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The Elementary Particles
The Basic Interactions of Particles
e−
u
γ
d
γ
γ
e−
uWeak Nuclear Force d
u, d
d
e−
Electromagnetic Force
Charged Current
g
Strong Nuclear Force
W+
u Neutral Current
u, d
e−
ν
Z0
e−
W+
νe
u, d
Z0
ν
Z0
u, d
Processes Involving Neutrinos
e−
d
W+
Charged Current
e−
+
u
This diagram represent process such as:
W+
νe
νe
np μ+
u d du
e−
νμ
eν+e
time
β decay: n → p + e− + νe
Inverse β decay: p + νe → e+ + n
Pion decay: π+ → μ+ + νμ
u d du
u
np
π+
νe
d
Processes
Involving
Neutrinos
Number
of Neutrinos
Neutral Current
u, d, e, ν
ν
ν
ν
Z0
e+
u, d, e, ν
Z0
e−
ν
particle
e−
antiparticle
e+
LEP Collider
The natural width (in mass) of a short lived
particle is determined in part by how many decay
channels it has available to it. The Z0 width
unaccounted for in seen decay modes is consistent
with exactly three neutrino states.
Neutrino Sources
Cosmic Rays
Neutrino Sources
Accelerators
50 m decay pipe
FNAL 8 GeV Booster
p
Decay region:
→, K→
Target and toroidal
focusing magnet

Earth Shielding:
Toroidal Magnet
Stops particles that
are not neutrinos
Detector
Neutrino Sources
Nuclear Reactors
Nuclear reactors are a very intense
sources of νe coming from the bdecay of the neutron-rich fission
fragments.
Know Isotopes
Z
235
92
140
55
94
37
Rb
Cs
U
Typical
Fission
N
A commercial reactor,
with 3 GW thermal
power, produces
6×1020 νe/s
Neutrino Sources
Solar Fusion Processes
The sun produces νe as a by-product
of the fusion process that fuel it.
The Sun
Other Neutrino Sources
Supernova produce a huge burst of neutrinos as all the protons
in the star are converted to neutrons to form a neutron star.
β-decay isotopes can be used as a source of neutrinos or
antineutrinos
A
A


N

N

e
 e
Z
Z 1
A
Z
N ZA1 N  e    e
Electron capture isotopes produce a mono-energetic beam of
neutrinos
A

A

N

e

Z
atomic
Z 1 N   e
Big Bang relic neutrino are as copious as photons, but they are
so low in energy that no one knows how to see them
Important Experiments
Solar Neutrinos
Radiochemical solar neutrino experiments are designed to count neutrinos above
the reaction threshold
Homestake:
νe (E>814 keV) + 37Cl → e− + 37Ar
SAGE and Gallex:
νe (E>234 keV) + 71Ga→ e− + 71Ge
The resulting isotope is chemically separated and
counted when they decay.
Homestake saw only 33% of the expected solar
neutrinos.
While SAGE and Gallex found about 75% of the
expected neutrinos.
HOMESTAKE
Important Experiments
Kamiokande and later Super-Kamiokande detect
neutrinos produced by cosmic rays in the
atmosphere from all around the world.
Atmospheric Neutrinos
They see the Čerenkov rings produced by the
charged leptons as they emerge inside the
detector from the neutrino charged current
interaction.
In the atmosphere, two νμ are produced for each
νe. This 2:1 ratio was observed for neutrinos
coming from directly above the detector where
the upper atmosphere is only 30 km away, but
from te other side of the Earth the rate was much
lower
Super-Kamiokande
Oscillations and Neutrinos Mass
Remember: there are three flavors of neutrinos (νe, νμ and ντ), so we might
expect three different masses (m1, m2 and m3)
But neutrinos are quantum mechanical particles → They behave in strange
ways
For example: the masses and flavors don’t have to be aligned. In fact, the
masses form a second basis
In quantum mechanics this happens a lot. We use the linear algebra for
the rotation of vectors to handle this.
ν2
Now
νμ
ν1
θ
νe
and
 e  cosθ 1  sinθ 2
 e   cosθ sinθ  1 
   
   sinθ cosθ  
 2 
  
   - sin θ 1  cos θ 2
How Does Neutrino Mass Lead to Oscillations?
Follow the prescription of quantum mechanics:
• The ν’s are “Wave Functions”
• Their evolution in time is given by the Schrödinger
Equation…
ν
ν
ν
Schrödinger's
Equation
2 p  m 2p

  iE2 2t Em
  i  
L
i 
d
 iE1t 
2
12

2 cos
((0t)e) 
e  θ) 
cos
 12θθsin
e2 isin θ 2 H
 e (t P
θsin
1 sin
LProbability”
 ct  dt4E p  E
P “Oscillation
 (t )
• This is the




 
• It has constant amplitude piece: sin22θ

ν
2
ν



m
2
12 L

• And an oscillatory piece: sin 
 4E 
ν
Δm212 = m12-m22 (Not only need mass, but different masses!)
Generalizing for Three Neutrinos
For three neutrinos just add another dimension to the mixing
matrix
 ν e   U e1 U e2 U e3  ν1 
  
 
 ν μ    U μ1 U μ2 U μ3  ν 2 
 ν   U U U  ν 
 τ   τ1 τ2 τ3  3 
It can be parameterized in terms of three rotation (mixing)
angles: θ12, θ13 and θ23
0
0   cos θ13
0 e i sin θ13   cos θ12 sin θ12 0 
1
 

 

1
0
    sin θ12 cos θ12 0 
U MNS   0 cos θ 23 sin θ 23    i 0
  0
 0  sin θ
  e sin θ 0

cos
θ
cos
θ
0
1
23
23  
13
13  


There are three corresponding mass squared differences:
Δm122, Δm132 and Δm232
Important Experiments
More Solar Neutrinos
SNO used a heavy water (D2O) target to
measure the solar flux with neutral current
(NC), charges current (CC) and elastic
scattering (mixed NC and CC)
CC: νe + d → e− + p + p
NC: ν + d → ν + p + n
ES: ν + e− → ν + e−
They definitively showed that some of the
solar neutrinos, which began life as νe, where
interacting in the SNO detector as νμ and ντ.
ν-e Elastic Scattering
νe
e−
ν
Z0
W−
e−
e−
νe
ν
e−
For electron neutrinos elastic scattering is part charged current and part neutral
current, while for νμ and ντ it is pure neutral current. This results in a 6 times
larger probability of elastic scattering for νe.
Elastic scattering with a very low momentum transfer (forward scattering) has
a very high probability. This causes a “drag” on neutrinos as they pass through
matter. This drag is greater on νe causing accelerated mixing which is a
function of electron density. This is know as the matter effect (or MSW effect)
and it is the dominant oscillation effect in the dense solar core.
Important Experiments
More “Solar” Neutrinos
The KamLAND experiment used neutrinos from all of the
nuclear reactors in Japan and Korea (flux averaged baseline of
180 km and average energy of 3 MeV) to study oscillations at
the solar neutrino Δm2.
Neutrinos were detected with inverse β-decay in scintillator.
Δm2 (eV2)
Neutrino Oscillation Data
U MNS
Atmospheric (θ23)
 0.8 0.5

~  0.4 0.6

 0.4 0.6



0.7 

0.7 
 0.2
ν3
m232
Solar (θ12)
sin22θ
ν2
ν1
m122
m132 ≈ Δm122 + Δm232
Two of the three mixing angles are known. Only θ13 is unknown.
Other Unknowns and Big Questions
The absolute mass scale:
Oscillation experiment are sensitive to the differences
between mass2, but not the actual masses
mass2
ν3
m22
ν2
ν1
m12
Other Unknowns and Big Questions
The mass hierarchy:
Not knowing the absolute mass of the mass eigenstates
means that we don’t know which is heaviest
ν3
mass2
mass2
ν3
ν2
ν1
Normal Hierarchy
m22
m22
ν2 2
m
ν11
m12
Inverted Hierarchy