Medida de la sección eficaz y masa del quark top en las desintegraciones dileptónicas de pares top-antitop en el experimento CMS del LHC

Transcription

1 Universidad de Oviedo Departamento de Física Medida de la sección eficaz y masa del quark top en las desintegraciones dileptónicas de pares top-antitop en el experimento CMS del LHC Autor: D. Jesús Manuel Vizán García Director: D. Francisco Javier Cuevas Maestro

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3 Universidad de Oviedo Departamento de Física Medida de la sección eficaz y masa del quark top en las desintegraciones dileptónicas de pares top-antitop en el experimento CMS del LHC Autor: Jesús Manuel Vizán García Director: Francisco Javier Cuevas Maestro

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5 D. F. Javier Cuevas, doctor en Ciencias Físicas y profesor titular del Departamento de Física de la Universidad de Oviedo, Certifica: Que la memoria: MEDIDA DELA SECCION EFICAZ Y MASA DEL QUARK TOP EN LAS DESINTEGRACIONES DILEPTONICAS DE PARES TOP-ANTITOP EN EL EXPER- IMENTO CMS DEL LHC ha sido realizada bajo su dirección en el Departamento de Física de la Universidad de Oviedo por Jesús Manuel Vizán García constituyendo su tesis doctoral en Ciencias Físicas. Y para que así conste, en cumplimiento de la legislación vigente, presento ante la Universidad de Oviedo dicha Tesis Doctoral, firmando el presente certificado: Oviedo, 8 de Mayo de 2009

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7 Contents Introducción 3 Introduction 5 1 Top Quark Physics as a Part of the Standard Model The Standard Model of Elementary Particles The elementary particles and the fundamental interactions The massless Standard Model Lagrangian The Higgs mechanism Top Quark Physics Top quark production Decay of top quark Importance of top quark physics The Large Hadron Collider The LHC Design and Operation The LHC Physics Program Experiments at the LHC The CMS Detector and Monte-Carlo Simulation The CMS Detector The CMS tracker The electromagnetic calorimeter The hadronic calorimeter The muon spectrometer Online selection and data acquisition Alignment and calibration of the CMS detector and integrated luminosity scenarios Monte-Carlo Simulation Simulation of proton-proton collisions The CMS software framework The CMS computing model

8 4 Object reconstruction in CMS Muon Reconstruction in CMS Electron Reconstruction in CMS Leptonic Signatures in t t Studies Lepton Identification Lepton Isolation Lepton Performance in t t Dilepton Channel Missing Transverse Energy Reconstruction Jet Reconstruction Jet input objects Jet clustering Jet energy scale corrections Jet reconstruction in t t dilepton events b-jet Identification Tools t t Cross Sections Estimation and Signal Selection Signal and Backgrounds Monte-Carlo Samples of the Different Processes Trigger Paths and Efficiencies and Sample Composition Event Selection Lepton selection Jet selection Missing transverse energy b-jet identification Selection using ET miss and b-jet identification Selection without b-jet identification Selection without ET miss Sensitivity to misalignment Sensitivity to JES Statistical Uncertainty in the t t Cross-Section Measurement Data-Driven Methods The Matrix Method Control of the fake rates from data ET miss resolution measurement with data b-tagging and mistag efficiencies Lepton reconstruction efficiency Systematic Uncertainties Perspectives for Higher Luminosities Conclusions Top Mass measurement Experimental Knowledge of the Top Quark Mass t t Kinematical Reconstruction

9 1 6.3 Mass Determination Systematics Affecting the Top Mass Measurement Prospects for s = 10 TeV Run Simulation of Samples at s = 10 TeV Objet Definition Lepton identification Lepton isolation The Event Selection HLT performance Lepton selection Jet selection b-jet identification Results Conclusions 175 Conclusiones 183 Acknowledgements 201

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11 Introducción El comportamiento de todas las partículas subatómicas conocidas se puede describir dentro de un único marco teórico llamado el Modelo Estándar (ME). Esta teoría cuántica de campos incorpora los quarks y los leptones así como sus interacciones a través de fuerzas fundamentales excepto la gravedad. El bosón de Higgs, la única partícula no observada dentro del Modelo Estándar y posibles extensiones del mismo serán investigadas en un nuevo dominio de energías con el comienzo del LHC (gran colisionador de hadrones), un acelerador que producirá colisiones protón-protón a una energía en centro de masas de s = 14 TeV, que es más de siete veces más alta que la que corresponde a los aceleradores que funcionan en la actualidad. El quark top, el más pesado de todos los quarks conocidos está considerado como una ventana altamente sensible para la búsqueda de nueva Física. Asimismo, un mejor conocimiento de las propiedades del quark top, tales como su masa y la sección eficaz del proceso t t producirá una prueba adicional de la corrección del ME. Durante el año 2009 se espera que tengan lugar las primeras colisiones protón-protón en el LHC. Está previsto un primer periodo de funcionamiento a energías en centro de masas de s = 10 TeV con alrededor de pb 1 de luminosidad integrada recogida. El canal dileptónico t t b bl lν ν, debido a la presencia de dos leptones cargados en el estado final, es uno de los procesos posibles en Física del quark top más adecuados para ser observados y medidos en CMS (Compact Muon Solenoid), uno de los dos detectores de propósito general instalados en el túnel del LHC y el experimento donde se desarrolla esta tesis doctoral. El detector CMS está caracterizado por su excelente dispositivo de medida de trazas, por su espectrómetro de muones, y la hermeticidad de su sistema de calorímetros, satisfaciendo todos los requisitos necesarios para estudiar de manera muy eficiente el amplio abanico que contempla el programa de Física del quark top en LHC. El objetivo principal de esta tesis es el de caracterizar un método para explotar este tipo de procesos físicos de modo que se produzca una muestra muy limpia de sucesos de señal para poder medir la sección eficaz de producción del proceso t t. Además de proporcionar estos métodos como punto de partida de estudios más avanzados relacionados con el quark top, los resultados que se presentan tienen una especial relevancia en el estudio de otros muchos procesos físicos en el LHC, entre los que se incluyen la búsqueda del bosón de Higgs, puesto que en ella y en otras búsquedas de nuevas partículas, los sucesos producidos en el proceso t t constituyen uno de los fondos principales. Esta tesis comienza en el Capítulo 1 con la descripción del Modelo Estándar y el sector del quark top como parte de él. En el Capítulo 2 se describe el acelerador LHC. Después, en el Capítulo 3 se describe el detector CMS así como los métodos de simulación de colisiones protón-protón que se usarán posteriormente en el análisis. El Capítulo 4 se concentra en aspectos de reconstrucción y selección de los observables físicos 3

12 4 que se utilizarán en la selección del proceso t t tales como muones o jets. La selección final de sucesos producidos en el proceso t t dileptónico, así como el método de medida de la sección eficaz se describen en el Capítulo 5. En el Capítulo 7 se describen estos métodos adaptados a la energía y condiciones de funcionamiento del LHC esperados durante sus dos primeros años de funcionamiento, en particular teniendo en cuenta la energía esperada en centro de masas de s = 10 TeV. En el Capítulo 6 se describe el modo de medir la masa del quark top utilizando los sucesos producidos en la desintegración dileptónica, que previsiblemente será posible utilizar en una fase mas avanzada de la toma de datos de CMS. Las conclusiones se exponen en la parte final de la memoria.

13 Introduction The behaviour of all known subatomic particles can be described within a single theoretical framework called the Standard Model (SM). This quantum field theory incorporates the quarks and leptons as well as their interactions through all fundamental forces except gravity. The Higgs boson, the only unobserved Standard Model particle, and possible extensions of the Standard Model will be investigated in a new energy domain with the advent of the Large Hadron Collider, a hadron accelerator that will produce proton-proton collisions at a centre of mass energy of s = 14 TeV, an energy more than seven times higher than the corresponding to present-day accelerators. The top quark, the heaviest of all quarks is considered to be a highly sensitive window for this search of new physics. Also, a better knowledge of the top quark properties such as its mass and the t t-production cross-section will result in an ultimate confinement test of the Standard Model. During 2009, the first proton-proton collisions at the LHC are expected to take place. A first physics run has been planned to start this year at a centre of mass energy of s = 10 TeV and to accumulate an amount data of about pb 1 until the end of The t t dilepton channel t t b bl lν ν, due to the presence of two charged leptons in the final state, presents one of the most reliable signatures related to top quarks to be spotted in the Compact Muon Solenoid (CMS), one of the two general-purpose detectors installed along the LHC tunnel and the experiment that constitutes the framework in which this work has been performed. The CMS detector, characterized by its excellent tracker device, muon spectrometer, electromagnetic calorimeter, and by the hermeticity of their calorimeter systems, fulfills all the requirements to efficiently study the broad top-quark physics programme provided by proton-proton collisions in LHC. One of the main goals of this work is to provide a robust method to exploit the physics run mentioned previously in order to produce a very clean selection of signal events and to measure the t t-pair production cross-section in the final state containing two charged leptons. In addition, this study can serve as the basis of more advanced top-quark studies, for instance, the results presented here are also relevant to many other analysis, including searches of the Higgs boson. t t dilepton events are in summary one of the most important backgrounds to many physics channels in CMS. The work starts with a description of the Standard Model and the top quark sector as a part of it in Chapter 1. In Chapter 2 the LHC collider is described. Next, in Chapter 3 the CMS detector and the principles of the simulation of the proton-proton collisions used in the analyses presented in this thesis are described. Chapter 4 concentrates on reconstruction aspects and selection of the physics objects used to select the t t dilepton events such as muons or jets. 5

14 6 The final selection of t t dilepton events and the prospects for the measurement of the t t-pair cross-section are given in Chapter 5. This analysis, that has been carried out using simulated events at s = 14 TeV has been also optimized for events at s = 10 TeV in Chapter 7. A discussion of the prospects to measure the top-quark mass using t t dilepton events in CMS, an example of a top-quark analysis more suitable to a more advanced phase of the data-taking, is presented in Chapter 6. Finally, at the end of this document, the conclusions of this work are presented.

15 Chapter 1 Top Quark Physics as a Part of the Standard Model The Standard Model (SM) is a field theory that combines special relativity and quantum mechanics, compressing the present understanding of the fundamental constituents of the matter and their interactions. This description is the result of decades of worldwide fundamental scientific research based on a fruitful interplay between improved experimental data-taking and theoretical insights. After about 30 years of extensive testing, the SM is one of the best theories of modern physics. In fact, most of its building blocks have been tested up to a very high precision over a large range of energies and an agreement at the per mill level with the theoretical predictions has been found. A description of the Standard Model is given in Section 1.1 and, as the main goal of this thesis is the study of the methods and perspectives to measure properties of one of the particles predicted by this model, the top quark, Section 1.2 will concentrate on the current experimental knowledge and the theoretical importance of this particle. 1.1 The Standard Model of Elementary Particles In this section only the most fundamental aspects of the Standard Model will be reviewed [1, 2], while more detailed descriptions can be found in [3 9]. In Section an overview of all elementary particles introduced in the Standard Model is given. A more mathematical approximation to the Standard Model is given in Section 1.1.2, while the mechanism that generates the masses of the particles according to the theory is summarized in Section The elementary particles and the fundamental interactions The Standard Model provides a description of the world in terms of interacting fields. Each field represents a particle and all fields are divided into two categories according to their intrinsic angular momentum (spin). All matter is built from only 12 spin-1/2 particles called fermions 7

16 8 1. Top Quark Physics as a Part of the Standard Model Generation Flavour Electric charge Mass First electron e e MeV Generation electron neutrino ν e 0 < 2.2 ev Second muon µ e MeV Generation muon neutrino ν µ 0 < MeV Third tau τ e MeV Generation tau neutrino ν τ 0 < 15.5 MeV Table 1.1: The three generations of leptons. Generation Flavour Electric charge Mass 2 First up u e MeV 3 Generation down d 1 e 3-7 MeV 3 2 Second charm c e 1.25 GeV 3 Generation strange s 1 e MeV 3 2 Third top t e GeV 3 Generation bottom b 1 e 4.7 GeV 3 Table 1.2: The three generations of quarks. and interactions between these fermions happen through the exchange of spin-1 particles called bosons. The fermions are divided into leptons and quarks. Both groups of particles are further divided into three generations that behave identically under interactions. No experimental evidence has been found so far for the existence of a fourth generation [10 12]. The six known lepton flavours: electron e, muon µ, tau τ and three corresponding neutrinos ν e, ν µ, ν τ are listed in Table 1.1. The three charged leptons carry electric charge 1 e and their masses vary from MeV to GeV. Neutrinos are chargeless particles and have very small masses, but not exactly zero, as it has been shown by recent results from neutrino oscillation measurements [13,14]. In addition, each lepton generation carries a lepton number which along with the electric charge is conserved in all processes of the Standard Model. The six known quark flavours: up u, down d, strange s, charm c, bottom b, and top t are listed in Table 1.2. The u, c and t quarks are known as up-type quarks and all of them carry a charge of 2/3 e, while d, s and b quarks are known as down-type quarks and carry a charge of 1/3 e. There is also a hierarchy in the mass of the quarks, which vary from about 1.5 MeV for an up quark to 173 GeV for a top quark. All of these quark masses, and also the corresponding to leptons, are free parameters of the Standard Model. Each of the fermions described above has its anti-particle, which has the same mass but opposite quantum numbers. However, no stable anti-matter has been detected so far. In fact, all stable matter observed in the universe consist only of particles from the first generation: the atoms are formed of electrons and the atomic nuclei, which constituents, protons and neutrons, are composed of up and down quarks. The particles of the second and third generations are

17 1.1. The Standard Model of Elementary Particles 9 Interaction Mediator Electric charge Mass ( GeV) Electromagnetic photon γ 0 0 Weak W ± ±1 e Z Strong 8 gluons g 0 0 Table 1.3: The gauge bosons of the Standard Model. exact copies of the particles of the first, apart from the increasing particle mass. Within the SM, the spin-1 bosons are the quanta of the fields responsible for the interactions between particles. These gauge bosons mediate the three experimentally observed types of fundamental interactions between fermions: the electromagnetic interaction is mediated by the photon, the weak interaction by the W +, the W and the Z 0 bosons, and the strong interaction by gluons. The fourth known fundamental interaction, gravity, is not described by the Standard Model, but since it dominates only for very large masses, it can usually be ignored in fundamental particle interactions. The bosons introduced in the SM and their associated fundamental interactions are listed in Table 1.3. Because the gauge boson of the electromagnetic interaction is massless, the range corresponding to this interaction is infinite. This interaction, which was first described independently by the Quantum Electrodynamics (QED), affects all charged particles and its coupling strength, α EM, is equal to the fine structure constant ( 1/137) at low energies, and increases with increasing energies. On the other hand, the range of the electroweak interaction, as their force carriers are massive, is very short ( 10 3 fm). This force, which affects all leptons and quarks, and the EM one are unified in the electroweak theory [4,5]. In this model, the photon and the three weak bosons are the physical manifestation of the four gauge fields generated by the SU(2) L U(1) Y local gauge group. The quarks are the only fermions that interact via the strong force. The coupling constant of this interactions decreases with energy, and as consequence, the quarks are only observed as bounded states called hadrons. The addition of extra energy results in the production of extra quark/anti-quark pairs created from the increasing energy density in the intermediate gluon field. These phenomena are explained in terms of colour charge. Quarks have a colour charge (red (r), green(g) or blue(b)), and anti-quarks carry corresponding anti-colour charges. To build a hadron, the sum of the colours of the involved quarks must be colourless. This can be achieved by a combination of three quarks (r+ g+ b), a quark system known as baryon, or by a combination of a quark and an anti-quark (r r, gḡ, or b b), a quark system known as meson. The quark flavours are not separately conserved, but changes are only possible through the weak interaction. The QCD mediators or gluons are also colour charged, and will hence interact with one another. The theory of the strong interaction, Quantum Chromodynamics (QCD), is incorporated and described in the Standard Model, together with the electroweak theory.

18 10 1. Top Quark Physics as a Part of the Standard Model The massless Standard Model Lagrangian Interactions from gauge symmetries The principle of gauge symmetry is essential in the construction of the Standard Model since all fundamental interactions can be described by local gauge field theories. The electroweak model is based on the gauge group SU(2) L U(1) Y and QCD is based on the SU(3) symmetry. In the Standard Model, a free fermion with mass m is described as a spinor ψ by the Lagrangian L = i ψγ µ µ ψ m ψψ, (1.1) from which the Dirac equation of motion (iγ µ µ m)ψ = 0 can be derived. The Dirac Lagrangian 1.1 is invariant under the phase transformation ψ e iα ψ, (1.2) where α is a real constant. The fact that the Lagrangian remains invariant under phase transformation means that the Lagrangian possesses global U(1) gauge symmetry. Since α is constant in space and time, it has no physical meaning. If the fermion s wave function changes now under a local phase transformation with rotation parameter ǫ (x) in an internal space represented by the generators τ as ψ = Uψ = e i ǫ(x) τ 2 ψ, (1.3) the Lagrangian 1.1 is not invariant under such transformation, what means that it does not possess local gauge invariance. In order to make the Lagrangian invariant under local gauge transformation, the covariant derivative D µ is introduced: D µ = µ ig τ 2 A µ, (1.4) where A µ is a new interacting vector field which compensates the local gauge transformation and g is an arbitrary parameter which will determine the universal interaction strength associated to the field. Substituting 1.4 into 1.1 yields to the Lagrangian L = i ψγ µ D µ ψ m ψψ = i ψγ µ µ ψ m ψψ ig ψγ µ τ 2 A µ ψ, (1.5) where the last term expresses the coupling between the fermion field and the new vector field. By demanding that D µψ = U (D µ ψ), (1.6) such that the Lagrangian 1.5 is invariant under 1.3, the transformation relations for the components of the field A µ are derived to be τ i 2 Ai µ = i g ( µu)u 1 + U τ i 2 Ai µu 1. (1.7)

19 1.1. The Standard Model of Elementary Particles 11 This relation, with U being a transformation matrix in some internal space, is very general. In the case where U = e iχ(x) represents a simple U(1) phase transformation, the theory is Abelian and 1.7 simplifies to A µ = A µ µ χ (x) /g. A theory with a local non-abelian phase invariance is called a Yang-Mills theory. It is found that the requirement of a theory to be invariant under certain symmetry transformations, which are generally called gauge transformations, entails the introduction of associated vector fields, called gauge fields. These fields imply the existence of spin-1 particles, the gauge bosons, that couple to the fermions. In addition, gauge bosons in a Yang-Mills theory also exhibit self-interactions. The electroweak theory The gauge symmetry group able to give an appropriate description of the observed electroweak phenomena was determined to be the SU(2) L U(1) Y group. Requiring the Lagrangian to be gauge invariant towards local phase-space transformations of this group allowed to unify the weak nuclear force with the electromagnetic force, up to then described by Quantum Electrodynamics (QED). The EM force is characterized by unitary e iǫ(x) phase transformations in one dimension according to the U(1) group symmetry. The weak force on the other hand is described by SU(2). Consequently, it is convenient to group the fermions into doublets interacting under the weak force: ( ) ( ) ( ) ( ) ( ) ( ) u c t νe νµ ντ Ψ EW =,,,,, (1.8) d s b e µ τ Each of these doublets corresponds to a field comprising two Dirac spinors. Any SU(2) U(1) local phase-space transformation can be written as: Ψ EW = e i ǫ(x) σ e iθ(x) Ψ EW. (1.9) The covariant derivative which makes the Lagrangian invariant under these SU(2) L U(1) Y gauge transformation takes the form D µ = µ + ig ˆσ 2 W µ + ig Y 2 B µ, (1.10) with W µ and B µ the gauge fields associated to the SU(2) and U(1) groups respectively. Hence, for the electroweak theory to be gauge invariant, one scalar gauge boson B 0 and three vector gauge bosons W α (α = 1, 2, 3) are required. The latter bosons can only couple to left-handed fermion doublets; right-handed fermion fields remain unchanged under the SU(2) L gauge transformation. This way the parity-violating nature of the weak interactions is incorporated into the theory. The electroweak symmetry is not only expected to spoil parity, it must also be broken as a rather high mass is measured for its vector bosons. However, adding explicit mass terms to the Lagrangian would break the gauge invariance. In the next section a solution known as

20 12 1. Top Quark Physics as a Part of the Standard Model spontaneous symmetry breaking will be introduced. It will be shown that with this electroweak symmetry breaking procedure, the mass terms for the more familiar physical states 1 ( W µ ± = W 1 2 µ iwµ) 2 Zµ 0 = Wµ 3 cos θ ω B µ sin θ ω (1.11) A µ = W 3 µ sin θ ω + B µ cos θ ω arise naturally from the Higgs mechanism. In the above equations, θ w denotes the Weinberg mixing angle, defined as tanθ ω = g (1.12) g Quantum chromodinamics QCD is formulated in an analogue way to QED and the electroweak theory, in the sense that also the strong force mediating gluon fields are introduced in the theory by requiring gauge invariance. For this interaction the relevant gauge group is found to be the SU(3) C symmetry group, where the C subscript corresponds to the quark colour triplets. Restoring the gauge invariance of the theory with respect to local SU(3) phase-space transformations invokes the introduction of eight gauge fields, corresponding to the eight SU(3) group generators. The non- Abelian character of the SU(3) group will ensure that gluons self-interact, which is expected as gluons are colour charged themselves. The observation of CP violation and processes violating the conservation of strangeness, are allowed in the Standard Model by the assumption that the strong force eigenstates of the quarks slightly differ from their weak force eigenstates. This mismatch of quantum states is given by the Cabibbo-Kobayashi-Maskawa (CKM) matrix: d weak s weak b weak L = V ud V us V ub V cd V cs V cb V td V ts V tb d s b L. (1.13) This CKM matrix describes the probability of a transition from one quark q to another q due to a flavour changing weak interaction, and is proportional to V qq 2. Finally, it should be noted that in addition to the Lagrangian terms describing the free fermion propagation and the terms introducing the interactions of these fermions to the various gauge bosons, for each gauge field a gauge invariant kinetic term has to be introduced. These terms will allow the propagation of free gauge bosons. Renormalization of the theory Despite the elegance and simplicity of the SM Lagrangian, the derivation of predictions from the theory is a highly non-trivial task. This is simplified by the introduction of Feynman diagrams and rules for their calculation, enabling a diagrammatic approach to calculations of probabilities

21 1.1. The Standard Model of Elementary Particles 13 associated to specific processes [6]. Quantum-mechanical corrections need to be accounted for when performing such calculations, which introduce extra loops and vertices in the Feynman diagrams. By ordering all the diagrams as a function of the number of vertices, a series is formed with increasing powers of the coupling constant. Such an expansion can be used for perturbative calculations, provided the coupling constant is smaller than unity. In such calculations, however, one is confronted with divergences, even in the easiest case of electromagnetism. In the Standard Model, however, these infinities can always be absorbed into the unobservable bare parameters (such as the electric charge) of the Lagrangian by a technique called renormalization [15]. Finite measured quantities would in general imply divergent bare quantities, and should be defined at a certain renormalization scale. To minimize the contribution of loop diagrams to a given calculation (and therefore make it easier to extract results), this scale is typically chosen close to the energies and momenta actually exchanged in the interaction. However, in principle each physics quantity should be invariant under this choice. Changes in the renormalization scale will only affect how much of the result comes from Feynman diagrams without loops ( tree level diagrams ) and how much comes from the leftover finite parts of loop diagrams The Higgs mechanism The coupling of the SM fermions to electroweak gauge bosons has required the introduction of the gauge group SU(2) L U(1) Y. To guarantee massive W and Z bosons and consequently weak interactions with a short range compared to the EM force, the electroweak symmetry has to be broken in a way that conserves the gauge invariance and renormalizability of the theory. An explanation of this phenomenon is given by the Higgs mechanism. It is based on the idea of spontaneous symmetry breaking, according to which the vacuum state of a system does not possess the same symmetry as the Lagrangian density [16,17]. The simplest way to break the SU(2) L U(1) Y gauge symmetry is to introduce an extra scalar field in the doublet representation of SU(2) to the SM Lagrangian: ( ) φ + φ =, (1.14) with φ + and φ 0 complex fields. The Lagrangian density for such a field can be written with a specific potential in the form: φ 0 L = (D µ φ) D µ φ V (φ) = (D µ φ) D µ φ µ 2 λ ( φ φ ) 2, (1.15) where D µ is the covariant derivative in the SU(2) L U(1) Y gauge given in 1.10, µ 2 a mass parameter and λ > 0 the strength of the Higgs boson field s self interaction. By requiring µ 2 < 0, the symmetry is spontaneously broken because the minimum of the potential is no longer unique, but takes a value on a continuous ring in the complex plane as shown in Figure 1.1. In this ring the vacuum expectation value v is equal to < φ φ >= v 2 = µ2 λ > 0. (1.16)