DOCSLIB.ORG

Study of Electroweak Gauge Boson Scattering in the WZ Channel

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Study of Electroweak Gauge Boson Scattering in the WZ Channel Study of Electroweak Gauge Boson Scattering in the WZ Channel with the ATLAS Detector at the Large Hadron Collider DISSERTATION zur Erlangung des akademischen Grades Doctor rerum naturalium (Dr. rer. nat.) CERN-THESIS-2016-213 30/09/2016 vorgelegt der Fakult¨atMathematik und Naturwissenschaften der Technischen Universit¨atDresden von Diplom-Physiker Felix Socher (geb. Thomas) geboren am 01. Februar 1986 in Riesa Allons-y! 1. Gutachter: Prof. Dr. Michael Kobel 2. Gutachter: Prof. Dr. Chara Petridou Tag der m¨undlichen Pr¨ufung: 30.09.2016 Tag der Einreichung: 15.07.2016 Abstract The Standard Model of particle physics is a very well tested gauge theory describing the strong, weak and electromagnetic interactions between elementary particles through the exchange of force carriers called gauge bosons. Its high predictive power stems from its ability to derive the properties of the interactions it describes from fundamental symmetries of nature. Yet, it is not a final theory as there are several phenomena it cannot explain. Furthermore, not all of its predictions have been studied with suf- ficient precision, e.g. the properties of the newly discovered Higgs boson. Therefore, further probing of the Standard Model is necessary and may result in finding possible indications for new physics. The non-abelian SU(2)L U(1)Y symmetry group determines the properties of the elec- × tromagnetic and weak interactions giving rise to self-couplings between the electroweak gauge bosons, i.e. the massive W and Z boson, and the massless photon, via triple and quartic gauge couplings. Studies carried out over the past 20 years at various particle accelerator experiments have shed light on the structure of the triple gauge couplings but few results on quartic gauge couplings are available. The electroweak self-couplings are intertwined with the electroweak symmetry breaking and thus the Higgs boson through the scattering of massive electroweak gauge bosons. Both the W and Z boson couple to the Higgs boson and may interact with each other by exchanging it. Theory predictions yield physical results at high energies only if either both the self-couplings and Higgs boson properties are as described by the Standard Model or if they deviate from its predictions and contributions from new physics are present to render the calculations finite. This makes electroweak gauge boson scattering a powerful tool to probe the Standard Model and search for possible effects of new physics. The small cross section of massive electroweak gauge boson scattering necessitates high centre-of-mass energies and luminosities to study these processes successfully. The Large Hadron Collider (LHC) at CERN is a circular proton-proton collider equipped to supply a suitable environment for such studies with the colliding protons being the sources for the scattering of massive electroweak gauge bosons. The dataset collected in 2012 by the ATLAS detector at the LHC with a total lumi- nosity of 20:3 fb−1 and a centre-of-mass energy of 8 TeV is analysed in this work. The elastic scattering process WZ WZ is studied due to its clean signal properties. It ! provides a complementary measurement to W ±W ± W ±W ± which reported the first ! significant evidence for massive electroweak gauge boson scattering. Given the current data, WZ WZ scattering is not observed with large significantly. ! A cross section upper limit of 2:5 fb at 95 % confidence level is measured, compatible with the cross section of 0:54 fb predicted by the Standard Model. In addition, distributions for several observables sensitive to electroweak gauge boson scattering are unfolded, removing effects caused by the measuring process. Physics beyond the Standard Model is probed in the framework of the electroweak chiral Lagrangian which expresses the size of effects from new physics in terms of strength parameters. The two strength parameters influencing the quartic gauge couplings are constrained to 0:44 < α4 < 0:49 and 0:49 < α5 < 0:47 thus limiting the possible − − size of new physics contributions. Kurzdarstellung Das Standardmodell der Teilchenphysik beschreibt die starken, schwachen und elektro- magnetischen Wechselwirkungen zwischen Elementarteilchen uber¨ den Austausch von Kraftteilchen, sogenannten Eichbosonen. Es ist eine anerkannte theoretische Beschrei- bung der Natur, da es in der Lage ist, aus fundamentalen Symmetrien die Charakterisi- ken der einzelnen Wechselwirkungen abzuleiten. Die so getroffenen Vorhersagen wurden durch eine Vielzahl von Experimenten erfolgreich uberpr¨ uft.¨ Dennoch ist es keine abge- schlossene Theorie, da es nicht alle in der Natur beobachteten Ph¨anomene beschreiben kann. Uberdies¨ konnten die von ihm gemachten Vorhersagen wie z.B. die Eigenschaften des kurzlich¨ gefundenen Higgs Bosons, noch nicht mit ausreichender Pr¨azision uberpr¨ uft¨ werden. Deshalb sind weitere Tests des Standardmodells notwendig. Die Eigenschaften der elektromagnetischen und schwachen Wechselwirkungen werden durch die nicht-abelsche Symmetriegruppe SU(2)L U(1)Y bestimmt. Eine direkte × Konsequenz ist die Existenz von Selbstwechselwirkungen zwischen den elektroschwa- chen Eichbosonen, den massiven W und Z Bosonen und dem masselosen Photon, die durch Dreier- und Vierer-Kopplungen beschrieben werden. Die Struktur der Dreier- Kopplungen ist in den letzten 20 Jahren an Teilchenbeschleunigern eingehend studiert worden. Erst seit kurzem sind durch neue Beschleuniger pr¨azise Untersuchungen der Vierer-Kopplungen m¨oglich. Das Higgs Boson koppelt an W und Z Bosonen da diese eine Masse haben. Damit kann, durch die Untersuchung der Streuung massereicher elektroschwacher Eichbosonen so- wohl die elektroschwache Selbstwechselwirkung, als auch die elektroschwache Symme- triebrechung untersucht werden. Die Vorhersagen des Standardmodells sind bei hohen Energien nur dann gultig,¨ wenn die Eigenschaften des Higgs Bosons jenen entsprechen, die vom Standardmodell vorhergesagt werden. Falls diese Bedingung nicht erfullt¨ ist, werden Beitr¨age neuer physikalische Prozesse ben¨otigt um unphysikalische Vorhersa- gen zu vermeiden. Somit ist die Streuung massereicher elektroschwacher Eichbosonen geeignet, das Standardmodell zu testen und nach neuer Physik zu suchen. Die kleinen Wirkungsquerschnitte fur¨ die zu untersuchenden Prozesse bedingen eine hohe Schwerpunktsenergie und hohe Luminosit¨aten um eine ausreichend große Daten- menge zu erhalten. Der Large Hadron Collider am CERN ist ein Kreisbeschleuniger der diese Voraussetzungen erfullt,¨ indem er Protonen, die Quellen fur¨ die streuenden elektroschwachen Eichbosonen sind, mit einer Schwerpunktsenergie von 8 TeV zur Kol- lision bringt. Diese Arbeit basiert auf dem im Jahr 2012 vom ATLAS Detektor auf- gezeichnete Datensatz, der einer Luminosit¨at von 20:3 fb−1 entspricht. Der untersuchte Prozess ist die elastische Streuung WZ WZ, welche komplement¨ar zum Prozess ! W ±W ± W ±W ± ist, in dem erstmalig signifikante Hinweise auf die Streuung mas- ! sereicher elektroschwacher Eichbosonen gefunden wurden. Mit der derzeit verfugbaren¨ Datenmenge kann WZ WZ nicht mit ausreichender ! Signifikanz beobachtet werden. Fur¨ den Wirkungsquerschnitt wird eine obere Schranke von 2:5 fb mit 95 % Konfidenz gemessen, welche kompatibel mit der Standardmodell- vorhersage von 0:54 fb ist. Beitr¨age neuer Physik jenseits des Standardmodells k¨onnen generisch im Rahmen effek- tiver Feldtheorien durch St¨arkeparameter beschrieben werden. Die beobachteten Daten erm¨oglichen eine Einschr¨ankung der St¨arkeparameter α4 und α5, welche die Vierer- Kopplungen beeinflussen, auf die Bereiche 0:44 < α4 < 0:49 und 0:49 < α5 < 0:47. − − Contents 1. Introduction 1 2. Theoretical Foundations 5 2.1. Introduction . .5 2.2. The Standard Model . .5 2.2.1. Local Gauge Theory . .7 2.2.2. Quantum Chromodynamics . .9 2.2.3. Electroweak Theory . 10 2.2.4. Electroweak Symmetry Breaking . 12 2.2.5. The Lagrangian of the Standard Model . 14 2.3. Electroweak gauge boson scattering . 14 2.3.1. Definition . 14 2.3.2. Motivation . 15 2.3.3. VBS Topology . 16 2.3.4. Choice Of Observation Channel . 18 2.4. Effective Field Theories . 23 2.4.1. Introduction . 23 2.4.2. Effective Theory of the Muon Decay . 24 2.4.3. Anomalous Quartic Gauge Couplings . 24 2.4.4. Electroweak Chiral Lagrangian . 24 2.4.5. Linear Symmetry Breaking Approach . 25 2.4.6. K-Matrix Unitarisation . 26 3. Experiment 29 3.1. CERN . 29 3.2. Large Hadron Collider . 29 3.3. The ATLAS Detector . 31 3.3.1. ATLAS coordinate system . 34 3.3.2. Inner Detector . 34 3.3.3. Electromagnetic Calorimeter . 36 3.3.4. Hadronic Calorimeter . 37 3.3.5. Muon Spectrometer . 38 3.3.6. Trigger System . 40 3.3.7. Luminosity Monitoring . 41 3.4. Object Reconstruction . 42 3.4.1. Muons . 42 3.4.2. Electrons . 44 3.4.3. Jets . 45 3.4.4. Missing Transverse Momentum . 47 4. Datasets 49 4.1. Introduction . 49 4.2. Real Data . 49 4.3. Simulated Data . 50 4.3.1. Introduction . 50 4.3.2. Event Generation . 51 4.3.3. Event Record . 55 4.3.4. Detector Simulation . 55 4.3.5. Data Format for Analysis . 56 4.3.6. Description of Used Generators . 56 4.4. Simulated Processes . 57 4.4.1. W ±Zjj-EW . 58 4.4.2. W ±Zjj-QCD . 59 4.4.3. Background processes . 60 4.4.4. Scaling Factors . 62 5. Object and Event Selection 63 5.1. Object Selection on Detector Level . 63 5.1.1. Electron Definition . 64 5.1.2. Muon Definition . 66 5.1.3. Jet Definition . 68 5.1.4. Missing Transverse Momentum . 69 5.2. Event Selection . 69 5.2.1. Detector Level Event Selection for the Inclusive Phase Space . 69 5.2.2. Event Selection for the VBS Phase Space . 72 5.2.3. Event Selection for the aQGC Phase Space . 72 5.3. Object Selection on Particle Level . 73 5.3.1. Lepton Definition . 73 5.3.2. Jet Definition . 74 5.3.3. Neutrino Definition . 74 5.4. Event Selection on Particle Level . 75 5.4.1. Event Selection for the Inclusive Phase Space . 75 5.4.2. Event Selection for the VBS Phase Space . 76 5.4.3.
Load more

Recommended publications
  • Higgs Bosons and Supersymmetry
    Higgs bosons and Supersymmetry 1. The Higgs mechanism in the Standard Model | The story so far | The SM Higgs boson at the LHC | Problems with the SM Higgs boson 2. Supersymmetry | Surpassing Poincar´e | Supersymmetry motivations | The MSSM 3. Conclusions & Summary D.J. Miller, Edinburgh, July 2, 2004 page 1 of 25 1. Electroweak Symmetry Breaking in the Standard Model 1. Electroweak Symmetry Breaking in the Standard Model Observation: Weak nuclear force mediated by W and Z bosons • M = 80:423 0:039GeV M = 91:1876 0:0021GeV W Z W couples only to left{handed fermions • Fermions have non-zero masses • Theory: We would like to describe electroweak physics by an SU(2) U(1) gauge theory. L ⊗ Y Left{handed fermions are SU(2) doublets Chiral theory ) right{handed fermions are SU(2) singlets f There are two problems with this, both concerning mass: gauge symmetry massless gauge bosons • SU(2) forbids m)( ¯ + ¯ ) terms massless fermions • L L R R L ) D.J. Miller, Edinburgh, July 2, 2004 page 2 of 25 1. Electroweak Symmetry Breaking in the Standard Model Higgs Mechanism Introduce new SU(2) doublet scalar field (φ) with potential V (φ) = λ φ 4 µ2 φ 2 j j − j j Minimum of the potential is not at zero 1 0 µ2 φ = with v = h i p2 v r λ Electroweak symmetry is broken Interactions with scalar field provide: Gauge boson masses • 1 1 2 2 MW = gv MZ = g + g0 v 2 2q Fermion masses • Y ¯ φ m = Y v=p2 f R L −! f f 4 degrees of freedom., 3 become longitudinal components of W and Z, one left over the Higgs boson D.J.
    [Show full text]
  • Quantum Mechanics Quantum Chromodynamics (QCD)
    Quantum Mechanics_quantum chromodynamics (QCD) In theoretical physics, quantum chromodynamics (QCD) is a theory ofstrong interactions, a fundamental forcedescribing the interactions between quarksand gluons which make up hadrons such as the proton, neutron and pion. QCD is a type of Quantum field theory called a non- abelian gauge theory with symmetry group SU(3). The QCD analog of electric charge is a property called 'color'. Gluons are the force carrier of the theory, like photons are for the electromagnetic force in quantum electrodynamics. The theory is an important part of the Standard Model of Particle physics. A huge body of experimental evidence for QCD has been gathered over the years. QCD enjoys two peculiar properties: Confinement, which means that the force between quarks does not diminish as they are separated. Because of this, when you do split the quark the energy is enough to create another quark thus creating another quark pair; they are forever bound into hadrons such as theproton and the neutron or the pion and kaon. Although analytically unproven, confinement is widely believed to be true because it explains the consistent failure of free quark searches, and it is easy to demonstrate in lattice QCD. Asymptotic freedom, which means that in very high-energy reactions, quarks and gluons interact very weakly creating a quark–gluon plasma. This prediction of QCD was first discovered in the early 1970s by David Politzer and by Frank Wilczek and David Gross. For this work they were awarded the 2004 Nobel Prize in Physics. There is no known phase-transition line separating these two properties; confinement is dominant in low-energy scales but, as energy increases, asymptotic freedom becomes dominant.
    [Show full text]
  • PDF) of Partons I and J
    TASI 2004 Lecture Notes on Higgs Boson Physics∗ Laura Reina1 1Physics Department, Florida State University, 315 Keen Building, Tallahassee, FL 32306-4350, USA E-mail: [email protected] Abstract In these lectures I briefly review the Higgs mechanism of spontaneous symmetry breaking and focus on the most relevant aspects of the phenomenology of the Standard Model and of the Minimal Supersymmetric Standard Model Higgs bosons at both hadron (Tevatron, Large Hadron Collider) and lepton (International Linear Collider) colliders. Some emphasis is put on the perturbative calculation of both Higgs boson branching ratios and production cross sections, including the most important radiative corrections. arXiv:hep-ph/0512377v1 30 Dec 2005 ∗ These lectures are dedicated to Filippo, who listened to them before he was born and behaved really well while I was writing these proceedings. 1 Contents I. Introduction 3 II. Theoretical framework: the Higgs mechanism and its consequences. 4 A. A brief introduction to the Higgs mechanism 5 B. The Higgs sector of the Standard Model 10 C. Theoretical constraints on the Standard Model Higgs bosonmass 13 1. Unitarity 14 2. Triviality and vacuum stability 16 3. Indirect bounds from electroweak precision measurements 17 4. Fine-tuning 22 D. The Higgs sector of the Minimal Supersymmetric Standard Model 24 1. About Two Higgs Doublet Models 25 2. The MSSM Higgs sector: introduction 27 3. MSSM Higgs boson couplings to electroweak gauge bosons 30 4. MSSM Higgs boson couplings to fermions 33 III. Phenomenology of the Higgs Boson 34 A. Standard Model Higgs boson decay branching ratios 34 1. General properties of radiative corrections to Higgs decays 37 + 2.
    [Show full text]
  • Introduction to Supersymmetry
    Introduction to Supersymmetry Pre-SUSY Summer School Corpus Christi, Texas May 15-18, 2019 Stephen P. Martin Northern Illinois University [email protected] 1 Topics: Why: Motivation for supersymmetry (SUSY) • What: SUSY Lagrangians, SUSY breaking and the Minimal • Supersymmetric Standard Model, superpartner decays Who: Sorry, not covered. • For some more details and a slightly better attempt at proper referencing: A supersymmetry primer, hep-ph/9709356, version 7, January 2016 • TASI 2011 lectures notes: two-component fermion notation and • supersymmetry, arXiv:1205.4076. If you find corrections, please do let me know! 2 Lecture 1: Motivation and Introduction to Supersymmetry Motivation: The Hierarchy Problem • Supermultiplets • Particle content of the Minimal Supersymmetric Standard Model • (MSSM) Need for “soft” breaking of supersymmetry • The Wess-Zumino Model • 3 People have cited many reasons why extensions of the Standard Model might involve supersymmetry (SUSY). Some of them are: A possible cold dark matter particle • A light Higgs boson, M = 125 GeV • h Unification of gauge couplings • Mathematical elegance, beauty • ⋆ “What does that even mean? No such thing!” – Some modern pundits ⋆ “We beg to differ.” – Einstein, Dirac, . However, for me, the single compelling reason is: The Hierarchy Problem • 4 An analogy: Coulomb self-energy correction to the electron’s mass A point-like electron would have an infinite classical electrostatic energy. Instead, suppose the electron is a solid sphere of uniform charge density and radius R. An undergraduate problem gives: 3e2 ∆ECoulomb = 20πǫ0R 2 Interpreting this as a correction ∆me = ∆ECoulomb/c to the electron mass: 15 0.86 10− meters m = m + (1 MeV/c2) × .
    [Show full text]
  • Unitarity Constraints on Higgs Portals
    SLAC-PUB-15822 Unitarity Constraints on Higgs Portals Devin G. E. Walker SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, U.S.A. Dark matter that was once in thermal equilibrium with the Standard Model is generally prohibited from obtaining all of its mass from the electroweak phase transition. This implies a new scale of physics and mediator particles to facilitate dark matter annihilation. In this work, we focus on dark matter that annihilates through a generic Higgs portal. We show how partial wave unitarity places an upper bound on the mass of the mediator (or dark) Higgs when its mass is increased to be the largest scale in the effective theory. For models where the dark matter annihilates via fermion exchange, an upper bound is generated when unitarity breaks down around 8.5 TeV. Models where the dark matter annihilates via fermion and higgs boson exchange push the bound to 45.5 TeV. We also show that if dark matter obtains all of its mass from a new symmetry breaking scale that scale is also constrained. We improve these constraints by requiring perturbativity in the Higgs sector up to each unitarity bound. In this limit, the bounds on the dark symmetry breaking vev and the dark Higgs mass are now 2.4 and 3 TeV, respectively, when the dark matter annihilates via fermion exchange. When dark matter annihilates via fermion and higgs boson exchange, the bounds are now 12 and 14.2 TeV, respectively. Given the unitarity bounds, the available parameter space for Higgs portal dark matter annihilation is outlined.
    [Show full text]
  • Modern Methods of Quantum Chromodynamics
    Modern Methods of Quantum Chromodynamics Christian Schwinn Albert-Ludwigs-Universit¨atFreiburg, Physikalisches Institut D-79104 Freiburg, Germany Winter-Semester 2014/15 Draft: March 30, 2015 http://www.tep.physik.uni-freiburg.de/lectures/QCD-WS-14 2 Contents 1 Introduction 9 Hadrons and quarks . .9 QFT and QED . .9 QCD: theory of quarks and gluons . .9 QCD and LHC physics . 10 Multi-parton scattering amplitudes . 10 NLO calculations . 11 Remarks on the lecture . 11 I Parton Model and QCD 13 2 Quarks and colour 15 2.1 Hadrons and quarks . 15 Hadrons and the strong interactions . 15 Quark Model . 15 2.2 Parton Model . 16 Deep inelastic scattering . 16 Parton distribution functions . 18 2.3 Colour degree of freedom . 19 Postulate of colour quantum number . 19 Colour-SU(3).............................. 20 Confinement . 20 Evidence of colour: e+e− ! hadrons . 21 2.4 Towards QCD . 22 3 Basics of QFT and QED 25 3.1 Quantum numbers of relativistic particles . 25 3.1.1 Poincar´egroup . 26 3.1.2 Relativistic one-particle states . 27 3.2 Quantum fields . 32 3.2.1 Scalar fields . 32 3.2.2 Spinor fields . 32 3 4 CONTENTS Dirac spinors . 33 Massless spin one-half particles . 34 Spinor products . 35 Quantization . 35 3.2.3 Massless vector bosons . 35 Polarization vectors and gauge invariance . 36 3.3 QED . 37 3.4 Feynman rules . 39 3.4.1 S-matrix and Cross section . 39 S-matrix . 39 Poincar´einvariance of the S-matrix . 40 T -matrix and scattering amplitude . 41 Unitarity of the S-matrix . 41 Cross section .
    [Show full text]
  • Symmetries in Quantum Field Theory and Quantum Gravity
    Symmetries in Quantum Field Theory and Quantum Gravity Daniel Harlowa and Hirosi Oogurib;c aCenter for Theoretical Physics Massachusetts Institute of Technology, Cambridge, MA 02139, USA bWalter Burke Institute for Theoretical Physics California Institute of Technology, Pasadena, CA 91125, USA cKavli Institute for the Physics and Mathematics of the Universe (WPI) University of Tokyo, Kashiwa, 277-8583, Japan E-mail: [email protected], [email protected] Abstract: In this paper we use the AdS/CFT correspondence to refine and then es- tablish a set of old conjectures about symmetries in quantum gravity. We first show that any global symmetry, discrete or continuous, in a bulk quantum gravity theory with a CFT dual would lead to an inconsistency in that CFT, and thus that there are no bulk global symmetries in AdS/CFT. We then argue that any \long-range" bulk gauge symmetry leads to a global symmetry in the boundary CFT, whose consistency requires the existence of bulk dynamical objects which transform in all finite-dimensional irre- ducible representations of the bulk gauge group. We mostly assume that all internal symmetry groups are compact, but we also give a general condition on CFTs, which we expect to be true quite broadly, which implies this. We extend all of these results to the case of higher-form symmetries. Finally we extend a recently proposed new motivation for the weak gravity conjecture to more general gauge groups, reproducing the \convex hull condition" of Cheung and Remmen. An essential point, which we dwell on at length, is precisely defining what we mean by gauge and global symmetries in the bulk and boundary.
    [Show full text]
  • The Effective Action for Gauge Bosons Arxiv:1810.06994V1 [Hep-Ph]
    October 2018 The effective action for gauge bosons Jeremie Quevillon1 , Christopher Smith2 and Selim Touati3 Laboratoire de Physique Subatomique et de Cosmologie, Universit´eGrenoble-Alpes, CNRS/IN2P3, Grenoble INP, 38000 Grenoble, France. Abstract By treating the vacuum as a medium, H. Euler and W. Heisenberg estimated the non-linear interactions between photons well before the advent of Quantum Electrodynamics. In a modern language, their result is often presented as the archetype of an Effective Field Theory (EFT). In this work, we develop a similar EFT for the gauge bosons of some generic gauge symmetry, valid for example for SU(2), SU(3), various grand unified groups, or mixed U(1) ⊗ SU(N) and SU(M) ⊗ SU(N) gauge groups. Using the diagrammatic approach, we perform a detailed matching procedure which remains manifestly gauge invariant at all steps, but does not rely on the equations of motion hence is valid off-shell. We provide explicit analytic expressions for the Wilson coefficients of the dimension four, six, and eight operators as induced by massive scalar, fermion, and vector fields in generic representations of the gauge group. These expressions rely on a careful analysis of the quartic Casimir invariants, for which we provide a review using conventions adapted to Feynman diagram calculations. Finally, our computations show that at one loop, some operators are redundant whatever the representation or spin of the particle being arXiv:1810.06994v1 [hep-ph] 16 Oct 2018 integrated out, reducing the apparent complexity of the operator basis that can be constructed solely based on symmetry arguments. 1 [email protected] 2 [email protected] 3 [email protected] Contents 1 Introduction 1 2 Photon effective interactions3 3 Gluon effective interactions6 4 SU(N) effective interactions 11 4.1 Reduction to SU(3) and SU(2) .
    [Show full text]
  • Higgs Boson(S) and Supersymmetry
    Higgs Boson(s) and Supersymmetry Quantum Electrodynamics • Mass for the photon forbidden (gauge invariance). • Mass for the electron allowed. Anomalous magnetic moment of the electron: D. Hanneke et.al. (2011) M. Hayakawa Weak Interactions • Still cannot give mass to the gauge boson B, thus, neither to the Z gauge boson! • Cannot write a mass term for the electron neither, due to the splitting between the left and right component. • Need Brout-Englert-Higgs mechanism. Higgs Mechanism It does not explain why the masses are so different. Simultaneous work: Englert y Brout. Higgs Potential The field must have spin 0, and a non-zero vacuum expectation value. Buttazzo et.al. (2013) But, lifetime of meta-stable vacuum is very large! Higgs Boson It is well established the existence of a scalar with Standard Model couplings and a mass ≈ 125 GeV. Evidence points to spin cero and couplings to fermions as well as gauge bosons. Supersymmetry Neutralino Gravitino SM MSSM Rp Conserving Rp Violating Dark Matter De Boer et.al. (2004) Supersymmetric Searches Squarks, sleptons, and gluinos seem to be heavier than ~1 TeV. Mysteries Triple Higgs coupling: • ããbb-bar channel. • hhh in SM is too low to be seen by the LHC. • Hhh in 2HDM may be seen (excess?). • arXiv:1406.5053 CMS and LHCb observe the rare decay BS to mu mu (arXiv:1411.4413). ~2.5 σ (CMS PAS HIG-14-005) B(B→μμ) / B(BS→μμ) too large! Heavy squarks and gluinos and low tan(β) (arXiv:1501.02044)? Heavy Supersymmetry Split Supersymmetry hep-th/0405159, hep-ph/0406088 High Scale Supersymmetry • Gauge coupling unification • All supersymetry partners are heavy.
    [Show full text]
  • Arxiv:2012.00774V2 [Hep-Ph] 9 Mar 2021 Converges to One to 40% Precision While at the 27 Tev HE-LHC the Precision Will Be 6%
    Electroweak Restoration at the LHC and Beyond: The V h Channel Li Huang,1, ∗ Samuel D. Lane,1, 2, y Ian M. Lewis,1, z and Zhen Liu3, 4, x 1Department of Physics and Astronomy, University of Kansas, Lawrence, KS 66045 USA 2Department of Physics, Brookhaven National Laboratory, Upton, NY 11973 U.S.A. 3Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, MD, 20742 USA 4School of Physics and Astronomy, University of Minnesota, Minneapolis, MN, 55455 USA Abstract The LHC is exploring electroweak (EW) physics at the scale EW symmetry is broken. As the LHC and new high energy colliders push our understanding of the Standard Model to ever-higher energies, it will be possible to probe not only the breaking of but also the restoration of EW sym- metry. We propose to observe EW restoration in double EW boson production via the convergence of the Goldstone boson equivalence theorem. This convergence is most easily measured in the vec- tor boson plus Higgs production, V h, which is dominated by the longitudinal polarizations. We define EW restoration by carefully taking the limit of zero Higgs vacuum expectation value (vev). h EW restoration is then measured through the ratio of the pT distributions between V h production in the Standard Model and Goldstone boson plus Higgs production in the zero vev theory, where h pT is the Higgs transverse momentum. As EW symmetry is restored, this ratio converges to one at high energy. We present a method to extract this ratio from collider data. With a full signal and background analysis, we demonstrate that the 14 TeV HL-LHC can confirm that this ratio arXiv:2012.00774v2 [hep-ph] 9 Mar 2021 converges to one to 40% precision while at the 27 TeV HE-LHC the precision will be 6%.
    [Show full text]
  • Beyond the Standard Model
    Beyond the Standard Model B.A. Dobrescu Theoretical Physics Department, Fermilab, Batavia, IL, USA Abstract Despite the success of the standard model in describing a wide range of data, there are reasons to believe that additional phenomena exist, which would point to new theoretical structures. Some of these phenomena may be discovered in particle physics experiments in the near future. These lectures overview hypo- thetical particles, solutions to the hierarchy problem, theories of dark matter, and new strong interactions. 1 What is the standard model? The Standard Model of particle physics is an SU(3) SU(2) U(1) gauge theory with quarks c × W × Y transforming in the qi (3, 2, 1/6), ui (3, 1, 2/3) and di (3, 1, 1/3) representations of the L ∼ R ∼ R ∼ − gauge group, and leptons transforming as Li (1, 2, 1/2) and ei (1, 1, 1). The index i = 1, 2, 3 L ∼ − R ∼ − labels the generations of fermions. The Standard Model also includes a single Higgs doublet [1] trans- forming as H (1, 2, 1/2). The vacuum expectation value (VEV) of the Higgs doublet, H = (v , 0), ∼ h i H breaks the electroweak SU(2) U(1) symmetry down to the gauge symmetry of electromagnetism, W × Y U(1)em. With these fields of spin 1 (gauge bosons), 1/2 (quarks and leptons) and 0 (Higgs doublet), the Standard Model is remarkably successful at describing a tremendous amount of data [2] in terms of a single mass parameter (the electroweak scale v 174 GeV) and 18 dimensionless parameters [3].
    [Show full text]
  • TASI 2013 Lectures on Higgs Physics Within and Beyond the Standard Model∗
    TASI 2013 lectures on Higgs physics within and beyond the Standard Model∗ Heather E. Logany Ottawa-Carleton Institute for Physics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario K1S 5B6 Canada June 2014 Abstract These lectures start with a detailed pedagogical introduction to electroweak symmetry breaking in the Standard Model, including gauge boson and fermion mass generation and the resulting predictions for Higgs boson interactions. I then survey Higgs boson decays and production mechanisms at hadron and e+e− colliders. I finish with two case studies of Higgs physics beyond the Standard Model: two- Higgs-doublet models, which I use to illustrate the concept of minimal flavor violation, and models with isospin-triplet scalar(s), which I use to illustrate the concept of custodial symmetry. arXiv:1406.1786v2 [hep-ph] 28 Nov 2017 ∗Comments are welcome and will inform future versions of these lecture notes. I hereby release all the figures in these lectures into the public domain. Share and enjoy! [email protected] 1 Contents 1 Introduction 3 2 The Higgs mechanism in the Standard Model 3 2.1 Preliminaries: gauge sector . .3 2.2 Preliminaries: fermion sector . .4 2.3 The SM Higgs mechanism . .5 2.4 Gauge boson masses and couplings to the Higgs boson . .8 2.5 Fermion masses, the CKM matrix, and couplings to the Higgs boson . 12 2.5.1 Lepton masses . 12 2.5.2 Quark masses and mixing . 13 2.5.3 An aside on neutrino masses . 16 2.5.4 CKM matrix parameter counting . 17 2.6 Higgs self-couplings .
    [Show full text]