M. Cobal, PIF 2006/7

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

 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) 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
M. Cobal, PIF 2006/7

• Leptons are s = ½ fermions, not subject to strong interactions

 n e e
 m e



 n m
< m m
 m


< m

 n t t t



• Electron e , muon m and tauon t have corresponding neutrinos: n e
, n m and n t
• 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


 e n
 e





 m n m






 t n t




• Neutrinos and anti-neutrinos differ by the lepton number.
For leptons L a
= 1 ( a = e, m or t )
For anti-leptons L a
= -1
• Lepton numbers are conserved in any reaction
Lepton e
 n m e n m lepton
 number
1
1
1
1 electron
 number
1
1
0
0 muon
 number
0
0
1
1

Consequence of the lepton nr conservation: some processes are not allowed.....
n n n n m m e
 e m



 n n p


 e
 p
 e
 p

 m


 e

 n p
 e

 n
Neutrinos
Yes
No
No
Yes
No
Lederman, Schwarts, Steinberger
• 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
N ( Z , A )

N ( Z

1 , A )
 e
  n e
M. Cobal, PIF 2006/7

• Electron is a stable particle, while muon and tauon have a finite lifetime: t m
= 2.2 x 10 -6 s and t t
= 2.9 x 10 -13 s
Muon decay in a purely leptonic mode: m   e
  n e
 n m
Tauon has a mass sufficient to produce even hadrons, but has leptonic decays as well:
( a )
( b ) t  t 
 e

 m 
 n e
 n m
 n t
 n t
 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) One can neglect final state lepton masses for many basic calculations
The decay rate for a muon is given by:

( m   e
  n e
 n m
)

G
F
2 m
5 m
195

3
Where G
F is the Fermi constant
Substituting m m with m have very close values t one obtains decay rates of tauon leptonic decays, equal for (a) and (b). It explains why BR of (a) and (b)
M. Cobal, PIF 2006/7

Using the decay rate, the lifetime of a lepton is: t l

B

(
( l l



 e e

 n n e e n n l l
)
)
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  , one obtaines the ratio of m and t lifetimes: t t t m

0 .
178


 m m m t


5

1 .
3

10

7
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
M. Cobal, PIF 2006/7

M. Cobal, PIF 2006/7
e m t
0.511 MeV
105.66 MeV
1777 MeV

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

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 Li 6 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
M. Cobal, PIF 2006/7

• What is a b -decay ? It is a neutron decay : n
 p
 e
  n e
• 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!
of the b -decay: n m e

E e
 
M
N
 m n e
• Best results are obtained from tritium decay
3
H
 3
He
 e
  n e
M. Cobal, PIF 2006/7 m n


• Cowan & Reines
– Cowan nobel prize 1988 with Perl (for discovery of t -lepton)
• Intense neutrino flux from nuclear reactor n e
 p
 n
 e
 followed by e
  e
    
Power plant
(Savannah river plant USA)
Producing n e n e
M. Cobal, PIF 2006/7 n -capture n e +


Scintillator counters and target tanks e + e  annihilation

• An inverse b -decay also takes place: n e
 n
 e
  p or n  p
 e
  n e
• 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 CdCl
2
(Cd used to capture n)
(200 l + 40 kg) used as target o To separate the signal from background, “delayed coincidence” used: signal from n appears later than from e
M. Cobal, PIF 2006/7

Scheme of the Reines and Cowan experiment
2m
(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
M. Cobal, PIF 2006/7

For a massless fermion of positive energy, E = |p| helicity


H

 p
 p






 p
 p
 
 
1
H measures the sign of the component of the particle spin, in the direction of motion:
H=+1  right-handed (RH)
E
   


 p
 j z
 
1 / 2 
H=-1  left handed (LH)
 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

Nobel prize 2002
(Davis, Koshiba and Giacconi)
• Davis & Harmer
– If the neutrino is same particle as anti-neutrino then close to power plant: n e
 p
  e
  n n e
 n
 e
  p n e
 37
Cl
17
 e
  37
18
Ar
-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?) n
– Rumor spread in Dubna that reaction did occur: Pontecorvo hypothesis of neutrino oscillation e
+ 37 Cl  e  + 37 Ar

• Neutrino’s from π → m
+ n identified as n m
– ‘Two neutrino’ hypothesis correct: n e and n m
– Lederman, Schwartz, Steinberger (nobel prize 1987)
M. Cobal, PIF 2006/7

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 n
M
Z0

Z 0
2.984±0.0017
91.1852
2.4948
M. Cobal, PIF 2006/7


0.0030 GeV
0.0041 GeV
Existence of only 3 neutrinos
Unless the undiscovered neutrinos have mass m n
>M
Z
/2

t
collaboration
Production and detection of t -neutrino’s c t t
 s t n t n t
M. Cobal, PIF 2006/7 n
T