Transcript Neutrinos

Leptoni
M. Cobal, PIF 2006/7
Fermions: the elementary players
The elementary particle families: fermions
1st generation
2nd generation
Why 3 families?
Are there more?
3rd generation
2/3
2/3
-1/3
-1/3
Quarks
0
Leptons
-1
M. Cobal, PIF 2006/7
Leptons and
quarks
form doublets
under weak
interactions
0
-1
 Muons
Where first observed in 1936, in cosmic rays
Cosmic 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
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
• Leptons are s = ½ fermions, not subject to strong interactions
n e   n m  n t 
     
 e   m  t 
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
 e 
 
n e 
m 
 
n 
 m
t  
 
n t 
• 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
Lepto n
e
ne
m
nm
lepto n n u m b er
electro n n u m b er
m u o n n u m b er
1
1
0
1
1
0
1
0
1
1
0
1
Consequence of the lepton nr conservation:
some processes are not allowed.....
n e  n  p  e  Yes
n e  n  p  e  No
m   e  
No
n m  p  m   n Yes
n m  p  e  n
No
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
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:
tm = 2.2 x 10-6 s and tt = 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) t   e  n e n t
(b) t   m  n m 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%
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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:
2 5
G
F mm


( m  e  n e  n m ) 
195 3
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
M. Cobal, PIF 2006/7
Using the decay rate, the lifetime of a lepton
is:
B(l   e n en l )
tl 
(l   e n en 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:
5
 mm 
tt
  1.3 107
 0.178  
tm
 mt 
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
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Flavour
M. Cobal, PIF 2006/7
Mass
e
0.511 MeV
m
105.66 MeV
t
1777 MeV
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 b-decay:
3H
→3He+e-
Unique electron
energy?
Experimental
electron
energy
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 electron energy
Energy
conservation
violated?
Pauli’s hypothesis
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
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
n

p

e
n e
• 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 n e can be estimated from the precise measurements
of the b-decay:
me  Ee  M N  mn
e
• Best results are obtained from tritium decay
3
it gives
H 3He  e  n e
mn e  2 eV / c2 (~ zero mass)
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Neutrino’s detected… (1956)
• Cowan & Reines
– Cowan nobel prize 1988
with Perl (for discovery
of t-lepton)
• Intense neutrino flux from
nuclear reactor
n e  p  n  e
Scintillator
counters and
target tanks
followed by
e  e    
Power plant
(Savannah river
plant USA)
Producing ne
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n-capture

n
ne
e +e 
annihilation
e+


• An inverse b-decay also takes place: n e  n  e  p
or
n e  p  e  n
• 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
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2m
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
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Helicity states
 
For a massless fermion of positive energy, E = |p|   p    
p
 
p
helicity
H    1
p
H measures the sign of the component of the particle
spin, in the direction of motion: jz  1 / 2
H=+1  right-handed (RH)
H=-1  left handed (LH)
 
E    p
 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:
n e  p   e  n
ne  n

e  p

37
n e  37
17 Cl  e  18 Ar
-615 tons kitchen cleaning liquid
-Typically one 37Cl  37Ar per day
-Chemically isolate 37Ar
-Count radio-active 37Ar decay
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• 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
ne + 37Cl  e + 37Ar
Flavour neutrino’s
• Neutrino’s from π→m+n identified as nm
– ‘Two neutrino’ hypothesis correct: ne and nm
– 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”
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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,…
Nn
2.984±0.0017
MZ0
91.18520.0030 GeV
 Z0
2.4948 0.0041 GeV
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Existence of only 3 neutrinos
Unless the undiscovered
neutrinos have mass mn>MZ/2
Discovery of t-neutrino (2000)
DONUT collaboration
ct
Production and detection of t-neutrino’s
t
s
t
nt
nt
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nT