Neutrino
Phenomenology
Boris Kayser
Scottish Summer School
August 9, 2006 +
1
The Neutrino Revolution
(1998 – …)
Neutrinos have nonzero masses!
Leptons mix!
2
These discoveries come from
the observation of
neutrino oscillation.
3
The Physics of
Neutrino Oscillation
4
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
W boson
e
e
e
Detector
Short Journey



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 Mixing
Neutrino mass —
There is some spectrum of 3 or more neutrino mass
eigenstates i:
4
3
(Mass)2
2
1
Mass (i)  mi
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Leptonic mixing —
le  e, l  , l  
When W+  l+ +  ,
e, , or 
the produced neutrino state |> is
| > =  U*i |i> .
Neutrino of flavor 
i
Neutrino of definite mass mi
Leptonic Mixing Matrix
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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
The neutrino state | > produced together with l+
is | > =  U*i |i> .
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 > =  Ui |  > .
The flavor-fraction of i is —
|<|i>|2 = |Ui|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 —
Left-handed
LSM  
g

2  e, ,
g


2  e, ,
i  1,2,3







W



L
L 
L

W
L 




*


U

W



U
W
L
i Li 
Li
i L 
Taking mixing into account

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Insert Explanation
of Neutrino
Oscillation
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Experimental
Evidence
15
Evidence For Flavor Change
Neutrinos
Evidence of Flavor Change
Solar
Reactor
(L ~ 180 km)
Compelling
Compelling
Atmospheric
Accelerator
(L = 250 and 735 km)
Compelling
Compelling
Stopped  Decay
LSND
L  30 m
Unconfirmed
(
)
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What Happens To Solar Neutrinos
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.
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How Does the Large Mixing Angle
MSW Effect Work?
The solar matter effect is important for the highenergy 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,
2 cos 2
msol
sol
H

4E  sin 2 sol
e x
1 0 e
sin 2 sol 
 2GF N e 

cos 2 sol 
0 0 x
At the center of the sun,
√2GFNe ≈ 0.75 × 10-5 eV2 / MeV .
For m2sol ≈ 8 × 10-5 eV2 and typical 8B neutrino energy of
~ 8 MeV,
m2sol / 4E ≈ 0.25 × 10-5 eV2 / MeV .
The interaction term in H dominates, and  e is approximately
an eigenstate of H.*
*For the (E ~ 0.2MeV) pp neutrinos, HVac dominates.
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The 8B 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 = esinsol + xcossol,
(See 2  2 U matrix)
Prob[See e at earth] = sin2sol.
*Good to 91% (Nunokawa, Parke, Zukanovich-Funchal)
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