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Quark Flavour Quantum Numbers Y2 Neutrino Physics (spring term 2016) Lecture 2 Fundamental particles and interactions Dr E Goudzovski [email protected] http://epweb2.ph.bham.ac.uk/user/goudzovski/Y2neutrino Previous lecture The natural system of units (ħ=c=1) is used in particle physics: all quantities are expressed in powers of energy (GeV). By the Heisenberg’s uncertainty principle, momentum required to probe a distance scale is p 1/ (in natural units). Particle accelerators are the most powerful microscopes. Elementary particles often travel at speeds close to c: relativistic (rather than classical) kinematics applies. Lorentz-invariance and conservation of the 4-momenta provide a useful tool to solve simple kinematic problems (reaction thresholds, accelerator energy reach, etc.) 1 This lecture Introduction to particle physics (continued) The fundamental particles: quarks and leptons. Forces, their strengths and ranges. Internal quantum numbers and conservation laws. Feynman diagrams. Examples of electromagnetic processes. Textbooks: B.R. Martin and G. Shaw. Particle physics. Chapters 1, 2, 8. D. Perkins. Introduction to high energy physics. Chapters 1, 2. D. Griffiths. Introduction to Elementary Particles. Chapters 1, 2. 2 Fermions: 1st generation Point-like spin-1/2 fundamental fermions (1) Leptons: Electron (e ) and its neutrino (e). Particle Symbol Electric Type charge (q) (2) Quarks: Electron e 1 Up (u) and down (d). Lepton They form bound states (hadrons), Neutrino e 0 e.g. nucleons (p, n). Up quark u +2/3 Quark Down quark d 1/3 Proton (q=+1) Neutron (q=0) Example: the nuclear beta decay …at the nuclear level: Beta decay …at the nucleon level: …at the fundamental fermion level: 3 Fermions: the 3 generations st nd rd 1 generation 2 generation 3 generation Electrical charge (q) Electron e Muon Tauon 1 Electron neutrino e Muon neutrino Tau neutrino 0 Up quark u Charm quark c Top quark t +2/3 Down quark d Strange quark s Bottom quark b 1/3 Higher generations: Copies of (e , e, u, d). Undergo identical interactions. The principal difference among the generations: masses. Generations are successively heavier. Therefore particles of higher generations are unstable. 6 Example: (mean lifetime ~10 s) Why exactly three generations? We do not know. 4 Fermion mass spectrum TeV 197Au nucleus eV H O molecule Composite 2 objects Quarks p,n GeV Mass, Leptons MeV keV eV Generations 5 Antimatter Antimatter: antiparticles of “ordinary” particles. Positron (e+) track Predicted within relativistic field theory (for fermions: P. Dirac, 1929; Nobel prize 1933) First antiparticle discovered: the positron (e+) (C. Anderson, 1932; Nobel prize 1936) Compared to its matter partner, an antiparticle has: Pb plate equal mass and spin; opposite electric charge; Cloud chamber photograph opposite internal quantum numbers. of the first identified positron Track curvature: due to magnetic field. Baryon asymmetry: antimatter does not exist in large Direction: change of curvature quantities in the observable Universe. when crossing the Pb plate. (Baryon = bound state of 3 quarks, e.g. proton, neutron) The charge can then be inferred. Antiparticles of the first generation fermions: Examples for hadrons: 6 Interactions (forces) Classical description of interactions: Field of a source charge acting on other charges. Force is proportional to field intensity. Quantum field theory description: Discontinuous exchange of “virtual” field quanta (gauge bosons). Force = rate of exchange of momentum. Interaction Couples to; Boson mass Comment [GeV/c2] gauge boson(s) Mass; Negligible on Gravity 0 graviton G (?) particle physics scale Electromagnetic Electric charge; (almost all extranuclear 0 phenomena) photon All fundamental Weak Massive carriers: (e.g. nuclear beta-decays, fermions; 80.4, 91.2 limited range nuclear fusion) W, Z0 Colour (r, g, b); Gluon charge: rg, etc. Strong 0 (binds nucleons in nuclei) 8 gluons Self-coupling of gluons. Gravity vs electrostatic force Gravitational attraction vs Coulomb repulsion between two protons: (SI units) ~1036 [the hierarchy problem] However gravity must be weak for a complex universe to exist Q: Why is gravity dominant in everyday experience? A: Matter is electrically neutral: cancellation of attraction and repulsion. Gravity is cumulative: no repulsion no cancellation. The weak and strong forces have limited (sub-atomic) range. 8 Standard Model vertices NC = neutral current CC = charged current 9 Ranges of forces Neutron decay: Heisenberg’s uncertainty principle: Et ~ ħ. p(u) Massive force carrier limited range. Range of the weak force: n(d) W e R ct ħc / M weak W 200 MeV fm / 80 GeV 2×103 fm. e (proton radius Rp= 0.9 fm ≫ Rweak) Force Relative strength Range (fm) Strong (hadrons) 1 ~1 Electromagnetic ~102 ∞ Weak ~107 ~103 Gravity ~1039 ∞ 10 Internal quantum numbers Discrete (quantized) quantities conserved in fundamental interactions: widely known: the electric charge. But there are others: lepton family (flavour) numbers; total lepton number; quark flavour numbers; baryon number. 11 Lepton numbers (1) Lepton family (or lepton flavour) numbers (electronic number) (muonic number) (tauonic number) and the total lepton number are conserved in all known interactions (not a fundamental conservation law: its origin is a puzzle) Examples: 1) Violation of lepton flavour: [MEG experiment, PSI, Switzerland: Phys.Rev.Lett.110 (2013) 201801] 2) Violation of lepton number: [NA48/2 experiment, CERN, Switzerland: Phys.Lett.B697 (2011) 107] 3) Free neutron decay Allowed: lepton flavour is conserved by the anti-neutrino emission. 12 Baryon number (2) The baryon number is conserved in all interactions. Particles not formed of quarks (leptons, gauge bosons) have B=0. Mesons (quark-antiquark bound states) have B=0. Examples: 1) The proton (p = uud) is the lightest baryon and is therefore stable. Experimentally, (The age of Universe: ~ 1010 years) 2) Nucleon decays violating baryon number: never observed. FORBIDDEN: 13 Quark flavour (3) Quark flavour quantum numbers: (“strangeness”) (“charm”) (“bottomness”) (“topness”) are conserved in strong and electromagnetic interactions (convention: flavour number and electric charge have the same sign) Example: A number of strange particles (discovered in cosmic rays in 1947) are produced in pairs via the strong interaction (~1023 s), e.g. but decay “slowly” (~1010 s) via the weak interaction (with strangeness not conserved), e.g. 14 Feynman diagrams Quantum field theories: interactions between particles proceed discontinuously by exchange of mediator particles. A+B C+D Amplitude of a boson-mediated process (in natural units): A C space ga virtual “mediator” x particle • ga, gb: the fundamental gb coupling strengths at the vertices; B D • Squared momentum transfer (pA, pB, pC and pD are 4-vectors): 2 2 2 q = (pC pA) = (pD pB) ; 2 2 initial “how the final • 1/(q mx ): the boson propagator. state interaction state happened” The reaction rate is proportional to |A|2 time 15 Electromagnetic processes (1) Force carrier: photon (). Squared coupling constant (the fine structure constant): Example 1: e+e annihilation to photons e+ e e + e e In general, is process of order (n2) Higher-order electromagnetic processes are suppressed QED is a “perturbative theory”: very precise predictions 16 Single photon emission Q: Are e+e annihilation and + e e pair production (photon conversion) processes involving real (rather than virtual) photons allowed? e+ e A: The photon is a massless: E = p in any reference frame. + + + + In e e COM frame, p(e e ) = 0; E(e e ) = m(e e ) 2me > 0. + + Therefore, E(e e ) > p(e e ), contradicting E = p. Both processes are forbidden by energy-momentum conservation. 17 Electromagnetic processes (2) Example 2: e+e pair production (photon conversion) is allowed in the field of a nucleus (energy-momentum conserved due to nuclear recoil) Reaction rate: e+ (Z: electric charge of the nucleus) The dominant photon interaction process at e high energies (E>100MeV); Z-dependence is exploited for photon detection N N (e.g. Pb calorimeter pre-showers) Example 3: Bremsstrahlung e e is also allowed in the presence of a nucleus Reaction rate: N N Practical uses: e.g. X-ray generation in medical imaging 18 Summary The known matter is composed of 3 generations of fundamental fermions (leptons, quarks) and corresponding anti-particles. “Normal” matter is composed of 3 particle types: u, d, e. Four fundamental interactions are known. Their ranges and strengths are vastly different. QFT interactions = discontinuous exchange of field quanta. Internal quantum numbers: (a) lepton and baryon numbers: conserved in all interactions; (b) quark flavour numbers: conserved in all but weak interactions. Feynman diagrams are a powerful tool for qualitative predictions. Examples of electromagnetic processes: e+e annihilation, bremsstrahlung, photon conversion. 19 .
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