep in mind that HiggsBounds is also used in this fit, which ensures that in the H interpretation, where mh is below 100 GeV, the production rate of the h at LEP and the Tevatron is so low that it indeed would have evaded the strict model independent bounds described in Sections 4.1 and 4.3. This is a direct consequence of the coupling of MSSM Higgs bosons to gauge bosons, which is split between the h and the H. Thus, if H behaves SM-like, h does hardly contribute to the SM gauge boson mass generation and hence hardly couples to the gauge bosons. In addition to these important results, many more constraints in parameters can be set in the form of lower bounds on the parameters, or predictions for the allowed range in the MSSM of deviations of Higgs rates from the SM. As evident in the comparison of the predictions of the rates in the search channels shown in the two plots in Fig. 11, there can be an extremely small difference between the predictions of quite different scenarios, like the h and the H interpretation. Comparing the very small differences between the two hypotheses channel-by-channel with the still rather large individual uncertainties of the rate measurements from LHC, it is obvious that there is still a long way ahead in terms of ultimate precision physics on the Higgs, a way which could find its next step in the construction of the International Linear Collider (ILC) optimised for precision Higgs physics. An interesting observation is that there are other measurements which have been made since [134] was published, which have the potential to exclude the H hypothesis in favour of the h hypothesis, or the SM. The most important one is the search for charged Higgs bosons H± in top quark decays in the form of limits on the process t H+b τ +ν b, which since → → τ has been updated with more data, improving the limit significantly [101]. Whether there is still room for the H interpretation after these results is an important field of study which 46 Section 6 Interpretations

Figure 11: An overview of the fit results of the MSSM fit against the Higgs mass and rate measurements. The left side shows the h interpretation, the right side shows the H interpretation. The full blue squares denote the predictions of the fit to the full data, including low energy observables, the Higgs masses and all rates from ATLAS, CMS and the Tevatron. It can be observed that the differences between the two interpretations are much smaller than the individual measurement uncertainties, denoted by the error bars. Independently of the future fate of the H interpretation, this exemplifies the challenge which still lies ahead: To make the measurements so precise that these predictions on the left and right side can clearly be disentangled channel by channel. Only if this is the case, a full model dependent understanding of the Higgs sector can be claimed [134]. is currently in preparation.

An example for a CMSSM fit The CMSSM fit presented as an example in this Section follows a different motivation than the MSSM fit above. There, the parameter space was reduced phenomenologically to only those parameters directly influencing the Higgs sector, and the observables used on top of the Higgs sector were chosen such that only those directly influenced by the parameters also determining the Higgs sector are used. However, there is an orthogonal way of reducing the full MSSM parameter space to manageable sizes, which is to make global theory assumptions at the GUT scale, independent of individual sectors of measurements. Then, the resulting constraint model is fit to all relevant observables in a so-called global fit. Compared to the previous sections, a few important changes arise: First, the mass scales are coupled to each other, but overall free in the fit. Therefore, the limits on squark and gluino production at the LHC have to be included in detail, in contrast to the fit above. Further, also cosmology cannot be adjusted separately from other observables and is of global interest, and thus also the observed DM relic density and existing limits on direct detection of DM are used in the fit. In Fig. 12 an example for such a fit in the CMSSM using the fitting framework 47

∆ CMSSM, all Obs, mh=3.0 GeV 1σ Environment 5000 2σ Environment h → WW Best Fit Value 4000 h → γγ all observables ∆mtheo = 3 GeV 3000 h → ττ h

Best fit point 2000 h → bb 1D 1σ σ Particle Mass (GeV) 1D 2 → 1000 h gg

0 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 0 0 0 + 0 0 0 0 χ+ χ+ ~ ~ ∼ ∼ ~ ~ ~ ~ ~ ~ ~ h A H H χ χ χ χ τ τ q q g CMSSM SM CMSSM SM 1 2 3 4 1 2 lR lL 1 2 b b t1 t2 Γ Γ Γ Γ R L 1 2 ( / ) / ( h → ZZ / h → ZZ)

(a) (b)

M =452GeV, M =847GeV, A =-2300GeV, m =175GeV, tan β=20 2D 95% CL 0 1/2 0 t 1D 68% CL 2500 BR(B→ µ+µ-) / 10-9 3.20 +- 1.50+- 0.76 s 3.76 → ντ -4 BR(b ) / 10 0.72 +- 0.27 +- 0.11+- 0.07 0.80

BR(b→ sγ) / 10-4 3.55 +- 0.24 +- 0.09+- 0.23 2000 2.91 ∆ -1 ms / ps 17.719 +- 0.043+- 4.200 21.347

(a - aSM) / 10-10 28.7 +- 8.0+- 2.0 µ µ 4.3

(GeV) m / GeV 80.385 +- 0.015+- 0.010 1500 W 80.399 1/2

M sin2θl 0.23113 +- 0.00021 eff 0.23131 Ω h2 0.1187 +- 0.0017+- 0.0119 CDM 0.1169 1000 σSI / pb 2.2e-11 LHC

m / GeV 500 h 125.4 0 500 1000 1500 2000 2500 µ M (GeV) h 0 0 1 2 3 |Meas.-Fit|/ σ (c) (d)

Figure 12: In (a) the result of a global fit of the CMSSM to precision observables, cosmological observables, limits from LEP, the Tevatron and the LHC, and to the observed Higgs mass and rates is shown in terms of the allowed mass ranges of SUSY particles. Given the good agreement of the Higgs rates with the SM expectations, and given the high mass scales of the sparticles, it is no surprise that in (b) it is observed that the fitted double ratios of Higgs decay partial widths compared to their SM ratios is in good agreement with the SM, too. The high possible mass scales and the SM-like Higgs in the CMSSM make the CMSSM virtually impossible to exclude, unless the SM can be excluded first. These high mass scales beyond the LHC discovery reach are possible despite the upper bound on m1/2, visible in (c) and stemming mainly from ΩDM and (g 2)µ. There also is also a non-trivial upper bound on m0 at the 2σ level. In the direction of very − large m0, however, there is only a very shallow exclusion at the 2σ level, and slight changes of measurements, predictions or uncertainties can lead to significant changes. In (d) the pulls of the observables at the best fit point are shown. It can be seen in comparison to the SM fit (cf. Section 2.1) that there is a large similarity of the CMSSM to the SM, with the exception of the added DM [55,135].

Fittino [136]9 is shown. It represents an update to the ﬁts presented in [55,57,135].10 In the global ﬁt implemented via a Markov Chain Monte Carlo based on the Metropolis

9For the full details of the development and implementation of this code see the article “Fittino, a program for determining MSSM parameters from collider observables using an iterative method”, Com- put.Phys.Commun. 174, 47 (2006), which is contained in the full Habilitation treatise. 10For the full details of these analyses see the articles “Constraining SUSY models with Fittino using measurements before, with and beyond the LHC”, Eur.Phys.J. C66, 215 (2010), “What if the LHC does not find supersymmetry in the √s = 7 TeV run?”, Phys.Rev. D84, 011701 (2011), and “Constrained Supersymmetry after two years of LHC data: a global view with Fittino”, JHEP 1206, 098 (2012), which are contained in the full Habilitation treatise. 48 Section 6 Interpretations algorithm [137] and with added auto-adaptive techniques to optimise the proposal density locally [55], constraints from precision electroweak measurements in the form of MW and sin2 θ ,(g 2) , B-physics observables, direct and indirect constraints on DM, model inde- W − µ pendent limits on charginos from LEP [138]. No further electroweak precision observables are used, since earlier studies [57] showed no significant impact of including them in the CMSSM fit or not. They simply enlarge the number of degrees of freedom, without a possibility of the fitted model to create individual deviations in individual parameters. Thus, they make the fit quality harder to interpret, without adding constraints. In addition, negative Higgs search results from LEP, the Tevatron, and the LHC are used via HiggsBounds, and the measured Higgs mass and rates from the Tevatron and LHC are included via HiggsSignals. The deviations from the SM noted in Section 2.2 in the (B D∗τν) decays and the Tevatron top quark forward backward asymmetry are not B → used in the fit, simply because they cannot be explained either in the CMSSM. Thus, they only degrade the fit quality but have no effect on the allowed parameter ranges, at least as long as these two deviations from SUSY and the SM are not yet strong enough to really exclude the SM. As indicated above, one final interesting piece of information is missing: The direct LHC search limits for SUSY particles. This issue is not easy to solve, first, because a χ2 contribution reasonably equivalent to the real likelihood from the limits of the SUSY searches at LHC at every possible model point is wanted. This is not available from ATLAS and CMS, who just publish 95% CL and no likelihoods, or CLs+b values at every possible model point. Second, the official limit in the CMSSM is only available in a two-dimensional plane in (m1/2, m0) and needs to be tested for its behaviour in the less sensitive directions of (tan β, A0). Also the simplified model searches (cf. Section 5.2) are not a full solution to this problem. They also contain only one limit and no likelihood, and they are much less sensitive than full model interpretations, as discussed in Section 5.2. Therefore, only the most significant LHC SUSY search limit for exactly the model under study is implemented, using Monte Carlo generations and detector simulations done independently from the experimental collaboration software. The result is compared in detail to the result from ATLAS and found in very good agreement at the expected 95% exclusion line (cf. [55,135]). For the CMSSM, it turns out that the 0-lepton generic search for SUSY produced in strong production [111] is the strongest existing limit. This however does not only depend on the model, but also on the other constraints on the model. If the low energy precision data, DM, and (g 2) were rather preferring a region with low m and − µ 1/2 large m0, then the 1-lepton generic search for SUSY would be dominant [114,115], due to its higher sensitivity on the production of third generation squarks, which get more important for very high squark masses of the first two generations at high m0. In order to correct for the influence from the third generation and its dependence not only on (m1/2, m0), but also (tan β, A0) due to mixing effects, the limit included in the global fit in Fittino uses an effective 4-dimensional implementation [135]. Using the experimental input briefly described above (cf. [55,135] for much more details), the CMSSM can be fitted in its four continuous parameters m1/2, m0, tan β, A0 to the data. The digital parameter sign(µ) is fixed to +1 to aid the description of the deviation of (g 2) from the SM [44]. In addition to the SM parameters, the top quark mass m is − µ t fitted and included as an independent observable. For a list of programs used to calculate the predictions, also see [55,135]. Estimates for theoretical uncertainties of the predictions are included. The results of the fit show that there are two consistent constraints which push the CMSSM into high sparticle mass scales: The relatively high Higgs boson mass requires large third generation squark masses to generate large enough loop effects on the Higgs 49 mass, to lift it from its maximally allowed tree level value of mZ up to around 125 GeV. At the same time, the direct LHC constraints from the SUSY search push the first generation squark masses above 1 TeV, as shown in Fig. 12(a). Thus, in constraint SUSY models, where the mass scales of the scalars are all coupled to one common parameter m0 at the GUT scale, the non-observation of SUSY at the LHC is actually naturally in good agreement with the observed Higgs mass. From the fit, only weak constraints on tan β and A0 are obtained, while the effects described above enforce a lower limit on m1/2 > 800 GeV and m0 > 50GeV at the 95% CL. The region allowed is mostly in the co-annihilation region concerning the process dominating the generation of the correct, low enough, DM relic density, with disfavoured but, depending on the exact observable set, sometimes still allowed contributions from the A-funnel and focus point regions. Thus, the predicted SUSY signals are not easy for kinematic reconstruction as outlined in Section 5.3. The co-annihilation 0 process requires small mass differences between the LSP, in this case the χ1, and the NLSP, theτ ˜1. Thus, the visible momenta of the final state particles emitted at the end of the decay chain would be very small. The predominance of the decay chains through the NLSPτ ˜1 further motivates the specific τ signature SUSY searches outlined in Sections 5.1 and 5.2. A combination of the constraints from DM and (g 2) is responsible for the upper − µ limit on m m < 2.2TeV at the 95% CL, which is clearly visible in Fig. 12(c). 1/2 ≈ 0 Thus, in principle a non-trivial allowed area is found for the CMSSM, with a best fit point at around m 1000 GeV, m 500GeV, albeit with large uncertainties as quoted 1/2 ≈ 0 ≈ above. The fit quality in terms of the χ2/ndf is found to be acceptable, however a correctly calculated -value has not yet been published. The reason for that is twofold: First, P the fit still uses the full Higgs rate observable set from the Tevatron and the LHC as included in HiggsSignals. This is methodologically correct in terms of constraining the parameters, but since the CMSSM has no theoretical freedom to vary many of the individual channel predictions individually, the large number of observables (currently 67 mass and rate measurements) dilutes the χ2/ndf. Second, there is the problem mentioned already at the beginning of Section 6.2: The dependence of the observable predictions on the parameters is not linear. Hence, it is not expected that the outcomes of the minimal χ2 of an ensemble of fits would follow the χ2 distribution. Thus every statement on the -value based on the P theoretical χ2 distribution is probably wrong. In order to solve this problem, and in order to better determine the uncertainties on the parameters in a fully frequentist way free of the incorrect assumption of the linearity between observables and parameters, toy fit studies are underway. Despite the non-trivial outcome of the fit, the result is not anymore significantly different from the SM, due to the rather high enforced mass scales. This is evident e.g. from Fig. 12(b), which shows an observable at the LHC, the double ratio of the predicted CMSSM Higgs decay widths into different particles, normalised to ΓZZ∗ , and this again normalised to the SM prediction of the same. The central values are very close to the SM, and the allowed variations are tiny compared to the present experimental precision, and unfortunately also to future projections from the LHC [139], and partly even for the ILC [14]. Also other observables show no significant deviation from the SM, which is evident from the pull sof the observables with respect to the best fit predictions, shown in Fig. 12(d). The fact that also new measurements in the last two years, such as (B µµ) are in very good B s → agreement with the SM is therefore not really a bad sign for SUSY. In fact, this was a prediction [55] from CMSSM fits, and naturally occurs in the CMSSM if the mass scales are high. Thus, the hope to indirectly discriminate constraint SUSY from the SM through Higgs precision observables looks dim, and if possible at all will require the highest possible precision. Unfortunately, also the outlook to directly exclude the CMSSM at the LHC looks not 50 Section 6 Interpretations too bright: The upper range of the allowed mass scales at the 95% CL in Fig. 12(a) unfortunately lies high enough such that they will probably not be reached. Thus the CMSSM effectively becomes nothing else than the SM, plus DM. However, while the CMSSM cannot be excluded at the LHC, it should not be forgotten that the fit results do actually suggest that the sparticles in the CMSSM can be found soon at the LHC running at 13 or 14TeV, since the best fit point is close to the current reach of the SUSY searches. While the above mentioned results do show that even the most unflexible realistic implementation of SUSY, the CMSSM, is still allowed by the data, one question remains: SUSY was deemed attractive in Section 2.3 mainly since it allows to cure the hierarchy problem of 2 the SM, explain electroweak symmetry breaking, predict sin θW and describe DM, without destroying the great agreement of the SM with the precision data anywhere. However, if the SM was unattractive due to its hierarchy problem, one can ask whether SUSY has a similar problem (apart from its problem with the scale of µ in the MSSM, which shall not be further discussed here): It predicts m m at the tree level and requires large loop corrections h ≤ Z to lift the Higgs mass to around m 125.5GeV. The classical measure of the finetuning h ≈ needed to arrange for these large loop corrections is to look for the strongest dependence of a precisely measured quantity which is a boundary condition for SUSY on each parameter. The optimal choice for this observable is mZ : Its value must be maintained by SUSY, and thus it is used as a boundary condition when calculating the SUSY spectrum from the SUSY parameters. For a typical definition of such a measure of finetuning, which just looks at how strongly mZ depends on the parameter with the strongest influence, see [140]. The typical values obtained for this finetuning measure ∆ = max (a /m2 )(∂m2 /∂a ) , i | i Z Z i | where all relevant parameters ai are tested, are currently in the region of about 100 for the CMSSM. This means according to the above formula, that for typical values of ai 1 TeV 2 ≈ mZ changes 1000 times faster than ai itself. That definitely sounds not very elegant, but given the finetuning problems of the SM, where the finetuning of the Higgs mass has to occur by about 14 orders of magnitude (cf. Section 2.1), this is still not so catastrophic. Another important question is, whether ∆ is the right answer to the question. Of course it can happen that individual observables, like mZ , depend strongly on one parameter. And bare thus it might be necessary, as in this case, to adjust the bare input parameter mZ to the SM very finely, in the above case by a factor of √1000 more finely than the parameter ai with bare the strongest impact. However, it might be the case that the bare input mZ does not have to be adjusted at all, as long as other SUSY parameters all together make up for the strong impact of the strongest parameter. Therefore, it might be attractive to look for a measure of finetuning which does not only depend on one observable and the strongest parameter influencing that observable, but instead look at the global picture of the agreement of the theory with the data. Therefore, in [55] there is a proposal for another measure of finetuning directly based on the global fit: The χ2 contains the global agreement of the model to all relevant data. With that in mind, what is important in terms of finetuning is the degree of the strongest correlations observed amongst the parameters of the model for a given fixed agreement of the predictions with the data. Hence, the measure of the finetuning is the magnitude of the largest parameter correlation found in fixed χ2 slices. In [55] it is observed that the outcome of this test naturally depends strongly on the completeness of the parameter set of the model. E.g. if mt is omitted as a parametric uncertainty by not including mt as a parameter and observable in the fit, the maximal correlation tends to be close to 1, suggesting an extremely finetuned model. However, mt has strong input into the Higgs sector, and hence floating it relaxes the model considerably, yielding generally correlations below 20% in the allowed region at 95% CL. This suggests that the parameters of the CMSSM are actually not so finetuned at all, if all relevant parameters are studied at 51 once. Before concluding on the remaining beauty of the CMSSM, after the data has turned it (at least temporarily) into a SM plus DM, one more thought on finetuning has to be discussed. Of course a finetuned model (if it has to be regarded as finetuned at all after the above discussion) sounds not like a very elegant description of Nature. But one should not forget that there are very impressive examples of situations which seem finetuned, but are not. The best example for such a misguided fear of finetuning could be the moon [141], which seems to have exactly the same size as the sun, when seen from earth. This produces beautiful eclipses. Since the sun and the moon momentarily seem to be finetuned with respect to each other by about 1/100, there is nothing to worry about. There is no fundamental reason for this finetuning, it just occurs by chance, and it will disappear in the next billions of years by itself, when the moon moves further and further away from earth. Thus, there also could be more relaxed view on all finetuning issues. Of course the studies on global fits of SUSY are by far not the only ones. The numbers of similar studies go into the hundreds. The ones most closely connected in approach and content to the Fittino fits discussed here are probably the fits by the mastercode and SFitter [142] projects, which generally find similar results as Fittino. Despite the epis- temological problems of the Bayesian approach when it comes to fundamental parameters, such as in SUSY, there are of course also global fits based on Bayesian statistics, such as [143] and [144]. As long as Bayesian techniques are only used to interpret the Markov Chain Monte Carlo [143], the results are different, but not entirely unsimilar to those of the frequentist fits (for a direct comparison based on one Markov Chain Monte Carlo, also under different prior assumptions, see [55]). However, also questions of belief into SUSY are tried to be studied [144], which naturally will have a different focus than the fits discussed here. In the future, several methodological improvements on the current generation of global fits can be expected. As already outlined, fully frequentist -values would be very attractive, P and also uncertainties from toy fits. In terms of the implementation of observables, a combination of the number of Higgs search channels to the configuration in which there can be individually varying predictions for each individual channel rate would be beneficial. Generally, in the future there could be improvements in the way the experimental results are presented, e.g. in terms of full likelihoods in all relevant parameters. For an interesting list of proposals to that regard, see [145]. Finally, the number of parameters could be increased and more general models could be fitted. However, given the survival of a very constraint model up to this point, the results of more complex models will only qualitatively differ from the CMSSM results in one direction: towards larger allowed areas of sparticle masses and parameters. Thus, one very interesting information could be searched for in a fit where the slepton and gaugino sector is truly decoupled from the Higgs and squark sector: What are the lowest available mass scales of gauginos and sleptons? This cannot be inferred from the CMSSM fit, because there the uncoloured SUSY particles are coupled theoretically to the coloured ones of the first generation and to the gluino, which are moved up in mass scale by the generic searches. In order for such a study to work, it would also be beneficial if all simplified model searches would be available in an algorithmic interpretation (following the example of HiggsBounds). On that several groups are working. One little caveat remains, though: As outlined in Section 2.1, the SM has the interesting feature that within the current uncertainties on the Higgs boson and the top quark mass, it is unknown whether the SM vacuum is actually stable. The analogous test for the SUSY models fitted here has not yet been done consistently, but tools to do this test are available since a short time [146]. Including stability requirements into the global fits would be another interesting step forward. Another possible way forward are fits of models with a very large number of param- 52 Section 6 Interpretations eters, such as pMSSM fits with at least 19 SUSY parameters. This is attempted within the experimental collaborations, with one public result from CMS [147]. However, since in this study the SUSY searches are applied on each model point using signal Monte Carlo events, the statistics is extremely poor, with (100000) tested points. For 19 parameters, O this corresponds to on average 19√100000 = 1.8 points per dimension. Even though the points are sampled randomly, such that observables which do not depend on all parameters effectively enjoy a finer sampling, this is still too low to draw conclusions. Other more phenomenological fits of the pMSSM [148] enjoy much higher sampling density but inevitably also a less accurate implementation of the plethora of searches available at the LHC. In summary, the status of the CMSSM, and thus of the highest constraint form of SUSY, is: it is by far not dead, but dull. In more complex models, there naturally is much more freedom than in the CMSSM. Whether using that freedom or not is deemed attractive is a matter of choice. The important outcome from the studies presented here, deliberately using a very strongly constraint SUSY model such as the CMSSM is: The CMSSM, and thus SUSY, cannot be excluded at the LHC, unless the SM is excluded, too. This is a very interesting and maybe unexpected outcome, which is not widely debated. 53

7 Summary and Outlook

As outlined in the previous sections, particle physics and the understanding of the fundamental forces and constituents of Nature have reached an extremely interesting situation. A Higgs boson has been found at ATLAS and CMS, which could be the key to understanding electroweak symmetry breaking, the arguably biggest mystery in the construction of the SM. Finding out whether this Higgs boson is actually the SM Higgs boson has just begun. At present experimental uncertainties, the measured properties of the Higgs boson are in general agreement with the SM, but uncertainties in the range of around 30 % for each individual measurement of Higgs production times decay rates still leave a lot of room for deviations from the SM. Measuring such deviations would be the most stringent way towards finally finding out of what the SM is an effective theory. It would be timely – The Higgs mechanism turns 50 years old in 2014, and thus it would be nice if after such along successful reign a successor to the almighty SM could slowly emerge. Which in turn probably would still be an effective theory, and particle physicists would stay busy. Over the next 10 years, it can be expected that the LHC experiments will significantly improve the precision of their measurements in the Higgs sector and widen the covered areas. (see e.g. [149]). This will allow uncertainties on measurements of σ in the order ×B of magnitude of 5%. Many possibilities for fascinating discoveries in this range of precision exist. In addition, the refinement of the presentation of the experimental findings, e.g. in the form of more unfolded differential measurements [89], would make it possible to test many more effective models of Higgs sectors which could involve changes in the kinematics of production and decay (see e.g. [40]). However, due to the missing possibility to measure the Higgs production independently from the decay, there is no completely model independent way of transferring these measurements into model independent absolute measurements of couplings. Given the fact that 15 out of 17 of the electroweak SM Lagrangian parameters are directly connected to the Higgs sector (9 Yukawa couplings, 4 CKM parameters, 2 Higgs potential parameters), and all the rest of the electroweak Lagrangian is indirectly influenced by them, it would be a shame not to attempt anything to measure the Higgs sector as precisely and model-independently as possible. The by far most realistic possibility for such measurements is the possible construction of a 250GeV to 1TeV e+e− linear collider (ILC) in Japan [14], where a model independent precision on the Higgs mass of around 30MeV [14] and on couplings in a range of 2 % [150,151] is possible. For the direct discovery of New Physics particles, such as in the search for SUSY, the outlook is much less clear as in case of the Higgs measurements. Projecting uncertainties for future measurements of properties of an already discovered particle is only based on the understanding of future experiments, while projecting the particle content of unknown new theories of Nature is not really possible. Thus, an almost infinite number of possibilities exists. New Higgs bosons from extended Higgs sectors could still be discovered, both above and below the 125GeV Higgs boson. SUSY states could finally be discovered at the LHC at √s = 13 or 14TeV [139], lifting e.g. the accessible mass scale of the all-important third generation stops from the current maximum of around 600GeV to around 1400GeV. That would be interesting, because as outlined in Section 6.2, the finetuning issue, which could render SUSY unattractive for explanations of electroweak symmetry breaking, could get severe if √mt˜1 mt˜2 > 1TeV. Thus, SUSY for sure cannot be directly excluded at the LHC alone, but it could be possible to find out whether it remains a partly attractive full explanation of electroweak symmetry breaking, all of particle physics and parts of cosmology, or not. A similar situation arises for the interpretation of messengers from many different exper- 54 Section 7 Summary and Outlook imental sources. Interpreting the available data in high-scale models such as the CMSSM shows that as long the SM is describing the precision data, SUSY is alive, but dull, a conclusion which unfortunately cannot be changed by the potential non-show of SUSY particles at the LHC running at √s = 13 or 14 TeV. In any case, tools like HiggsBounds, HiggsSignals, and Fittino can be of significant use in the future, either to make Higgs measurements accessible more easily for the interpretation outside the experimental collaborations, to make them statistically as precise as externally possible, and to test attractive models of New Physics directly against measurements in a multi messenger approach in global fits, SUSY or otherwise, whatever fascinating theory might be invented in the future. The negative outlook for physics at colliders could well be the following, leaving particle physics in a limbo after LHC 14: The SM could be known to still describe the precision data, this time including Higgs property measurements, just similar to before the LHC started and discovered the Higgs. And SUSY could still be known to be the “better” SM – including the SM wherever there is precision data, now including the SM-like Higgs, and explaining DM in addition. But, there still could be no positive hint for SUSY or any other new physics in the form of other new particles or measurements strongly deviating from the SM, maybe in the Higgs sector including precision measurements of triple Higgs couplings and thus a direct look at the Higgs potential, maybe in triple gauge couplings, maybe in 0 WLWL scattering, maybe in a return to the Z -pole. In such a situation, one could still hope for the ILC, to improve upon precision in all those areas very significantly and maybe finally find a concrete positive hint for New Physics. Or a future giant hadron collider in the farther future could just be lucky and find new states where there is no direct reason to expect them. Of course, there also is a positive scenario for the future: Maybe the next run of the LHC at √s = 13 or 14 TeV will open a new window of spectroscopy of new particles, maybe the more precise measurements of the Higgs properties will show clear deviations from the SM, or updated precision experiments such as Belle II and LHCb will show clear deviations from the SM in the flavour sector, and maybe the ILC will come in and add a set of complementary results giving a lot of clarity to the picture with many model independent measurements of the Higgs and the New States, which then can be uniquely interpreted in one new beautiful theory of Nature. Time will tell, soon. 55

Publications by the Author Contained in the Cumulative Habilitation Treatise

1. P. Bechtle, K. Desch, and P. Wienemann, Fittino, a program for determining MSSM parameters from collider observables using an iterative method, Com- put.Phys.Commun. 174, 47 (2006).

2. S. Schael et al., Search for neutral MSSM Higgs bosons at LEP, Eur.Phys.J. C47, 547 (2006).

3. P. Bechtle, O. Brein, S. Heinemeyer, G. Weiglein, and K. E. Williams, HiggsBounds: Confronting Arbitrary Higgs Sectors with Exclusion Bounds from LEP and the Teva- tron, Comput.Phys.Commun. 181, 138 (2010).

4. P. Bechtle, K. Desch, M. Uhlenbrock, and P. Wienemann, Constraining SUSY models with Fittino using measurements before, with and beyond the LHC, Eur.Phys.J. C66, 215 (2010).

5. P. Bechtle, O. Brein, S. Heinemeyer, G. Weiglein, and K. E. Williams, HiggsBounds 2.0.0: Confronting Neutral and Charged Higgs Sector Predictions with Exclusion Bounds from LEP and the Tevatron, Comput.Phys.Commun. 182, 2605 (2011).

6. P. Bechtle et al., What if the LHC does not ﬁnd supersymmetry in the √s = 7 TeV run?, Phys.Rev. D84, 011701 (2011).

7. G. Aad et al., Searches for supersymmetry with the ATLAS detector using ﬁnal states with two leptons and missing transverse momentum in √s = 7 TeV proton-proton collisions, Phys.Lett. B709, 137 (2012).

8. P. Bechtle et al., Constrained Supersymmetry after two years of LHC data: a global view with Fittino, JHEP 1206, 098 (2012).

9. J. Lees et al., Precision Measurement of the B X γ Photon Energy Spectrum, → s Branching Fraction, and Direct CP Asymmetry A (B X γ), Phys.Rev.Lett. CP → s+d 109, 191801 (2012).

10. G. Aad et al., Search for Supersymmetry in Events with Large Missing Transverse Momentum, Jets, and at Least One Tau Lepton in 7 TeV Proton-Proton Collision Data with the ATLAS Detector, Eur.Phys.J. C72, 2215 (2012).

11. P. Bechtle et al., MSSM Interpretations of the LHC Discovery: Light or Heavy Higgs?, Eur.Phys.J. C73, 2354 (2013).

12. P. Bechtle, S. Heinemeyer, O. St˚al, T. Stefaniak, and G. Weiglein, HiggsSignals: Confronting arbitrary Higgs sectors with measurements at the Tevatron and the LHC, (2013), arxiv:1305.1933 [hep-ph], accepted by EPJC.

13. P. Bechtle et al., HiggsBounds-4: Improved Tests of Extended Higgs Sectors against Exclusion Bounds from LEP, the Tevatron and the LHC, (2013), arxiv:1311.0055 [hep-ph], accepted by EPJC.

This summary of the Habilitation Treatise is based entirely on the own work published in the publications above and on the references at the end of this document. For a full list of collaborators on the topics relevant for the Habilitation, please see the author lists of the relevant publications.

Acknowledgments

The work summarised in this article – as far as only the authors own work is concerned – was carried out over the course of many years, in the OPAL, BaBar and ATLAS Collaborations, in the Linear Collider project, and in the collaboration with theorists in the Fittino and HiggsBounds/HiggsSignals projects. In this time the author was working as a Postdoc at the Stanford Linear Accelerator Centre in the group of Vera L¨uth, as a Young Investigator Group Leader at DESY with Rolf Heuer and Klaus Desch as the initial University partners, and ﬁnally at the present position at the University of Bonn. The author is grateful for the great support received at any of these institutions, and for the collaboration with so many great students and fellow scientists, without whom this work would not have been possible. Obviously the biggest and most important gratitude is owed to Klaus Desch, instructor, inspiration, support and friend for many years, and to the family of the author.

Curriculum Vitae

Personal Data

Name PhilipMoritzBechtle Born 5. Januar 1976 Address Carl-Duisberg-Straße 331, 51373 Leverkusen E-Mail [email protected]

Education

Sep 2004 Dissertation in Physics at the University of Hamburg “SUSY Higgs Searches at LEP and SUSY Parameter Measurements at TESLA”, Grade: “summa cum laude” 2001 – 2004 PhD Thesis, advisor Prof. Dr. Rolf-Dieter Heuer at DESY and the University of Hamburg Mar2001 DiplomsinPhysics,grade: “sehrgut” 1999 – 2001 Diploma thesis, advisor Prof. Dr. Peter Buchholz at the University of Dortmund “Inbetriebnahme des HERA-B Myon-Pretrigger-Systems” (Commissioning of the HERA-B muon pretrigger system) 1995 – 2001 Studies of Physics at the University of Dortmund Jun1995 Abitur,Grade: “sehrgut”(1,2)

Scientiﬁc Career

Since July 2011 Akademischer Rat, University of Bonn Oct 2010 – Jul 2011 Permanent research staﬀ scientist at DESY 2008 – 2012 Co-Speaker of a project in the collaborative research center SFB 676 “Interpretation of Physics Results from LHC and other Experiments” 2008 – 2010 Co-Speaker of a second project in SFB 676 “Physics beyond the Standard Model at the e+e− linear collider ILC” Mar – Sep 2008 Interim Professor (“Lehrstuhlvertretung”) for Prof. Dr. Karl Jakobs, University of Freiburg 2007 – 2012 Helmholtz-Young-Investogator-Group Leader at DESY Group working on ATLAS and ILC 2005 – 2007 Research Associate at Stanford Linear Accelerator Center (SLAC), Working on b sγ decays at BaBar → Sep – Dec 2004 Research Associate at DESY

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