M. Cobal, PIF 2006/7

Leptoni

M. Cobal, PIF 2006/7

Leptons and quarks form doubletsunder weakinteractions

Fermions: the elementary players

Quarks

Leptons

2/3

-1/3

0

-1

1st generation 2nd generation

The elementary particle families: fermions

3rd generation

2/3

-1/3

0

-1

Why 3 families?Are there more?

M. Cobal, PIF 2006/7

MuonsWhere first observed in 1936, in cosmic raysCosmic rays have two components:

1) Primaries: high-energy particles coming from outer space mostly H2 nuclei

2) Secondaries: particles produced in collisions primaries-nuclei in

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)

TauonsIs the heaviest of the leptons, discovered in e+e- annihilationexperiments in 1975

Leptons• Leptons are s = ½ fermions, not subject to strong interactions

me < m < 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

ee

• Anti-leptons are positron e+, positive muons and tauons and anti-neutrinos

• Neutrinos and anti-neutrinos differ by the lepton number. For leptons L = 1 ( = e, or ) For anti-leptons L = -1 • Lepton numbers are conserved in any reaction

e

e

101

101

011

011

ee

numbermuonnumberelectronnumberleptonLepton

M. Cobal, PIF 2006/7

Nonep

Yesnp

Noe

Noepn

Yesepn

e

e

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 eeAZNAZN ),1(),(

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:

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%

ee

)(

)(

b

ea e

M. Cobal, PIF 2006/7

Important assumptions:

1) 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 m with mone obtains decay rates of tauon

leptonic decays, equal for (a) and (b). It explains why BR of (a) and (b) have very close values

3

52

195)(

mGe F

e

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

Universality of lepton interaction proved to big extent. Basically no difference between lepton generations, apart from the mass

)(

)(

le

lel el

elB

7

5

103.1178.0

m

m

M. Cobal, PIF 2006/7

Flavour Mass

e 0.511 MeV

105.66 MeV

1777 MeV

M. Cobal, PIF 2006/7

Crisis around 1930• Matter is made of:

– Particles: , e-, p – Atoms: Small nucleus of

protons surrounded by a cloud of electrons

before Pauli:

Unique electron energy?

Experimentalelectronenergy

electron energy

e

ven

ts

Observations:Nuclear -decay:

3H →3He+e-

Energy Energy conservationconservationviolated?violated?

M. Cobal, PIF 2006/7

Pauli: Variable electron energy!

Pauli's letter of the 4th of December 1930

Dear Radioactive Ladies and Gentlemen,

As the bearer of these lines, to whom I graciously ask you to listen, will explain to you in more detail, how because of the "wrong" statistics of the N and Li6 nuclei and the continuous beta spectrum, I have hit upon a deseperate remedy to save the "exchange theorem" of statistics and the law of conservation of energy. Namely, the possibility that there could exist in the nuclei electrically neutral particles, that I wish to call neutrons, which have spin 1/2 and obey the exclusion principle and which further differ from light quanta in that they do not travel with the velocity of light. The mass of the neutrons should be of the same order of magnitude as the electron mass and in any event not larger than 0.01 proton masses. The continuous beta spectrum would then become understandable by the assumption that in beta decay a neutron is emitted in addition to the electron such that the sum of the energies of the neutron and the electron is constant... … Unfortunately, I cannot appear in Tubingen personally since I am indispensable here in Zurich because of a ball on the night of 6/7 December. With my best regards to you, and also to Mr Back. Your humble servant . W. Pauli

Pauli’s hypothesis

M. Cobal, PIF 2006/7

• 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 can be estimated from the precise measurements of the-decay:

• Best results are obtained from tritium decay

it gives (~ zero mass)

eepn

e

emMEm Nee

eeHeH 33

2/2 ceVme

M. Cobal, PIF 2006/7

Neutrino’s detected… (1956)• Cowan & Reines

– Cowan nobel prize 1988with Perl (for discovery of -lepton)

• Intense neutrino flux from nuclear reactor

ee

enpe

by followed

e+e

annihilation

-capture

e

n

e+

Power plant(Savannah river plant USA)Producing e

Scintillator counters and target tanks

M. Cobal, PIF 2006/7

• An inverse -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 CdCl2 (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

nep

or

pen

e

e

M. Cobal, PIF 2006/7

(a) 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 experiment2

m

2m

M. Cobal, PIF 2006/7

Helicity states

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

1

p

pH

p

p

helicity

H measures the sign of the component of the particlespin, in the direction of motion: H=+1 right-handed (RH) H=-1 left handed (LH)

2/1zj

pE

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

• Davis & Harmer– If the neutrino is same

particle as anti-neutrino then close to power plant:

Ar Cl

3718

3717

e

pen

nep

e

e

e

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)

M. Cobal, PIF 2006/7

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

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)

N 2.984±0.0017

MZ0 91.18520.0030 GeV

Z0 2.4948 0.0041 GeV

Existence of only 3 neutrinosUnless the undiscovered neutrinos have mass m>MZ/2

M. Cobal, PIF 2006/7

Discovery of -neutrino (2000)

DONUT collaborationProduction and detection of -neutrino’s

c

s