DOCSLIB.ORG

Electronics II Physics 3620 / 6620

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Electronics II Physics 3620 / 6620 IntroIntro toto NuclearNuclear andand ParticleParticle PhysicsPhysics (5110)(5110) Apr 17, 2009 4/17/2009 1 PathsPaths toto thethe StandardStandard ModelModel • We’ve reached the point of understanding elementary particles roughly comparable to the world of the early 1960’s – Four fundamental forces. Three of these we (somewhat) understand: symmetries, conservation laws and either powerful (EM) or rudimentary (strong, weak) quantitative tools – Many, many particles: hadrons (mesons and baryons), leptons, the photon. Many more (esp. hadrons) being discovered – A few really powerful clues to the details: patterns in masses and decay properties among particles, CP violation, absence of “strangeness- changing neutral currents” • Some particle physicists were content with the situation, continually adding to the complexity with more particles, and more details of their properties and behavior • Others found it intolerable and were already looking for ways to bring order to the confusion. Still others were methodically pushing farther into the structure of nuclear matter with “deep inelastic scattering” of electron beams • Both paths would converge by the early 1970’s on the Standard Model of quarks and leptons 4/17/2009 2 ManyMany particles!particles! Patterns!Patterns! Nucleons: p (938 MeV) n (940 MeV) Pions: π+ (140 MeV) π0 (135 MeV) π− (140 MeV) Kaons: K+ (494 MeV) K0 (498 MeV) K− (494 MeV) • Isospin Members of multiplets are different states of the same particle: nucleon doublet, pion triplet, kaon and anti-kaon doublets But…the original premise of isospin was that only EM broke an otherwise perfect symmetry. If this is valid, how do we explain… MM>> and M M, but M>M? np KK00±±ππ Perhaps…observed elementary particles are different assemblies of a small set of basic building blocks. First suggested by Fermi and Yang in 1949! 4/17/2009 3 Fermi-Yang “Pre-Quark Model” π + = pn 1 π 0 =−()pp nn SU(2) 2 π − = np Problems: No experimental or theoretical basis for baryons as building blocks With more particles, some repetition of patterns for excited versions of known particles, but no place for strangeness! 4/17/2009 4 MoreMore Patterns:Patterns: Strangeness,Strangeness, Hypercharge,…Hypercharge,… Gell-Mann, Nishijima and others noted that electric charge (Q) of all particles could be related to isospin (I3), baryon number (B) and strangeness (S): ()SB+ Y QI=+ =+I YS= + B Y: Hypercharge 3322 Interesting patterns became evident when Y was plotted vs. I3: Y 0 Model of Sakata (1956): K K + → +1 Known mesons (7) and baryons (8) can − 0 + be built from three fundamental baryons π π π (p, n, Λ) and their antiparticles: -1 0+1 I3 + 0 1 − π = pn π =+()pp nn π = np − 2 K K 0 K + = pΛ K 0 = nΛ -1 K 0 = nΛ K − = pΛ (Baryons : Σ=+ Λpn, etc.) Good step! Explained known particles, got statistics right. But why should p, n, Λ be fundamental? Lots of tinkering, incl. weakening of connection between the building blocks and the physical baryons. Sakata model could not accommodate some decays and new particle discoveries 4/17/2009 5 Next step: SU(3) and the “Eightfold Way” Gell-Mann, Ne’eman (1961) Isospin SU(2) + Strangeness → SU(3) Pseudoscalar Vector Spin-1/2 Spin-3/2 Mesons Mesons Baryons Baryons K 0 K + K ∗0 K ∗+ n p ∆− ∆0 ∆+ ∆++ − 0 + − 0 + − 0 + ∗− ∗0 ∗+ π π η π ρ ρ ω ρ Σ Σ Λ Σ Σ Σ Σ K − K 0 K ∗− K ∗0 Ξ− Ξ0 Ξ∗− Ξ∗0 Octet of SU(3), consisting of an isotriplet, a singlet and two ? isodoublets is asserted to be the basic unit of organization: 8⊗8=18⊕⊕⊕810⊕10∗ ⊕27 Spin-3/2 baryons pose a puzzle – not an octet. 10? 27? 4/17/2009 6 • Many competing predictions were made of particle masses and decays expected under the Sakata model and the “10” and “27” interpretations of the “eightfold way” • Gell-Mann predicted that the “10” is correct and that the “?” in the spin- 3/2 decuplet would be the Ω−, a baryon with S = −3 at ~ 1700 MeV Samios, et al. BNL - 1964 • Last step! Gell-Mann and Zweig in 1964 independently postulated that the constitutents of hadrons were not known particles, but as-yet- unseen building blocks in the fundamental (“3”) representation of SU(3). Zweig thought they were observable, Gell-Mann just “bookkeeping” 4/17/2009tools 7 TheThe QuarkQuark ModelModel • Initially these hypothetical particles were named p, n and λ, but within a decade the modern names u (“up”), d (“down”), and s (“sideways”→”strange”) had been adopted Observed hadrons constructed from quarks: + 0 1 − π = ud π =−()uu dd π = du Mesons 2 quark/antiquark pairs Ku+ = s Kd0 = s Ks0 = d Ks− = u Baryons pu= u d nu= d d Λ = ud s three quarks (antibaryons are p= uud three antiquarks) nu= dd Λ=uds +− P 11 11 Fundamental, pointlike; J = ; baryon number − ; Quark 22 33 2121 (antiquark) charges +−ee and −e and +e; nonzero masses T.B.D.; properties: 3333 isodoublet (ud, ) and isosinglet ()s; "feel" all four interactions 4/17/2009 8 3 3 Quark Model Successes Quark Model Problems − Classified known particles (early 60s), − Free quarks? Many looked, no one predicted others found later found − Accommodated many not-yet imagined − Quantum statistics problems, e.g. ∆++ − Explained absence of some particles, is a fermion, but constructed wave like S = +1, Q = 0 baryon function is totally symmetric − Explained mass splittings, isospin, − No satisfactory understanding of magnetic moments, cross-section quark binding in hadrons ratios (σπp/σpp = 2/3) − “Family problem” 4/17/2009 9 SU(2)SU(2) →→ SU(3)SU(3) Isospin Quarks • n = 2, n2 –1 = 3generators (2×2 • n = 3, n2 –1 = 8generators (3×3 linearly independent, traceless linearly independent, traceless Hermitian matrices) Hermitian matrices) Pauli Matrices Gell-Mann Matrices One is diagonal ⇒ one quantum number: I3 Two are diagonal ⇒ two quantum numbers: I3, Y = B + S More quarks? SU(3) → SU(4) → SU(5) → … 4/17/2009 10 GroupGroup Theory:Theory: thethe MathMath ofof SymmetrySymmetry We say that the set of transformations G G = ( gg12, ,..., gn ) constitutes a group if the following four conditions hold: 1. Closure: If gi and gj are in G, then the product gigj is also in G. 2. Existence of Identity: ∃ I in G such that Igi = giI = gi ∀ gi -1 -1 -1 3. Existence of Inverse: ∀ gi ∃ gi such that gi gi = gi gi = I ∀ gi 4. Associativity: gi (gj gk) = (gigj )gk More terminology: – A representation of a group is the action of the transformations in the group on a specific set of objects – Generating set of a group – subset of the group such that every element of the group can be generated as a product of elements of the generating set and their inverses – Types of groups: finite, infinite, continuous, discrete – correspond to different transformations/symmetries – Abelian group ⇒ elements commute (e.g. translation in space) – Non-Abelian group ⇒ elements do not commute (e.g. rotation) 4/17/2009 11 GroupGroup TheoryTheory (continued)(continued) • Consider a transformation U that acts on a wave function ψ: ψ' = U(ψ) • Let U be a continuous transformation and it can be expressed U = eiθ where θ is an operator • If θ = θ† (Hermitian), then U is a unitary transformation: ∗T ∗T † iiθ − θθ−i Ue==( ) e=e UU † ==eiiθθe− I (Note: U ≠ U† ⇒ U is not Hermitian) • Important groups in physics – Members are matrices, operation is matrix multiplication U(n) n × n unitary group SU(n) n × n special unitary group (det = 1) SO(3) (rotations O(n) n × n orthogonal group (UTU = UUT = I) in 3D) is almost identical to SU(2) SO(n) n × n special orthogonal group (det = 1) 4/17/2009 12 SUSU(2)(2) isis especiallyespecially importantimportant becausebecause itit describesdescribes angularangular momentummomentum andand givesgives aa modelmodel forfor internalinternal symmetriessymmetries ofof elementaryelementary particlesparticles • SU(2) – the set of all 2 × 2 unitary matrices with unit determinant - forms a group under matrix multiplication Elements of SU ()2 can be represented as r r iT ()α Ue()α = rr αα is a vector parameter that gives the phase and T ( ) is a 22× matrix generated by the Pauli matrices : 3 iTα r ∑ j j r iT ()α j=1 Ue()α ==e 01 0−i 1 0 σσ12== σ3= 1 10 i 0 0−1 T = σ jj2 (This is spin! We now apply it to something new.) 4/17/2009 13 Charge independence! IsospinIsospin Heisenberg’s assertion: Turn off EM and n and p would be the same • Determine experimentally that isospin is conserved by the strong interaction, not by the electromagnetic or weak [HIweak ,0] ≠ ⇒= HIstrong ,0 []HIEM , ≠ 0 • Isospin conservation means strong interactions are invariant under rotations of states in “I space,” which means that the interactions for the particles with the same total I but different projections I3 are identical. This is the case for the proton and neutron, for the three pions, and for the other isomultiplets • Isospin is an internal quantum number that must be incorporated into the description of a state, along with all of the other internal quantum numbers to come • How do we use it? 4/17/2009 14 FundamentalFundamental RepresentationRepresentation ofof SU(2)SU(2) (That representation from which all others can be constructed.) • Two-component spinor ( j = ½ ) – the “2” of SU(2) • These are symmetries – we should be able to construct them by manipulating physical models (graphically): m m m m 1 + +1 1 + 2 0 = 0 + 0 2 1 − 2 −1 −1 22× = 3 + 1 Isospin is all about counting Triplet (“3”) Singlet (“1”) carefully. Next job is to see of SU(2) of SU(2) how isospin symmetry Trivial quantitatively constrains the Representation rates of related processes 4/17/2009 15 Determine relative rates for processes ApplicationsApplications ofof IsospinIsospin involving different charge states Modeled after the treatment of angular momentum: r rr JJ= 12+ J m m m m +1 1 +1 + 2 0 0 0 1 = + − 2 −1 −1 11 1 1 22 1 0 0 0 11 − 22 1 −1 jj12+ jm j m= Cjj,,12j j m mm= + m 112 2 ∑ mm,12,m 12 jj=−j 12 Clebsch-Gordan Coefficients 4/17/2009 16.
Load more

Recommended publications
  • The Role of Strangeness in Ultrarelativistic Nuclear
    HUTFT THE ROLE OF STRANGENESS IN a ULTRARELATIVISTIC NUCLEAR COLLISIONS Josef Sollfrank Research Institute for Theoretical Physics PO Box FIN University of Helsinki Finland and Ulrich Heinz Institut f ur Theoretische Physik Universitat Regensburg D Regensburg Germany ABSTRACT We review the progress in understanding the strange particle yields in nuclear colli sions and their role in signalling quarkgluon plasma formation We rep ort on new insights into the formation mechanisms of strange particles during ultrarelativistic heavyion collisions and discuss interesting new details of the strangeness phase di agram In the main part of the review we show how the measured multistrange particle abundances can b e used as a testing ground for chemical equilibration in nuclear collisions and how the results of such an analysis lead to imp ortant con straints on the collision dynamics and spacetime evolution of high energy heavyion reactions a To b e published in QuarkGluon Plasma RC Hwa Eds World Scientic Contents Introduction Strangeness Pro duction Mechanisms QuarkGluon Pro duction Mechanisms Hadronic Pro duction Mechanisms Thermal Mo dels Thermal Parameters Relative and Absolute Chemical Equilibrium The Partition Function The Phase Diagram of Strange Matter The Strange Matter Iglo o Isentropic Expansion Trajectories The T ! Limit of the Phase Diagram
    [Show full text]
  • Particle Physics Dr Victoria Martin, Spring Semester 2012 Lecture 12: Hadron Decays
    Particle Physics Dr Victoria Martin, Spring Semester 2012 Lecture 12: Hadron Decays !Resonances !Heavy Meson and Baryons !Decays and Quantum numbers !CKM matrix 1 Announcements •No lecture on Friday. •Remaining lectures: •Tuesday 13 March •Friday 16 March •Tuesday 20 March •Friday 23 March •Tuesday 27 March •Friday 30 March •Tuesday 3 April •Remaining Tutorials: •Monday 26 March •Monday 2 April 2 From Friday: Mesons and Baryons Summary • Quarks are confined to colourless bound states, collectively known as hadrons: " mesons: quark and anti-quark. Bosons (s=0, 1) with a symmetric colour wavefunction. " baryons: three quarks. Fermions (s=1/2, 3/2) with antisymmetric colour wavefunction. " anti-baryons: three anti-quarks. • Lightest mesons & baryons described by isospin (I, I3), strangeness (S) and hypercharge Y " isospin I=! for u and d quarks; (isospin combined as for spin) " I3=+! (isospin up) for up quarks; I3="! (isospin down) for down quarks " S=+1 for strange quarks (additive quantum number) " hypercharge Y = S + B • Hadrons display SU(3) flavour symmetry between u d and s quarks. Used to predict the allowed meson and baryon states. • As baryons are fermions, the overall wavefunction must be anti-symmetric. The wavefunction is product of colour, flavour, spin and spatial parts: ! = "c "f "S "L an odd number of these must be anti-symmetric. • consequences: no uuu, ddd or sss baryons with total spin J=# (S=#, L=0) • Residual strong force interactions between colourless hadrons propagated by mesons. 3 Resonances • Hadrons which decay due to the strong force have very short lifetime # ~ 10"24 s • Evidence for the existence of these states are resonances in the experimental data Γ2/4 σ = σ • Shape is Breit-Wigner distribution: max (E M)2 + Γ2/4 14 41.
    [Show full text]
  • The Eightfold Way Model, the SU(3)-flavour Model and the Medium-Strong Interaction
    The Eightfold Way model, the SU(3)-flavour model and the medium-strong interaction Syed Afsar Abbas Jafar Sadiq Research Institute AzimGreenHome, NewSirSyed Nagar, Aligarh - 202002, India (e-mail : [email protected]) Abstract Lack of any baryon number in the Eightfold Way model, and its intrin- sic presence in the SU(3)-flavour model, has been a puzzle since the genesis of these models in 1961-1964. In this paper we show that this is linked to the way that the adjoint representation is defined mathematically for a Lie algebra, and how it manifests itself as a physical representation. This forces us to distinguish between the global and the local charges and between the microscopic and the macroscopic models. As a bonus, a consistent under- standing of the hitherto mysterious medium-strong interaction is achieved. We also gain a new perspective on how confinement arises in Quantum Chro- modynamics. Keywords: Lie Groups, Lie Algegra, Jacobi Identity, adjoint represen- tation, Eightfold Way model, SU(3)-flavour model, quark model, symmetry breaking, mass formulae 1 The Eightfold Way model was proposed independently by Gell-Mann and Ne’eman in 1961, but was very quickly transformed into the the SU(3)- flavour model ( as known to us at present ) in 1964 [1]. We revisit these models and look into the origin of the Eightfold Way model and try to un- derstand as to how it is related to the SU(3)-flavour model. This allows us to have a fresh perspective of the mysterious medium-strong interaction [2], which still remains an unresolved problem in the theory of the strong interaction [1,2,3].
    [Show full text]
  • On the Kaon' S Structure Function from the Strangeness Asymmetry in The
    On the Kaon’ s structure function from the strangeness asymmetry in the nucleon Luis A. Trevisan*, C. Mirez†, Lauro Tomio† and Tobias Frederico** *Departamento de Matemática e Estatística, Universidade Estadual de Ponta Grossa, 84010-790, Ponta Grossa, PR, Brazil † Institute de Física Tedrica, Universidade Estadual Paulista, UNESP, 01405-900, São Paulo, SP, Brazil **Departamento de Física, Instituto Tecnológico de Aeronáutica, CTA, 12228-900, São José dos Campos, SP, Brazil Abstract. We propose a phenomenological approach based in the meson cloud model to obtain the strange quark structure function inside a kaon, considering the strange quark asymmetry inside the nucleon. Keywords: Kaon, strange quark, structure function, asymmetry PACS: 13.75.Jz, 11.30.Hv, 12.39.x, 14.65.Bt The experimental data from CCFR and NuTeV collaborations [1] show that the distri­ bution function for strange and anti-strange quark are asymmetric. If we consider only gluon splitting processes, such asymmetry cannot be found, since the quarks generated by gluons should have the same momentum distribution. So, among the models that have been proposed (or considered) to explain the asymmetry, the most popular are based on meson clouds or A - K fluctuations [2, 3]. By using this kind of model, we analyze the behavior of some parameterizations for the strange quark distribution s(x), in terms of the Bjorken scale x, and discuss how to estimate the structure function for a constituent quark in a Kaon. The strange quark distribution in the nucleon sea, as well as the distribution for u and d quarks, can be separated into perturbative and nonperturbative parts.
    [Show full text]
  • The Results and Their Interpretation
    178 Part C the postulate of quarks as the fundamental building blocks The results and their of matter. interpretation Strangeness, parity violation, and charm Chapter 16 The decays of the strange particles, in particular of the kaons, paved the way for the further development of our The CKM matrix and the understanding. Before 1954, the three discrete symmetries Kobayashi-Maskawa mechanism C (charge conjugation), P (parity) and T (time rever- sal) were believed to be conserved individually, a conclu- Editors: sion drawn from the well known electromagnetic interac- Adrian Bevan and Soeren Prell (BABAR) tion. Based on this assumption, the so called θ-τ puzzle Boˇstjan Golob and Bruce Yabsley (Belle) emerged: Two particles (at that time called θ and τ, where Thomas Mannel (theory) the latter is not to be confused with the third generation lepton) were observed, which had identical masses and lifetimes. However, they obviously had different parities, since the θ particle decayed into two pions (a state with 16.1 Historical background even parity), and the τ particle decays into three pions (a state with odd parity). Fundamentals The resolution was provided by the bold assumption by Lee and Yang (1956) that parity is not conserved in In the early twentieth century the “elementary” particles weak interactions, and θ and τ are in fact the same par- known were the proton, the electron and the photon. The ticle, which we now call the charged kaon. Subsequently first extension of this set of particles occurred with the the parity violating V A structure of the weak interac- neutrino hypothesis, first formulated by W.
    [Show full text]
  • Sakata Model Precursor 2: Eightfold Way, Discovery of Ω- Quark Model: First Three Quarks A
    Introduction to Elementary Particle Physics. Note 20 Page 1 of 17 THREE QUARKS: u, d, s Precursor 1: Sakata Model Precursor 2: Eightfold Way, Discovery of ΩΩΩ- Quark Model: first three quarks and three colors Search for free quarks Static evidence for quarks: baryon magnetic moments Early dynamic evidence: - πππN and pN cross sections - R= σσσee →→→ hadrons / σσσee →→→ µµµµµµ - Deep Inelastic Scattering (DIS) and partons - Jets Introduction to Elementary Particle Physics. Note 20 Page 2 of 17 Sakata Model 1956 Sakata extended the Fermi-Yang idea of treating pions as nucleon-antinucleon bound states, e.g. π+ = (p n) All mesons, baryons and their resonances are made of p, n, Λ and their antiparticles: Mesons (B=0): Note that there are three diagonal states, pp, nn, ΛΛ. p n Λ Therefore, there should be 3 independent states, three neutral mesons: π0 = ( pp - nn ) / √2 with isospin I=1 - - p ? π K X0 = ( pp + nn ) / √2 with isospin I=0 0 ΛΛ n π+ ? K0 Y = with isospin I=0 Or the last two can be mixed again… + 0 Λ K K ? (Actually, later discovered η and η' resonances could be interpreted as such mixtures.) Baryons (B=1): S=-1 Σ+ = ( Λ p n) Σ0 = ( Λ n n) mixed with ( Λ p p) what is the orthogonal mixture? Σ- = ( Λ n p) S=-2 Ξ- = ( Λ Λp) Ξ- = ( Λ Λn) S=-3 NOT possible Resonances (B=1): ∆++ = (p p n) ∆+ = (p n n) mixed with (p p p) what is the orthogonal mixture? ∆0 = (n n n) mixed with (n p p) what is the orthogonal mixture? ∆- = (n n p) Sakata Model was the first attempt to come up with some plausible internal structure that would allow systemizing the emerging zoo of hadrons.
    [Show full text]
  • An Introduction to the Quark Model Arxiv:1205.4326V2 [Hep-Ph]
    An introduction to the quark model Jean-Marc Richard Université de Lyon & Institut de Physique Nucléaire de Lyon IN2P3-CNRS & UCB, 4 rue Enrico Fermi, 69622 Villeurbanne, France [email protected] May 25, 2012 Abstract This document contains a review on the quark model, prepared for lectures at the Niccolò Cabeo School at Ferrara in May 2012. It includes some historical aspects, the spectral properties of the 2-body and 3-body Schrödinger operators applied to mesons and baryons, the link between meson and baryon spectra, the role of flavour independence, and the speculations about stable or metastable multiquarks. The analogies between few-charge systems and few-quark bound states will be under- lined. Contents 1 Prelude: few charge systems in atomic physics 3 1.1 Introduction . .3 1.2 The atomic two-body problem . .3 1.3 Three-unit-charge ions . .5 arXiv:1205.4326v2 [hep-ph] 24 May 2012 1.4 Three-body exotic ions . .5 1.5 Molecules with four unit charges . .6 2 A brief historical survey 7 2.1 Prehistory . .7 2.2 Early hadrons . .7 2.3 Generalised isospin . .9 2.4 The success of the eightfold way . 10 2.5 The fundamental representation: quarks . 10 2.6 The OZI rule . 12 2.7 First quark models . 13 2.8 Heavy quarks . 14 2.9 Confirmation . 15 1 2 AN INTRODUCTION TO THE QUARK MODEL 3 The quark–antiquark model of mesons 16 3.1 Introduction . 16 3.2 Quantum numbers . 16 3.3 Spin averaged spectrum . 17 3.4 Improvements to the potential .
    [Show full text]
  • Isospin and Isospin/Strangeness Correlations in Relativistic Heavy Ion Collisions
    Isospin and Isospin/Strangeness Correlations in Relativistic Heavy Ion Collisions Aram Mekjian Rutgers University, Department of Physics and Astronomy, Piscataway, NJ. 08854 & California Institute of Technology, Kellogg Radiation Lab 106-38, Pasadena, Ca 91125 Abstract A fundamental symmetry of nuclear and particle physics is isospin whose third component is the Gell-Mann/Nishijima expression I Z =Q − (B + S) / 2 . The role of isospin symmetry in relativistic heavy ion collisions is studied. An isospin I Z , strangeness S correlation is shown to be a direct and simple measure of flavor correlations, vanishing in a Qg phase of uncorrelated flavors in both symmetric N = Z and asymmetric N ≠ Z systems. By contrast, in a hadron phase, a I Z / S correlation exists as long as the electrostatic charge chemical potential µQ ≠ 0 as in N ≠ Z asymmetric systems. A parallel is drawn with a Zeeman effect which breaks a spin degeneracy PACS numbers: 25.75.-q, 25.75.Gz, 25.75.Nq Introduction A goal of relativistic high energy collisions such as those done at CERN or BNL RHIC is the creation of a new state of matter known as the quark gluon plasma. This phase is produced in the initial stages of a collision where a high density ρ and temperatureT are produced. A heavy ion collision then proceeds through a subsequent expansion to lower ρ andT where the colored quarks and anti-quarks form isolated colorless objects which are the well known particles whose properties are tabulated in ref[1]. Isospin plays an important role in the classification of these particles [1,2].
    [Show full text]
  • PHY401 - Nuclear and Particle Physics
    PHY401 - Nuclear and Particle Physics Monsoon Semester 2020 Dr. Anosh Joseph, IISER Mohali LECTURE 27 Wednesday, October 28, 2020 (Note: This is an online lecture due to COVID-19 interruption.) Contents 1 CP Violation 1 1.1 CP Eigenstates of Neutral Kaons . .5 1.2 Strangeness Oscillations . .5 2 Formulation of the Standard Model 6 2.1 Quarks and Leptons . .7 2.2 Quark Content of Mesons . .8 2.3 Quark Content of Baryons . 10 1 CP Violation In 1956 Wu and collaborators conducted an experiment to look for P violation in cobalt-60 decays. The presence of P violation in this system suggested that there is something unique about the weak force. If P and C can be violated individually, how about the combination of the two? CP takes a physical particle state to a physical anti-particle state. Thus, invariance under CP is equivalent to having a particle-anti-particle symmetry in nature. However, the universe is known to be dominated by matter, with essentially no antimatter present. That is, there is a definite particle-anti-particle asymmetry in the universe. CP may not be a symmetry of all fundamental interactions. There are in fact processes in which CP is violated. CP violation implies that there are microscopic (sub-atomic) processes in which time has a unique direction of flow. PHY401 - Nuclear and Particle Physics Monsoon Semester 2020 In 1964, James Cronin and Val Fitch tested CP violations in neutral kaons. Neutral kaons can be represented as jK0i = jsd¯ i; jK¯ 0i = jsd¯i: (1) K¯ 0 is the anti-particle of K0.
    [Show full text]
  • Introduction to Elementary Particle Physics
    Introduction to Elementary Particle Physics Néda Sadooghi Department of Physics Sharif University of Technology Tehran - Iran Elementary Particle Physics Lecture 9 and 10: Esfand 18 and 20, 1397 1397-98-II Leptons and quarks Lectrue 9 Leptons Lectrue 9 Remarks: I Lepton flavor number conservation: - Lepton flavor number of leptons Le; Lµ; Lτ = +1 - Lepton flavor number of antileptons Le; Lµ; Lτ = −1 Assumption: No neutrino mixing + + − + + Ex.: π ! µ + νµ; n ! p + e +ν ¯e; µ ! e + νe +ν ¯µ But, µ+ ! e+ + γ is forbidden I Two other quantum numbers for leptons - Weak hypercharge YW : It is 1 for all left-handed leptons - Weak isospin T3: ( ) ( ) e− − 1 ! 2 For each lepton generation, for example T3 = 1 νe + 2 I Type of interaction: - Charged leptons undergo both EM and weak interactions - Neutrinos interact only weakly Lectrue 9 Quarks Lectrue 9 Remarks I Hadrons are bound states of constituent (valence) quarks I Bare (current) quarks are not dressed. We denote the current quark mass by m0 I Dressed quarks are surrounded by a cloud of virtual quarks and gluons (Sea quarks) I This cloud explains the large constituent-quark mass M I For hadrons the constituent quark mass M = the binding energy required to make the hadrons spontaneously emit a meson containing the valence quark For light quarks (u,d,s): m0 ≪ M For heavy quarks (c,b,t): m0 ' M Lectrue 9 Remarks: I Type of interaction: - All quarks undergo EM and strong interactions I Mean lifetime (typical time of interaction): In general, - Particles which mainly decay through strong interactions have a mean lifetime of about 10−23 sec - Particles which mainly decay through electromagnetic interactions, signaled by the production of photons, have a mean lifetime in the range of 10−20 − 10−16 sec - Particles that decay through weak forces have a mean lifetime in the range of 10−10 − 10−8 sec Lectrue 9 Other quantum numbers (see Perkins Chapter 4) Flavor Baryon Spin Isospin Charm Strangeness Topness Bottomness El.
    [Show full text]
  • The Quark Model and Deep Inelastic Scattering
    The quark model and deep inelastic scattering Contents 1 Introduction 2 1.1 Pions . 2 1.2 Baryon number conservation . 3 1.3 Delta baryons . 3 2 Linear Accelerators 4 3 Symmetries 5 3.1 Baryons . 5 3.2 Mesons . 6 3.3 Quark flow diagrams . 7 3.4 Strangeness . 8 3.5 Pseudoscalar octet . 9 3.6 Baryon octet . 9 4 Colour 10 5 Heavier quarks 13 6 Charmonium 14 7 Hadron decays 16 Appendices 18 .A Isospin x 18 .B Discovery of the Omega x 19 1 The quark model and deep inelastic scattering 1 Symmetry, patterns and substructure The proton and the neutron have rather similar masses. They are distinguished from 2 one another by at least their different electromagnetic interactions, since the proton mp = 938:3 MeV=c is charged, while the neutron is electrically neutral, but they have identical properties 2 mn = 939:6 MeV=c under the strong interaction. This provokes the question as to whether the proton and neutron might have some sort of common substructure. The substructure hypothesis can be investigated by searching for other similar patterns of multiplets of particles. There exists a zoo of other strongly-interacting particles. Exotic particles are ob- served coming from the upper atmosphere in cosmic rays. They can also be created in the labortatory, provided that we can create beams of sufficient energy. The Quark Model allows us to apply a classification to those many strongly interacting states, and to understand the constituents from which they are made. 1.1 Pions The lightest strongly interacting particles are the pions (π).
    [Show full text]
  • Chapter 16 Constituent Quark Model
    Chapter 16 Constituent Quark Model 1 Quarks are fundamental spin- 2 particles from which all hadrons are made up. Baryons consist of three quarks, whereas mesons consist of a quark and an anti-quark. There are six 2 types of quarks called “flavours”. The electric charges of the quarks take the value + 3 or 1 (in units of the magnitude of the electron charge). − 3 2 Symbol Flavour Electric charge (e) Isospin I3 Mass Gev /c 2 1 1 u up + 3 2 + 2 0.33 1 1 1 ≈ d down 3 2 2 0.33 − 2 − ≈ c charm + 3 0 0 1.5 1 ≈ s strange 3 0 0 0.5 − 2 ≈ t top + 3 0 0 172 1 ≈ b bottom 0 0 4.5 − 3 ≈ These quarks all have antiparticles which have the same mass but opposite I3, electric charge and flavour (e.g. anti-strange, anti-charm, etc.) 16.1 Hadrons from u,d quarks and anti-quarks Baryons: 2 Baryon Quark content Spin Isospin I3 Mass Mev /c 1 1 1 p uud 2 2 + 2 938 n udd 1 1 1 940 2 2 − 2 ++ 3 3 3 ∆ uuu 2 2 + 2 1230 + 3 3 1 ∆ uud 2 2 + 2 1230 0 3 3 1 ∆ udd 2 2 2 1230 3 3 − 3 ∆− ddd 1230 2 2 − 2 113 1 1 3 Three spin- 2 quarks can give a total spin of either 2 or 2 and these are the spins of the • baryons (for these ‘low-mass’ particles the orbital angular momentum of the quarks is zero - excited states of quarks with non-zero orbital angular momenta are also possible and in these cases the determination of the spins of the baryons is more complicated).
    [Show full text]