Option 212: UNIT 2 Elementary Particles

1. Department of Physics and Astronomy Option 212: UNIT 2Elementary Particles SCHEDULE a5-Feb-04 1.30pm Physics LRA Dr M Burleigh Intro lecture a9-Feb-04 9.30am Eng 1 Dr M Burleigh Problem solving a(12-Feb-04 9.30am Physics F2 Problem Workshop) 16-Feb-04 9.30am Eng 1 Dr M Burleigh Follow-up

2. 1st Lecture Introduction Hadrons and LeptonsSpin & Anti-Particles The conservation laws: Lepton Number Baryon number Strangeness 2ndLecture 3rd Lecture Follow-upFundamental forces and field particles The standard model UNIT 2: OUTLINE SYLLABUS: Problem solving Check a decay for violation of conservation laws Quarks Properties of a particle given quark combination

3. Tipler Chap 41 Q8 (a) mp < mn : energy conservation is violated. Also Le=0 on lhs, but Le=-2 on rhs (b) mn < mp + mp : energy conservation is violated (c) Momentum conservation is violated: in pair annihilation, two photons (g rays) must be emitted to conserve momentum (d) Allowed (e) Le=-1 on both sides, but mp < mn so energy conservation violated • State which of the following decays or reactions violates one or more of the conservation laws, and give the law(s) violated in each case: • (a) p -> n + e+ + ne • (b) n -> p + p- • (c) e+ + e- -> g • (d) p + p -> g + g • (e) ne + p -> n + e+

4. Tipler Chap 41 Q29 • Consider the following decay chain • X0 -> L0 + p0 • L0 -> p + p- • p0 -> g + g • p- -> m- + nm • m- -> e- + ne + nm • (a) write the overall decay reaction for X0 to the final decay products • (b) are the final decay products stable? • (c) Check the overall decay reaction for the conservation of electric charge, baryon number, and lepton number • (d) Check the overall decay reaction for conservation of strangeness. Is the reaction possible via the weak or strong interactions?

5. Tipler Chap 41 Q29 (a) X0 -> p + 2g + nm + e- + ne + nm • (b) Use Table 41-1. The proton is stable for 1031 years. In contrast, the neutron is only stable for 930secs. Answer: yes, stable. • (c) Charge conservation: 0 -> p + e- = 0: conserved. Baryon number 1 -> 1: conserved. Lepton number Le: 0 -> e- + ne = 1 + (-1) = 0: conserved. Lm: 0 -> -1 + 1 = 0. • (d) See Tipler p.1322. Strangeness must be conserved if reaction occurs via strong interaction. Here S=-2 on lhs and S=0 on rhs. But if DS=+/-1, then can occur via weak interaction. In first two parts of reaction, DS=1 (L0 has S=-1) so is allowed via weak interaction.

6. True or false? (a) False: leptons are fundamental particles e.g e- (c) False: there is no left and right quark, but there are top and bottom quarks • (a) Leptons consist of three quarks • (b) Mesons consist of a quark and an anti-quark • (c) The six flavors of quark are up, down, charmed, strange, left and right • (d) Neutrons have no charm (d) True: neutrons are made of udd quarks (b) True

7. Quark confinement • No isolated quark has ever been observed • Believed impossible to obtain an isolated quark • If the PE between quarks increases with separation distance, an infinite amount of energy may be required to separate them • When a large amount of energy is added to a quark system, like a nucleon, a quark-antiquark pair is created • Original quarks remain confined in the original system • Because quarks always confined, their mass cannot be accurately known

8. Quark color • Consider the W-particle, which consists of three strange quarks • Remember that quarks have spin ½ • The W- has spin 3/2, so its three strange quarks must be arranged thus: • But Pauli exclusion principle forbids these identical (same flavor, same mag of spin, same direction of spin) quarks occupying identical quantum states • The only way for this to work is if each quark possesses a further property, color: • Quarks in a baryon always have these three colours, such that when combined they are “color-less” ( qr , qy , qb ) • In a meson, a red quark and its “anti-red” quark attract to form the particle

9. Field Particles (Tipler P.1325) • In addition to the six fundamental leptons (e-, m-, t-, ne, nm, nt) and six quarks, there are field particles associated with the fundamental forces (weak, strong, gravity and electro-magnetic) • For example, the photon mediates the electro-magnetic interaction, in which particles are given the property “charge” • The theory governing electro-magnetic interactions at the quantum level is called Quantum Electrodynamics (QED) • Similarly, gravity is mediated by the graviton • The “charge” in gravity is mass • The graviton has not been observed

10. Field Particles • The weak force, which is experienced by quarks and leptons, is carried by the W+, W-, and Z0 particles • These have been observed and are massive (~100 GeV/c2) • The “charge” they mediate is flavor • The strong force, which is experienced by quarks and hadrons, is carried by a particle called a gluon • The gluon has not been observed • The “charge” is color • The field theory for strong interactions (analagous to QED) is called Quantum Chromodynamics (QCD)

11. Electroweak theory • The electromagnetic and weak interactions are considered to be two manifestations of a more fundamental electroweak interaction • At very high energies, >100GeV the electroweak interaction would be mediated (or carried) by four particles: W+, W-, W0, and B0 • The W0 and B0 cannot be observed directly • But at ordinary energies they combine to form either the Z0 or the massless photon • In order to work, electroweak theory requires the existence of a particle called the Higgs Boson • The Higgs Boson is expected have a rest mass > 1TeV/c2 • Head-on collisions between protons at energies ~20TeV are required to produce a Higgs Boson (if they exist) • Such energies will only be achieved by the next generation of particle accelerators (eg Large Hadron Collider at CERN)

12. The Standard Model (Tipler P.1327) • The combination of the quark model, electroweak theory and QCD is called the Standard Model • In this model, the fundamental particles are the leptons, the quarks and the force carriers (photon, W+, W-, Z0, and gluons) • All matter is made up of leptons or quarks • Leptons can only exist as isolated particles • Hadrons (baryons and mesons) are composite particles made of quarks • For every particle there is an anti-particle • Leptons and Baryons obey conservation laws • Every force in nature is due to one of four basic interactions: • Stong, electromagnetic, weak and gravitational • A particle experiences one of these basic interactions if it carries a charge associated with that interaction

13. Properties of the basic interactions

14. Grand Unified Theories (GUTs) • In a GUT, leptons and quarks are considered to be two aspects of a single class of particle • Under certain conditions a quark could change into a lepton and vice-versa • Particle quantum numbers are not conserved • These conditions are thought to have existed in the very early Universe • A fraction of a second after the Big Bang • In this period a slight excess of quarks over anti-quarks existed, which is why there is more matter than anti-matter in out Universe today • One of the predictions of GUTs is that the proton will decay after 1031 years • In order to observe one decay, a large number of protons must be observed • Such experiments are being attempted

15. Crib sheet(or what you need to know to pass the exam) • The zoo of particles and their properties • Leptons (e-, m-, p-, ne , nm, np) • Hadrons (baryons and mesons) • Their anti-particles • The conservation laws and how to apply them (energy, momentum, baryon number, lepton numbers, strangeness) • Quarks and their properties • Flavors: up, down, strange, charm, top ,bottom • How to combine quarks to form baryons and mesons • Quark spin and color • The eight-fold way patterns • Fundamental forces and field particles • The standard model • And from special relativity, its important to understand the concepts of rest mass and energy, and the equations of conservation of relativistic energy and momentum