Department of Physics and Astronomy Option 212: UNIT 2 Elementary Particles SCHEDULE 26-Jan-15 13.00pm LRB Intro lecture 28-Jan-15 12.00pm LRB Problem solving (2-Feb-15 10.00am E Problem Workshop) 4-Feb-15 12.00pm LRB Follow-up
UNIT 2: OUTLINE SYLLABUS: 1st Lecture Introduction Hadrons and Leptons Spin & Anti-Particles The conservation laws: Lepton Number Baryon number Strangeness 2nd Lecture Problem solving Check a decay for violation of conservation laws Quarks Properties of a particle given quark combination 3rd Lecture Follow-up Fundamental forces and field particles The standard model
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 + + ν e (b) n -> p + π (c) e + + e - -> γ (d) p + p -> γ + γ (e) ν e + p -> n + e + (a) m p < m n : energy conservation is violated. Also L e =0 on lhs, but L e =-2 on rhs (b) m n < m p + m π : energy conservation is violated (c) Momentum conservation is violated: in pair annihilation, two photons (γ rays) must be emitted to conserve momentum (d) Allowed (e) L e =-1 on both sides, but m p < m n so energy conservation violated
Consider the following decay chain: Ω > Ξ 0 + π Ξ 0 > Σ + + e - + ν e π > µ + ν µ Σ + > n + π + π + > µ + + ν µ µ + > e + + ν µ + ν e µ > e - + ν e + ν µ (a) are all the final products stable? (b) write the overall decay reaction for Ω to the final products (c) Check the overall decay reaction for the conservation of electric charge, baryon number, lepton number, and strangeness
(a) neutron is not stable. Lifetime is 930s, compared to 10 31 years for proton. n -> p + + e - + ν e (b) simply add the particles up, including the products of neutron decay Ω > p + + e + + 3e - + ν e + 3ν e + 2ν µ + 2ν µ (c) check answer to (b) for conservation of charge, baryon number, lepton numbers, and strangeness. Find all conserved except strangeness -3 -> 0 In fact, ΔS = +/-1 is allowed in a decay that occurs via weak interaction (Tipler p.1321)
True or false? (a) Leptons consist of three quarks (b) Mesons consist of a quark and an antiquark (c) The six flavors of quark are up, down, charmed, strange, left and right (d) Neutrons have no charm (a) False: leptons are fundamental particles e.g e - (b) True (c) False: there is no left and right quark, but there are top and bottom quarks (d) True: neutrons are made of udd quarks
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
Quark color Consider the Ω particle, which consists of three strange quarks Remember that quarks have spin ½ The Ω - 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 ( q r, q y, q b ) In a meson, a red quark and its anti-red quark attract to form the particle
Field Particles In addition to the six fundamental leptons (e -, µ, τ, ν e, ν µ, ν τ ) and six quarks, there are field particles associated with the fundamental forces (weak, strong, gravity and electromagnetic) 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
Field Particles The weak force, which is experienced by quarks and leptons, is carried by the W +, W -, and Z 0 Bosons These have been observed and are massive (~100 GeV/c 2 ) 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)
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 Bosons: W +, W -, W 0, and B 0 The W 0 and B 0 cannot be observed directly But at ordinary energies they combine to form either the Z 0 or the massless photon In order to work, electroweak theory requires the existence of a particle called the Higgs Boson The Higgs Boson was expected have a rest mass up to > 1TeV/c 2 Head-on collisions between protons at energies ~20TeV are required to produce a Higgs Boson.Such energies can only be achieved by particle accelerators like the Large Hadron Collider at CERN The Higgs Boson was found in July 2012 at CERN with a rest mass ~ 126 GeV/c 2
The Standard Model 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 - & Z 0 Bosons 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: Strong, electromagnetic, weak and gravitational A particle experiences one of these basic interactions if it carries a charge associated with that interaction
Properties of the basic interactions Gravity Weak Electromagnetic Acts on Mass Flavor Electric charge Strong Color Particles participating All Quarks, leptons Electrical ly charged Quarks, Hadrons Mediating particle Graviton W +, W -, Z 0 Photon Gluon
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 10 31 years In order to observe one decay, a large number of protons must be observed Such experiments are being attempted
Crib sheet (or what you need to know to pass the exam) The zoo of particles and their properties Leptons (e -, µ, τ, ν e, ν µ, ν τ ) 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