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Neutrino Neutrino
PhenomenologPhenomenolog
yy Boris KayserScottish Summer
SchoolAugust 9, 2006 +
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The Neutrino Revolution(1998 – …)
Neutrinos have nonzero masses!
Leptons mix!
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These discoveries come from
the observation of neutrino oscillationneutrino oscillation.
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The Physics of The Physics of Neutrino Oscillation Neutrino Oscillation
The Physics of The Physics of Neutrino Oscillation Neutrino Oscillation
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Neutrinos Come in at Least Three Flavors
The known neutrino flavors: e ,
Each of these is associated with the corresponding charged-lepton flavor: e
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The Meaning of this Association
e Detectore
e
W boson
Short Journey
e
W
W
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Over short distances, neutrinos do not change flavor.
W
Short Journey
Does Not Occur
But if neutrinos have masses, and leptons mix, neutrino flavor changes
do occur during long journeys.
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Let Us Assume Neutrino Masses and Leptonic
MixingNeutrino mass —
There is some spectrum of 3 or more neutrino mass eigenstates i:
(Mass)2
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Mass (i) mi
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Leptonic mixing —
When W+ l+ + ,
the produced neutrino state |> is
|> = U*i |i> .
Neutrino of flavor Neutrino of definite mass mi
Leptonic Mixing Matrix
le e, l , l
e, , or
i
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Another way to look at W decay:
A given l+ can be accompanied
by any i.Amp(W+ l+ + i) = U*i
is |> = U*i |i> .
The neutrino state |> produced together with l
+ i
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According to the Standard Model, extended to include neutrino mass and leptonic mixing — The number of different i is the same as the number of different l.
The mixing matrix U is 3 x 3 and unitary:
UU† = U†U = 1.Some models include “sterile” neutrinos — neutrinos that experience none of the known forces of nature except gravity.
In such models, there are N > 3 i, and U is N x N, but still unitary.
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Just as each neutrino of definite flavor is a superposition of mass eigenstates i, so each mass eigenstate is a superposition of flavors .
From |> = i U*i |i> and the unitarity of U,
|i> = Ui | > .
The flavor-fraction of i is —
|<|i>|2 = |Ui|2 .
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The Standard Model (SM) description of neutrino interactions (not masses or leptonic mixing) is well-confirmed.
We will assume it is true, and extend it to include mixing.
For the lepton couplings to the W boson, we then have —
€
LSM = −g
2l Lα γ λ ν LαWλ
− + ν Lα γ λ l LαWλ+
( )α =e,μ ,τ
∑
= −g
2l Lα γ λ Uαiν LiWλ
− + ν Liγλ Uαi
*l LαWλ+
( )α =e,μ ,τi = 1,2,3
∑
Left-handed
Taking mixing into account
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Insert Insert Explanation of Explanation of
Neutrino Neutrino OscillationOscillation
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Experimental Experimental EvidenceEvidence
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Evidence For Flavor Change
Neutrinos
Solar Reactor
(L ~ 180 km)
AtmosphericAccelerator
(L = 250 and 735 km)
Stopped Decay LSND
L 30 m
Evidence of Flavor Change
CompellingCompelling
CompellingCompelling
Unconfirmed
( )
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Solar e is now well established.
The mechanism for this flavor conversion is the —
Large Mixing Angle version of the —
Mikheyev Smirnov Wolfenstein
— Effect.
This occurs as the neutrinos stream outward through solar material. It
requires both interactions with matter and neutrino mass and mixing.
What Happens To Solar Neutrinos
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How Does the Large Mixing Angle
MSW Effect Work?The solar matter effect is important for the high-energy 8B neutrinos, not the low-energy pp neutrinos.
Since 3 couples at most feebly to electrons (to be discussed), and solar neutrinos are born e, the solar neutrinos are mixtures of just 1 and 2. (Convention: 2 heavier than 1).
This is a 2-neutrino system.Solar neutrino flavor change is e x, where x is some combination of and .
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In the sun,
At the center of the sun,
√2GFNe ≈ 0.75 × 10-5 eV2 / MeV .
For Δm2sol ≈ 8 × 10-5 eV2 and typical 8B
neutrino energy of ~ 8 MeV,
Δm2sol / 4E ≈ 0.25 × 10-5 eV2 /
MeV .
The interaction term in H dominates, and e is approximately an eigenstate of H.*
€
H =Δmsol
2
4E
−cos2θsol sin2θsol
sin 2θsol cos2θsol
⎡
⎣ ⎢
⎤
⎦ ⎥+ 2GF Ne
1 0
0 0
⎡
⎣ ⎢
⎤
⎦ ⎥
e x
e
x
*For the (E ~ 0.2MeV) pp neutrinos, HVac
dominates.
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The 88B solar neutrino propagates outward adiabatically.
It remains the slowly - changing heavier eigenstate of the slowly - changing H.
It emerges from the sun as the heavier eigenstate of HVac, 2.*
It stays 2 until it reaches the earth. Nothing “oscillates”!
Since 2 = esinsol + xcossol, (See 2 2 U matrix)
Prob[See e at earth] = sin2sol.
*Good to 91% (Nunokawa, Parke, Zukanovich-Funchal)