Lecture notes Particle Physics pdf

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Lecture notes to the 1-st year master course Particle Physics 1 Nikhef - Autumn 2011 Marcel Merk email: marcel.merknikhef.nlContents 0 Introduction 1 1 Particles and Forces 11 1.1 The Yukawa Potential and the Pi meson . . . . . . . . . . . . . . . . . . 11 1.2 Strange Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.3 The Eightfold Way . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.4 The Quark Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.4.1 Color . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.5 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2 Wave Equations and Anti Particles 25 2.1 Non Relativistic Wave Equations . . . . . . . . . . . . . . . . . . . . . . 25 2.2 Relativistic Wave Equations . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.3 Interpretation of negative energy solutions . . . . . . . . . . . . . . . . . 28 2.3.1 Dirac’s interpretation . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.3.2 Pauli-Weisskopf Interpretation . . . . . . . . . . . . . . . . . . . . 29 2.3.3 Feynman-Stu¨ckelberg Interpretation . . . . . . . . . . . . . . . . . 29 2.4 The Dirac Deltafunction . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3 The Electromagnetic Field 33 3.1 Maxwell Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2 Gauge Invariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.3 The photon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.4 The Bohm Aharanov Effect . . . . . . . . . . . . . . . . . . . . . . . . . 38 4 Perturbation Theory and Fermi’s Golden Rule 41 4.1 Non Relativistic Perturbation Theory . . . . . . . . . . . . . . . . . . . . 41 4.1.1 The Transition Probability . . . . . . . . . . . . . . . . . . . . . . 42 4.1.2 Normalisation of the Wave Function . . . . . . . . . . . . . . . . 46 4.1.3 The Flux Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.1.4 The Phase Space Factor . . . . . . . . . . . . . . . . . . . . . . . 47 4.1.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.2 Extension to Relativistic Scattering . . . . . . . . . . . . . . . . . . . . . 50 iii Contents 5 Electromagnetic Scattering of Spinless Particles 53 5.1 Electrodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 5.2 Scattering in an External Field . . . . . . . . . . . . . . . . . . . . . . . 56 5.3 Spinless π−K Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.4 Particles and Anti-Particles . . . . . . . . . . . . . . . . . . . . . . . . . 62 6 The Dirac Equation 65 6.1 Dirac Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 6.2 Covariant form of the Dirac Equation . . . . . . . . . . . . . . . . . . . . 67 6.3 The Dirac Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 6.4 Current Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 6.4.1 Dirac Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . 69 7 Solutions of the Dirac Equation 71 7.1 Solutions for plane waves with p= 0 . . . . . . . . . . . . . . . . . . . . 71 7.2 Solutions for moving particles p6= 0 . . . . . . . . . . . . . . . . . . . . . 73 7.3 Particles and Anti-particles . . . . . . . . . . . . . . . . . . . . . . . . . 74 7.3.1 The Charge Conjugation Operation . . . . . . . . . . . . . . . . . 75 7.4 Normalisation of the Wave Function . . . . . . . . . . . . . . . . . . . . . 75 7.5 The Completeness Relation . . . . . . . . . . . . . . . . . . . . . . . . . 76 7.6 Helicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 8 Spin 1/2 Electrodynamics 81 8.1 Feynman Rules for Fermion Scattering . . . . . . . . . . . . . . . . . . . 81 8.2 Electron - Muon Scattering . . . . . . . . . . . . . . . . . . . . . . . . . 84 + − + − 8.3 Crossing: the process e e →μ μ . . . . . . . . . . . . . . . . . . . . . 90 9 The Weak Interaction 93 9.1 The 4-point interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 9.1.1 Lorentz covariance and Parity . . . . . . . . . . . . . . . . . . . . 96 9.2 The V −A interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 9.3 The Propagator of the weak interaction . . . . . . . . . . . . . . . . . . . 99 9.4 Muon Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 9.5 Quark mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 9.5.1 Cabibbo - GIM mechanism. . . . . . . . . . . . . . . . . . . . . . 103 9.5.2 The Cabibbo - Kobayashi - Maskawa (CKM) matrix . . . . . . . 105 10 Local Gauge Invariance 109 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 10.2 Lagrangian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 10.3 Where does the name “gauge theory” come from? . . . . . . . . . . . . . 112 10.4 Phase Invariance in Quantum Mechanics . . . . . . . . . . . . . . . . . . 112 10.5 Phase invariance for a Dirac Particle . . . . . . . . . . . . . . . . . . . . 113 10.6 Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 10.7 Yang Mills Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116Lecture 0 Introduction The particle physics master course will be given in the autumn semester of 2011 and contains two parts: Particle Physics 1 (PP1) and Particle Physics 2 (PP2). The PP1 course consists of 12 lectures (Monday and Wednesday morning) and mainly follows the material as discussed in the books of Halzen and Martin and Griffiths. These notes are my personal notes made in preparation of the lectures. They can be used by the students but should not be distributed. The original material is found in the books used to prepare the lectures (see below). The contents of particle physics 1 is the following: • Lecture 1: Concepts and History • Lecture 2 - 5: Electrodynamics of spinless particles • Lecture 6 - 8: Electrodynamics of spin 1/2 particles • Lecture 9: The Weak interaction • Lecture 10 - 12: Electroweak scattering: The Standard Model Each lecture of 2×45 minutes is followed by a 1 hour problem solving session. The particle physics 2 course contains the following topics: • The Higgs Mechanism • Quantum Chromodynamics In addition the master offers in the next semester topical courses (not obligatory) on the particle physics subjects: CP Violation, Neutrino Physics and Physics Beyond the Standard Model Examination Theexaminationconsistsoftwoparts: Homework(weight=1/3)andanExam(weight=2/3). 12 Lecture 0. Introduction Literature The following literature is used in the preparation of this course (the comments reflect my personal opinion): Halzen & Martin: “Quarks & Leptons: an Introductory Course in Modern Particle Physics ”: Although it is somewhat out of date (1984), I consider it to be the best book in the field for a master course. It is somewhat of a theoretical nature. It builds on the earlier work of Aitchison (see below). Most of the course follows this book. Griffiths: “Introduction to Elementary Particle Physics”, second, revised ed. The text is somewhat easier to read than H & M and is more up-to-date (2008) (e.g. neutrino oscillations) but on the other hand has a somewhat less robust treatment in deriving the equations. Perkins: “Introduction to High Energy Physics”, (1987) 3-rd ed., (2000) 4-th ed. The first three editions were a standard text for all experimental particle physics. It is dated, but gives an excellent description of, in particular, the experiments. The fourth edition is updated with more modern results, while some older material is omitted. Aitchison: “Relativistic Quantum Mechanics” (1972) A classical, very good, but old book, often referred to by H & M. Aitchison & Hey: “Gauge Theories in Particle Physics” (1982) 2nd edition: An updated version of the book of Aitchison; a bit more theoretical. (2003) 3rd edition (2 volumes): major rewrite in two volumes; very good but even more theoretical. It includes an introduction to quantum field theory. Burcham & Jobes: “Nuclear & Particle Physics” (1995) An extensive text on nuclear physics and particle physics. It contains more (modern) material than H & M. Formula’s are explained rather than derived and more text is spent to explain concepts. Das & Ferbel: “Introduction to Nuclear and Particle Physics” (2006) A book that is half on experimental techniques and half on theory. It is more suitable for a bachelor level course and does not contain a treatment of scattering theory for particles with spin. Martin and Shaw: “Particle Physics ”, 2-nd ed. (1997) A textbook that is somewhere inbetween Perkins and Das & Ferbel. In my opinion it has the level inbetween bachelor and master. Particle Data Group: “Review of Particle Physics” This book appears every two years in two versions: the book and the booklet. Both of them list all aspects of the known particles and forces. The book also contains concise, but excellent short reviews of theories, experiments, accellerators, analysis techniques, statistics etc. There is also a version on the web: http://pdg.lbl.gov4 Lecture 0. Introduction About Nikhef Nikhef is the Dutch institute for subatomic physics. Although the name Nikhef is kept, the acronym ”Nationaal Instituut voor Kern en Hoge Energie Fysica” is no longer used. The name Nikhef is used to indicate simultaneously two overlapping organisations: • Nikhef is a national research lab funded by the foundation FOM; the dutch foun- dation for fundamental research of matter. • NikhefisalsoacollaborationbetweentheNikhefinstituteandtheparticlephysics departements of the UvA (A’dam), the VU (A’dam), the UU (Utrecht) and the RU (Nijmegen) contribute. In this collaboration all dutch activities in particle physics are coordinated. In addition there is a collaboration between Nikhef and the Rijks Universiteit Gronin- gen (the former FOM nuclear physics institute KVI) and there are contacts with the Universities of Twente, Leiden and Eindhoven. For more information go to the Nikhef web page: http://www.nikhef.nl The research at Nikhef includes both accelerator based particle physics and astro- particle physics. A strategic plan, describing the research programmes at Nikhef can be found on the web, from: www.nikhef.nl/fileadmin/Doc/Docs & pdf/StrategicPlan.pdf . The accelerator physics research of Nikhef is currently focusing on the LHC exper- iments: Alice (“Quark gluon plasma”), Atlas (“Higgs”) and LHCb (“CP violation”). Each of these experiments search answers for open issues in particle physics (the state of matter at high temperature, the origin of mass, the mechanism behind missing an- timatter) and hope to discover new phenomena (eg supersymmetry, extra dimensions). The LHC started in 2009 and is currently producing data at increasing luminosity. The first results came out at the ICHEP 2010 conference in Paris, while the latest news of this summer on the search for the Higgs boson and ”New Physics” have been discussed in the EPS conference in Grenoble and the lepton-photon conference in Mumbai. So far no convincing evidence for the Higgs particle or for New Physics have been observed. In preparation of these LHC experiments Nikhef is/was also active at other labs: STAR (Brookhaven), D0 (Fermilab) and Babar (SLAC). Previous experiments that ended their activities are: L3 and Delphi at LEP, and Zeus, Hermes and HERA-B at Desy. A more recent development is the research field of astroparticle physics. It includes Antares & KM3NeT (“cosmic neutrino sources”), Pierre Auger (“high energy cosmic rays”), Virgo & ET (“gravitational waves”) and Xenon (”dark matter”). Nikhef houses a theory departement with research on quantum field theory and gravity, string theory, QCD (perturbative and lattice) and B-physics. Driven by the massive computing challenge of the LHC, Nikhef also has a scientific computing departement: the Physics Data Processing group. They are active in the5 development of a worldwide computing network to analyze the huge datastreams from the (LHC-) experiments (“The Grid”). Nikhef program leaders/contact persons: Name office phone email Nikhef director Frank Linde H232 5001 z66nikhef.nl Theory departement: Eric Laenen H323 5127 t45nikhef.nl Atlas departement: Stan Bentvelsen H241 5150 stanbnikhef.nl B-physics departement: Marcel Merk N243 5107 marcel.merknikhef.nl Alice departement: Thomas Peitzmann N325 5050 t.peitzmannuu.nl Antares experiment: Maarten de Jong H354 2121 mjgnikhef.nl Pierre Auger experiment: Charles Timmermans - - c.timmermanshef.ru.nl Virgo and ET experiment: Jo van den Brand N247 2015 jonikhef.nl Xenon experiment: Patrick Decowski H349 2145 p.decowskinikhef.nl Detector R&D Departement: Frank Linde H232 5001 z66nikhef.nl Scientific Computing: Jeff Templon H158 2092 templonnikhef.nl6 Lecture 0. Introduction History of Particle Physics The book of Griffiths starts with a nice historical overview of particle physics in the previous century. Here’s a summary: Atomic Models 1897 Thomson: Discovery of Electron. The atom contains electrons as “plums in a pudding”. 1911 Rutherford: Theatommainlyconsistsofemptyspacewithahardandheavy, positively charged nucleus. 1913 Bohr: First quantum model of the atom in which electrons circled in stable orbits, quatized as: L =h ¯·n 1932 Chadwick: Discovery of the neutron. The atomic nucleus contains both protonsandneutrons. Theroleoftheneutronsisassociatedwiththebinding force between the positively charged protons. The Photon 1900 Planck: Description blackbody spectrum with quantized radiation. No inter- pretation. 1905 Einstein: Realization that electromagnetic radiation itself is fundamentally quantized,explainingthephotoelectriceffect. Histheoryreceivedscepticism. 1916 Millikan: Measurement of the photo electric effect agrees with Einstein’s theory. 1923 Compton: Scatteringofphotonsonparticlesconfirmedcorpuscularcharacter of light: the Compton wavelength. Mesons 1934 Yukawa: Nuclear binding potential described with the exchange of a quan- tized field: the pi-meson or pion. 1937 Anderson & Neddermeyer: Search for the pion in cosmic rays but he finds a weakly interacting particle: the muon. (Rabi: “Who ordered that?”) 1947 Powell: Finds both the pion and the muon in an analysis of cosmic radiation with photo emulsions. Anti matter 1927 DiracinterpretsnegativeenergysolutionsofKleinGordonequationasenergy levels of holes in an infinite electron sea: “positron”. 1931 Anderson observes the positron.7 1940-1950 Feynman and Stu¨ckelberg interpret negative energy solutions as the positive energy of the anti-particle: QED. Neutrino’s 1930 Pauli and Fermi propose neutrino’s to be produced in β-decay (m = 0). ν 1958 Cowan and Reines observe inverse beta decay. 1962 LedermanandSchwarzshowedthatν = 6 ν . Conservationofleptonnumber. e μ Strangeness 0 0 1947 Rochester and Butler observe V events: K meson. 0 1950 Anderson observes V events: Λ baryon. The Eightfold Way − 1961 Gell-Mann makes particle multiplets and predicts the Ω . − 1964 Ω particle found. The Quark Model 1964 Gell-Mann and Zweig postulate the existance of quarks 1968 Discovery of quarks in electron-proton collisions (SLAC). 1974 Discovery charm quark (J/ψ) in SLAC & Brookhaven. 1977 Discovery bottom quarks (Υ) in Fermilab. 1979 Discovery of the gluon in 3-jet events (Desy). 1995 Discovery of top quark (Fermilab). Broken Symmetry 1956 Lee and Yang postulate parity violation in weak interaction. 1957 Wu et. al. observe parity violation in beta decay. 1964 Christenson,Cronin,Fitch&TurlayobserveCPviolationinneutralKmeson decays. The Standard Model 1978 Glashow, Weinberg, Salam formulate Standard Model for electroweak inter- actions 1983 W-boson has been found at CERN. 1984 Z-boson has been found at CERN. 1989-2000 LEP collider has verified Standard Model to high precision.8 Lecture 0. Introduction9 Natural Units We will often make use of natural units. This means that we work in a system where the action is expressed in units of Planck’s constant: −34 h ¯≈ 1.055×10 Js and velocity is expressed in units of the light speed in vacuum: 8 c = 2.998×10 m/s. In other words we often useh ¯ =c = 1. This implies, however, that the results of calculations must be translated back to measureable quantities in the end. Conversion factors are the following: quantity conversion factor natural unit normal unit 26 2 mass 1 kg = 5.61×10 GeV GeV GeV/c −1 −1 15 length 1 m = 5.07×10 GeV GeV h ¯c/GeV −1 −1 24 time 1 s = 1.52×10 GeV GeV h ¯/GeV √ √ unit charge e = 4πα 1 h ¯c −24 2 Crosssectionsareexpressedin barn,whichisequalto10 cm . Energyisexpressed 9 in GeV, or 10 eV, where 1 eV is the kinetic energy an electron obtains when it is accelerated over a voltage of 1V. Exercise -1: Derive the conversion factors for mass, length and time in the table above. Exercise 0: The Z-boson particle is a carrier of the weak force. It has a mass of 91.1 GeV. It can be produced experimentally by annihilation of an electron and a positron. The mass of an electron, as well as that of a positron, is 0.511 MeV. (a) Can you guess what the Feynman interaction diagram for this process is? Try to draw it. (b) Assume that an electron and a positron are accelerated in opposite directions and collide head-on to produce a Z-boson in the lab frame. Calculate the beam energy required for the electron and the positron in order to produce a Z-boson. (c) Assume that a beam of positron particles is shot on a target containing electrons. Calculate the beam energy required for the positron beam in order to produce Z-bosons. (d) This experiment was carried out in the 1990’s. Which method do you think was used? Why?10 Lecture 0. IntroductionLecture 1 Particles and Forces Introduction After Chadwick had discovered the neutron in 1932, the elementary constituents of matter were the proton and the neutron inside the atomic nucleus, and the electron circling around it. With these constituents the atomic elements could be described as well as the chemistry with them. The answer to the question: “What is the world made of?” was indeed rather simple. The force responsible for interactions was the electromagnetic force, which was carried by the photon. There were already some signs that there was more to it: • Dirac had postulated in 1927 the existence of anti-matter as a consequence of his relativistic version of the Schrodinger equation in quantum mechanics. (We will come back to the Dirac theory later on.) The anti-matter partner of the electron, the positron, was actually discovered in 1932 by Anderson (see Fig. 1.1). • Pauli had postulated the existence of an invisible particle that was produced in nuclear beta decay: the neutrino. In a nuclear beta decay process: − N →N +e A B theenergyoftheemittedelectronisdeterminedbythemassdifferenceofthenuclei N and N . It was observed that the kinetic energy of the electrons, however, A B showed a broad mass spectrum (see Fig. 1.2), of which the maximum was equal to the expected kinetic energy. It was as if an additional invisible particle of low mass is produced in the same process: the (anti-) neutrino. 1.1 The Yukawa Potential and the Pi meson The year 1935 is a turning point in particle physics. Yukawa studied the strong inter- action in atomic nuclei and proposed a new particle, a π-meson as the carrier of the nuclear force. His idea was that the nuclear force was carried by a massive particle 1112 Lecture 1. Particles and Forces Figure 1.1: The discovery of the positron as reported by Anderson in 1932. Knowing the direction of the B field Anderson deduced that the trace was originating from an anti electron. Question: how? 1.0 0.8 0.00012 0.00008 0.6 Mass = 0 0.00004 0.4 Mass = 30 eV 0 18.60 18.45 18.50 18.55 0.2 0 2 6 10 14 18 Energy (keV) Figure 1. The Beta Decay Spectrum for Molecular Tritium The plot on the left shows the probability that the emerging electron has a particular energy. If the electron were neutral, the spectrum would peak at higher energy and would be centered roughly on that peak. But because the electron is negatively charged, the positively charged nucleus exerts a drag on it, pulling the peak to a lower energy and generating a lopsided spectrum. A close-up of the endpoint (plot on the right) shows the subtle difference between the expected spectra for a massless neutrino and for a neutrino with a mass of 30 electron volts. Figure 1.2: The beta spectrum as observed in tritium decay to helium. The endpoint of the spectrum can be used to set a limit of the neutrino mass. Question: how? Relative Decay Probability1.1. The Yukawa Potential and the Pi meson 13 (in contrast to the massless photon) such that the range of this force is limited to the nuclei. The qualitative idea is that a virtual particle, the force carrier, can be created for a 2 time Δt h ¯/2mc . Electromagnetism is transmitted by the massless photon and has an infinite range, the strong force is transmitted by a massive meson and has a limited range, depending on the mass of the meson. The Yukawa potential (also called the OPEP: One Pion Exchange Potential) is of the form: −r/R e 2 U(r) =−g r where R is called the range of the force. For comparison, the electrostatic potential of a point charge e as seen by a test charge e is given by: 1 2 V(r) =−e r The electrostatic potential is obtained in the limit that the range of the force is infinite: R =∞. The constant g is referred to as the coupling constant of the interaction. Exercise 1: (a) The wave equation for an electromagnetic potential V is given by: 2 ∂ μ 2 2V = 0 ; 2≡∂ ∂ ≡ −∇ μ 2 ∂t which in the static case can be written in the form of Laplace equation: 2 ∇ V = 0 Assuming spherical symmetry, show that this equation leads to the Coulomb po- tential V(r) Hint: remember spherical coordinates. (b) The wave equation for a massive field is the Klein Gordon equation: 2 2U +m U = 0 which, again in the static case can be written in the form: 2 2 ∇ U−m U = 0 Show, again assuming spherical symmetry, that Yukawa’s potential is a solution of the equation for a massive force carrier. What is the relation between the mass m of the force carrier and the range R of the force? (c) Estimate the mass of theπ-meson assuming that the range of the nucleon force is −15 1.5×10 m = 1.5fm.14 Lecture 1. Particles and Forces Yukawacalledthisparticlea mesonsinceitisexpectedtohaveanintermediatemass between the electron and the nucleon. In 1937 Anderson and Neddermeyer, as well as Street and Stevenson, found that cosmic rays indeed consist of such a middle weight particle. However, in the years after, it became clear that two things were not right: (1) This particle did not interact strongly, which was very strange for a carrier of the strong force. (2) Its mass was somewhat too low. In fact this particle turned out to be the muon, the heavier brother of the electron. In1947Powell(aswellasPerkins)foundthepiontobepresentincosmicrays. They tooktheirphotographicemulsionstomountaintopstostudythecontentsofcosmicrays (see Fig. 1.3). (In a cosmic ray event a cosmic proton scatters with high energy on an atmospheric nucleon and produces many secondary particles.) Pions produced in the atmosphere decay long before they reach sea level, which is why they were not observed before. 1.2 Strange Particles After the pion had been identified as Yukawa’s strong force carrier and the anti-electron was observed to confirm Dirac’s theory, things seemed reasonably under control. The muonwasabitofamystery. ItleadtoafamousquoteofIsidoreRabiattheconference: “Who ordered that?” But in December 1947 things went all wrong after Rochester and Butler published 0 so-called V events in cloud chamber photographs. What happened was that charged cosmic particles hit a lead target plate and as a result many different types of particles were produced. They were classified as: baryons: particles whose decay product ultimately includes a proton. mesons: particles whose decay product ultimately include only leptons or photons. Whyweretheseeventscalled strange? Themysteryliesinthefactthatcertain(neutral) 0 −27 2 particleswereproduced(the“V ’s”)withalargecrosssection(∼ 10 cm ),whilethey −40 2 decay according to a process with a small cross section (∼ 10 cm ). The explanation to this riddle was given by Abraham Pais in 1952 and is called associated production. This means that strange particles are always produced in pairs by the strong interaction. It was suggested that strange particle carries a strangeness quantum number. In the strong interaction one then has the conservation rule ΔS = 0, such that a particle with S=+1 (e.g. a K meson) is simultaneously produced with a particle with S=-1 (e.g. a Λ baryon). These particles then individually decay through the weak interaction, which does not conserve strangeness. An example of an associated production event is seen in Fig. 1.4.1.2. Strange Particles 15 Figure 1.3: A pion entering from the left decays into a muon and an invisible neutrino.16 Lecture 1. Particles and Forces Figure 1.4: A bubble chamber picture of associated production.1.3. The Eightfold Way 17 In the years 1950 - 1960 many elementary particles were discovered and one started to speak of the particle zoo. A quote: “The finder of a new particle used to be awarded the Nobel prize, but such a discovery now ought to be punished by a 10.000 fine.” 1.3 The Eightfold Way In the early 60’s Murray Gell-Mann (at the same time also Yuvan Ne’eman) observed patterns of symmetry in the discovered mesons and baryons. He plotted the spin 1/2 baryons in a so-called octet (the “eightfold way” after the eighfold way to Nirvana in Buddhism). There is a similarity between Mendeleev’s periodic table of elements and the supermultiplets of particles of Gell Mann. Both pointed out a deeper structure of matter. The eightfold way of the lightest baryons and mesons is displayed in Fig. 1.5 and Fig. 1.6. In these graphs the Strangeness quantum number is plotted vertically. + n p S=0 − 0 + Σ Σ Σ S=−1 Λ 0 S=−2 − Ξ Ξ Q=0 Q=+1 Q=−1 Figure 1.5: Octet of lightest baryons with spin=1/2. 0 + K K S=1 − 0 + Π Π Π S=0 η S=−1 − − 0 Κ Κ Q=0 Q=1 Q=−1 Figure 1.6: Octet with lightest mesons of spin=0 Alsoheavierhadronscouldbegivenaplaceinmultiplets. Thebaryonswithspin=3/2 wereseentoformadecuplet, seeFig. 1.7. Theparticleatthebottom(atS=-3)hadnot been observed. Not only was it found later on, but also its predicted mass was found to − be correct The discovery of the Ω particle is shown in Fig. 1.8.18 Lecture 1. Particles and Forces mass ++ − 0 + Δ Δ Δ Δ 1230 MeV S=0 0 + − ∗ ∗ ∗ Σ Σ Σ 1380 MeV S=−1 Q=+2 − 0 ∗ ∗ Ξ Ξ 1530 MeV S=−2 Q=+1 − Ω 1680 MeV S=−3 Q=0 Q=−1 − Figure 1.7: Decuplet of baryons with spin=3/2. The Ω was not yet observed when this model was introduced. It’s mass was predicted. Figure 1.8: Discovery of the omega particle.

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