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The Elementary Particles
e−
e−
γ γ
u
u
γ
d
d
The Basic Interactions of Particles
g
u, d
u, d
W+
u
d
Z0
u, d
u, dν
ν
Z0
e−
e−
Z0
e−
νe
W+
Electromagnetic Force
Strong Nuclear Force
Weak Nuclear Force
Charged Current
Neutral Current
W
e−
νe
W++u
d
+
e−
νe
This diagram represent process such as:
β decay: n → p + e− + νe
Inverse β decay: p + νe → e+ + n
Pion decay: π+ → μ+ + νμ
tim
e
u
d e+
νe
u
u d
dn
p u
μ+ νμ
dπ+
Processes Involving NeutrinosCharged Current
u
d
e− νeu
u d
d
n
p
Processes Involving NeutrinosNeutral Current
u, d, e, ν
u, d, e, ν ν
ν
Z0
particle
νν
Z0
antiparticlee− e+
LEP Collider
e+
e−
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.
Number of Neutrinos
Neutrino SourcesCosmic Rays
Neutrino SourcesAccelerators
Earth Shielding:
Stops particles that are not neutrinos
Decay region: →, K→
50 m decay pipeFNAL 8 GeV Booster
n
p
Toroidal Magnet
Target and toroidal focusing magnet Detector
Z
N
N=Z
U235
92
Cs140
55
Rb94
37
Typical Fission
Nuclear reactors are a very intense sources of νe coming from the b-decay of the neutron-rich fission fragments.
A commercial reactor, with 3 GW thermal power, produces 6×1020 νe/s
Neutrino Sources
Know Isotopes
Nuclear Reactors
Neutrino SourcesThe Sun
Solar Fusion Processes
The sun produces νe as a by-product of the fusion process that fuel it.
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
Electron capture isotopes produce a mono-energetic beam of neutrinos
Big Bang relic neutrino are as copious as photons, but they are so low in energy that no one knows how to see them
ee NN A
1ZAZ
ee NN A1Z
AZ
ee NN A
1ZatomicAZ
Important Experiments
HOMESTAKE
Solar Neutrinos
Homestake: νe (E>814 keV) + 37Cl → e− + 37Ar
SAGE and Gallex: νe (E>234 keV) + 71Ga→ e− + 71Ge
Radiochemical solar neutrino experiments are designed to count neutrinos above the reaction threshold
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.
Important ExperimentsAtmospheric Neutrinos
Super-Kamiokande
Kamiokande and later Super-Kamiokande detect neutrinos produced by cosmic rays in the atmosphere from all around the world.
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
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.
Now and
2
1
cosθsinθ
sinθcosθ
e
νμ
ν2 ν1
νeθ
21 sinθcosθ e 21 θcosθsin-
Follow the prescription of quantum mechanics:
• The ν’s are “Wave Functions”
• Their evolution in time is given by the Schrödinger Equation…
• This is the “Oscillation Probability”
• It has constant amplitude piece: sin22θ
• And an oscillatory piece:
Δm212 = m1
2-m22 (Not only need mass, but different masses!)
E
LmP e 4
θsin2sin)(21222
21 θsinθcos)0(
te
How Does Neutrino Mass Lead to Oscillations?
21 θsinθcos)( 21 tiEtiE eet
Hdt
di
Schrödinger's Equation
E
Lm
4sin
2122
ν
ν
pmpE ii 2
Ep
ν
ν
2)(tP
ν
ν
ctL
3
2
1
τ3τ2τ1
μ3μ2μ1
e3e2e1
τ
μ
e
ν
ν
ν
UUU
UUU
UUU
ν
ν
ν
100
0θcosθsin
0θsinθcos
θcos0θsin
010
θsin0θcos
θcosθsin0
θsinθcos0
001
1212
1212
1313
1313
2323
2323
i
i
MNS
e
e
U
Generalizing for Three Neutrinos
For three neutrinos just add another dimension to the mixing matrix
It can be parameterized in terms of three rotation (mixing) angles: θ12, θ13 and θ23
There are three corresponding mass squared differences: Δm12
2, Δm132 and Δm23
2
Important ExperimentsMore 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
νee−
e−
W−
ν
Z0
ν e−
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 ExperimentsMore “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.
Neutrino Oscillation Data
sin22θ
Δm
2 (
eV2 )
Atmospheric (θ23)
Solar (θ12)
7.07.0
6.06.0
4.0
4.0
2.05.0
~
8.0MNSU
Two of the three mixing angles are known. Only θ13 is unknown.
ν3
ν2ν1
Dm232
Dm122
Dm132 ≈ Δm12
2 + Δm232
ν3
ν2ν1
Dm22
Dm12
mas
s2
Other Unknowns and Big QuestionsThe absolute mass scale:
Oscillation experiment are sensitive to the differences between mass2, but not the actual masses
ν3
Dm22
ν2ν1
Dm12
mas
s2
Other Unknowns and Big QuestionsThe mass hierarchy:
Not knowing the absolute mass of the mass eigenstates means that we don’t know which is heaviest
ν3
Dm22
ν2ν1
Dm12
mas
s2
ν3
Dm22
ν2ν1
Dm12
mas
s2
Normal Hierarchy Inverted Hierarchy
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