Leptoni M Cobal PIF 20067 Fermions the elementary

Leptoni M. Cobal, PIF 2006/7

Fermions: the elementary players The elementary particle families: fermions 1 st generation 2 nd generation Why 3 families? Are there more? 3 rd generation 2/3 -1/3 Quarks 0 Leptons -1 M. Cobal, PIF 2006/7 Leptons and quarks form doublets under weak interactions 0 -1

Ø Muons Where first observed in 1936, in cosmic rays Cosmic rays have two components: 1) Primaries: high-energy particles coming from outer space mostly H 2 nuclei 2) 2) Secondaries: particles produced in collisions primaries-nuclei in 3) the Earth atmosphere ’s are 200 heavier than e and are very penetrating particles Electromagnetic properties of ’s are identical to those of electron (upon the proper account of the mass difference) Ø Tauons Is the heaviest of the leptons, discovered in e+e- annihilation experiments in 1975 M. Cobal, PIF 2006/7

Leptons • Leptons are s = ½ fermions, not subject to strong interactions m e < m • Electron e-, muon - and tauon - have corresponding neutrinos: e, and • Electron, muon and tauon have electric charge of e-. Neutrinos are neutral • Neutrinos have very small masses • For neutrinos only weak interactions have been observed so far ATLAS- Marina Cobal Pisa-10/06/03

• 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, or ) For anti-leptons La = -1 • Lepton numbers are conserved in any reaction ATLAS- Marina Cobal Pisa-10/06/03

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 -decays of a nucleus N M. Cobal, PIF 2006/7

• Electron is a stable particle, while muon and tauon have a finite lifetime: = 2. 2 x 10 -6 s and = 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: Ø Fraction of a particular decay mode with respect to all possible decays is called branching ratio (BR) BR of (a) is 17. 84% and of (b) is 17. 36% M. Cobal, PIF 2006/7

Important assumptions: 1) Weak interactions of leptons are identical like electromagnetic ones (interaction universality) 2) 2) One can neglect final state lepton masses for many basic calculations 3) The decay rate for a muon is given by: 4) Where GF is the Fermi constant 5) 6) Substituting m with m one obtains decay rates of tauon leptonic 7) decays, equal for (a) and (b). It explains why BR of (a) and (b) 8) have very close values M. Cobal, PIF 2006/7

Using the decay rate, the lifetime of a lepton is: Here l stands for and . Since muons have basically one decay mode, B= 1 in their case. Using experimental values of B and formula for , one obtaines the ratio of and lifetimes: Again in very good agreement with independent experimental measurements Ø Universality of lepton interaction proved to big extent. Basically no difference between lepton generations, apart from the mass M. Cobal, PIF 2006/7

Flavour M. Cobal, PIF 2006/7 Mass e 0. 511 Me. V 105. 66 Me. V 1777 Me. V

Crisis around 1930 • Matter is made of: – Particles: , e-, p – Atoms: Small nucleus of protons surrounded by a cloud of electrons events before Pauli: Observations: Nuclear -decay: 3 H → 3 He+e- Unique electron energy? Experimental electron energy M. Cobal, PIF 2006/7 electron energy Energy conservation violated?

Pauli’s hypothesis Pauli: M. Cobal, PIF 2006/7 Variable electron energy!

• What is a -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 of the -decay: can be estimated from the precise measurements • Best results are obtained from tritium decay it gives M. Cobal, PIF 2006/7 (~ zero mass)

Neutrino’s detected… (1956) • Cowan & Reines – Cowan nobel prize 1988 with Perl (for discovery of -lepton) • Intense neutrino flux from nuclear reactor Power plant (Savannah river plant USA) Producing e M. Cobal, PIF 2006/7 Scintillator counters and target tanks -capture n e e+ e annihilation e+

• 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) o Using antineutrinos produced in a nuclear reactor, possible to obtain around 2 evts/h o Acqueous solution of Cd. Cl 2 (200 l + 40 kg) used as target (Cd used to capture n) o To separate the signal from background, “delayed coincidence” used: signal from n appears later than from e M. Cobal, PIF 2006/7

2 m Scheme of the Reines and Cowan experiment 2 m (a) Antineutrino interacts with p, producing n and e+ (b) Positron annihilates with an atomic electron produces fast (c) photon which give rise to softer photon through Compton effect (d) (c) Neutron captured by a Cd nucleus, releasing more photons M. Cobal, PIF 2006/7

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 • If extremely relativistic, also massive fermions can be described by Weyl equations M. Cobal, PIF 2006/7

Anti-neutrino’s Nobel prize 2002 (Davis, Koshiba and Giacconi) • Davis & Harmer – If the neutrino is same particle as anti-neutrino then close to power plant: -615 tons kitchen cleaning liquid -Typically one 37 Cl 37 Ar per day -Chemically isolate 37 Ar -Count radio-active 37 Ar decay M. Cobal, PIF 2006/7 • Reaction not observed: – Neutrino-anti neutrino not the same particle – Little bit of 37 Ar observed: neutrino’s from cosmic origin (sun? ) – Rumor spread in Dubna that reaction did occur: Pontecorvo hypothesis of neutrino oscillation e + 37 Cl e + 37 Ar

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” M. Cobal, PIF 2006/7

LEP (1989 -2000) Determination of the Z 0 line-shape: Reveals the number of ‘light neutrinos’ Fantastic precision on Z 0 parameters Corrections for phase of moon, water level in Lac du Geneve, passing trains, … N 2. 984± 0. 0017 MZ 0 91. 1852 0. 0030 Ge. V 2. 4948 0. 0041 M. Cobal, PIFGe. V 2006/7 Z 0 Existence of only 3 neutrinos Unless the undiscovered neutrinos have mass m >MZ/2

Discovery of -neutrino (2000) DONUT collaboration Production and detection of -neutrino’s c Ds M. Cobal, PIF 2006/7 T