lezione 5

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Published on October 15, 2007

Author: Reva

Source: authorstream.com

Leptons, Quarks, Hadrons:  Leptons, Quarks, Hadrons Fermions: the elementary players :  Leptons and quarks form doublets under weak interactions Fermions: the elementary players Quarks Leptons 1st generation The elementary particle families: fermions Leptons:  Leptons Leptons are s = ½ fermions, not subject to strong interactions me < mm < mt Electron e-, muon m- and tauon t- have corresponding neutrinos: ne, nm and nt Electron, muon and tauon have electric charge of e-. Neutrinos are neutral Neutrinos possibly have zero masses For neutrinos only weak interactions have been observed so far Slide4:  Anti-leptons are positron e+, positive muons and tauons and anti-neutrinos Neutrinos and anti-neutrinos differ by the lepton number. For leptons La = 1 (a = e,m or t) For anti-leptons La = -1 Lepton numbers are conserved in any reaction Slide5:  Consequence of the lepton nr conservation: some processes are not allowed..... Lederman, Schwarts, Steinberger Neutrinos Neutrinos cannot be registered by detectors, there are only indirect indications of them First indication of neutrino existence came from b-decays of a nucleus N Slide6:  Muons Where first observed in 1936, in cosmic rays Cosmic rays have two components: Primaries: high-energy particles coming from outer space mostly H2 nuclei 2) Secondaries: particles produced in collisions primaries-nuclei in the Earth atmosphere m’s are 200 heavier than e and are very penetrating particles Electromagnetic properties of m’s are identical to those of electron (upon the proper account of the mass difference) Tauons Is the heaviest of the leptons, discovered in e+e- annihilation experiments in 1975 Slide7:  Electron is a stable particle, while muon and tauon have a finite lifetime: tm = 2.2 x 10-6 s and tt = 2.9 x 10-13 s Muon decay in a purely leptonic mode: Tauon has a mass sufficient to produce even hadrons, but has leptonic decays as well: Fraction of a particular decay mode with respect to all possible decays is called branching ratio (BR) BR of (a) is 17.81% and of (b) is 17.37% Slide8:  Important assumptions: Weak interactions of leptons are identical like electromagnetic ones (interaction universality) 2) One can neglect final state lepton masses for many basic calculations The decay rate for a muon is given by: Where GF is the Fermi constant Substituting mm with mt one obtains decay rates of tauon leptonic decays, equal for (a) and (b). It explains why BR of (a) and (b) have very close values Slide9:  Using the decay rate, the lifetime of a lepton is: Here l stands for m and t. Since muons have basically one decay mode, B= 1 in their case. Using experimental values of B and formula for G, one obtaines the ratio of m and t lifetimes: Again in very good agreement with independent experimental measurements Universality of lepton interaction proved to big extent. Basically no difference between lepton generations, apart from the mass Slide11:  In 1930 Bothe and Becker sent alfa particles against Be, and discovered that from the berillium a neutral radiation, extremely penetrating, comes out 2 years after Joliot and Curie repeated the same experiment and demonstrated that these neutral particles can hit atomic nuclea and extract protons from them The same year Chadwick identified them as particles similar to the protons , but without an electric charge, and call them “neutrons”. The neutron is unstable Crisis around 1930:  Crisis around 1930 Matter is made of: Particles: , e-, p Atoms: Small nucleus of protons surrounded by a cloud of electrons before Pauli: Observations: Nuclear -decay: 3H →3He+e- Slide13:  Pauli: Pauli’s hypothesis Slide14:  What is a b-decay ? It is a neutron decay: Necessity of neutrino existence comes from the apparent energy and angular momentum non-conservation in observed reactions For the sake of lepton number conservation, electron must be accompanied by an anti-neutrino and not a neutrino! Mass limit for can be estimated from the precise measurements of the b-decay: Best results are obtained from tritium decay it gives (~ zero mass) Fermi’s ansatz for -decay (1934):  Fermi’s ansatz for -decay (1934) Gave respectability to Pauli’s ‘neutron’ which was dubbed ‘neutrino’ Energy conservation was restored Observed electron energy spectrum reproduced QED ala Dirac Beta decay At high energies: charged current W exchange e- e- e- e d u W Neutrino’s detected… (1956):  Neutrino’s detected… (1956) Cowan & Reines Cowan nobel prize 1988 with Perl (for discovery of -lepton) Intense neutrino flux from nuclear reactor e+e annihilation -capture e n e+   Power plant (Savannah river plant USA) Producing e Scintillator counters and target tanks Slide17:  An inverse b-decay also takes place: However the probability of these processes is very low. To register it one needs a very intense flux of neutrinos Reines and Cowan experiment (1956) Using antineutrinos produced in a nuclear reactor, possible to obtain around 2 evts/h Acqueous solution of CdCl2 (200 l + 40 kg) used as target (Cd used to capture n) To separate the signal from background, “delayed coincidence” used: signal from n appears later than from e Slide18:  Antineutrino interacts with p, producing n and e+ (b) Positron annihilates with an atomic electron produces fast photon which give rise to softer photon through Compton effect (c) Neutron captured by a Cd nucleus, releasing more photons Scheme of the Reines and Cowan experiment 2m 2m Helicity states:  Helicity states For a massless fermion of positive energy, E = |p| helicity H measures the sign of the component of the particle spin, in the direction of motion: H=+1  right-handed (RH) H=-1  left handed (LH) c is a LH particle or a RH anti-particle Helicity is a Lorentz invariant for massless particles Solutions of Dirac equation are not helicity eigenstates If extremely relativistic, also massive fermions can be described by Weyl equations Slide20:  Helicity: conserved in the relativistic limit for any interaction with Lorentz transformation properties of a vector or axial vector  it applies to: Strong Weak Electromagnetic Mediated by vector or axial vector bosons C.S. Wu (suggestion of Yang & Lee) 60Co  60Ni* + e e in B-field:  C.S. Wu (suggestion of Yang & Lee) 60Co  60Ni* + e e in B-field Parity violation (1957) In weak interactions: Parity ‘maximally’ violated i.e. physics in mirror-world different Up to that time: Physics identical in ‘mirror’ (left-right symmetry: parity) for known interactions Weak interactions :  Weak interactions Incorporation of parity violation in weak interactions (1957) Feynman and Gell-Mann Right Left Spin of neutrino pointing opposite to direction of motion Anti-neutrino’s:  Anti-neutrino’s Davis & Harmer If the neutrino is same particle as anti-neutrino then close to power plant: e + 37Cl  e + 37Ar -615 tons kitchen cleaning liquid -Typically one 37Cl  37Ar per day -Chemically isolate 37Ar -Count radio-active 37Ar decay Reaction not observed: Neutrino-anti neutrino not the same particle Little bit of 37Ar observed: neutrino’s from cosmic origin (sun?) Rumor spread in Dubna that reaction did occur: Pontecorvo hypothesis of neutrino oscillation Nobel prize 2002 (Davis, Koshiba and Giacconi) Flavour neutrino’s:  Flavour neutrino’s Neutrino’s from π→+ identified as  ‘Two neutrino’ hypothesis correct: e and  Lederman, Schwartz, Steinberger (nobel prize 1987) “For the neutrino beam method and the demonstration of the doublet structure of the leptons through the discovery of the muon neutrino” LEP (1989-2000):  Determination of the Z0 line-shape: Reveals the number of ‘light neutrinos’ Fantastic precision on Z0 parameters Corrections for phase of moon, water level in Lac du Geneve, passing trains,… LEP (1989-2000) Existence of only 3 neutrinos Unless the undiscovered neutrinos have mass m>MZ/2 Discovery of -neutrino (2000):  Discovery of -neutrino (2000) DONUT collaboration Production and detection of -neutrino’s

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