Leptoni

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

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

Leptons me < mm < mt 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 have very small masses For neutrinos only weak interactions have been observed so far

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

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

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 17.84% and of (b) is 17.36%

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

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

Flavour Mass e 0.511 MeV m 105.66 MeV t 1777 MeV

Crisis around 1930 Observations: before Pauli: Nuclear -decay: 3H →3He+e- Matter is made of: Particles: , e-, p Atoms: Small nucleus of protons surrounded by a cloud of electrons Energy conservation violated? Unique electron energy? before Pauli: Experimental electron energy  electron energy  events

Pauli’s hypothesis Variable electron energy! Pauli:

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)

Neutrino’s detected… (1956) Cowan & Reines Cowan nobel prize 1988 with Perl (for discovery of -lepton) Intense neutrino flux from nuclear reactor Scintillator counters and target tanks Power plant (Savannah river plant USA) Producing e -capture  n e+e annihilation e 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) 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

Scheme of the Reines and Cowan experiment 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

Helicity states For a massless fermion of positive energy, E = |p| 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

(Davis, Koshiba and Giacconi) 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: 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 -615 tons kitchen cleaning liquid -Typically one 37Cl  37Ar per day -Chemically isolate 37Ar -Count radio-active 37Ar decay e + 37Cl  e + 37Ar

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,… N 2.984±0.0017 MZ0 91.18520.0030 GeV Z0 2.4948 0.0041 GeV 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 ct t t Ds nt nT nt