The Neutrino World

1
Neutrino Phenomenology
Boris Kayser Scottish Summer School August 9,
2006
2
The Neutrino Revolution(1998 )
Neutrinos have nonzero masses!
Leptons mix!
3
These discoveries come from the observation of
neutrino oscillation.
4
The Physics of Neutrino Oscillation
5
Neutrinos Come in at Least Three Flavors

• The known neutrino flavors ?e , ?? , ??

6
The Meaning of this Association
e
e
W boson
Detector
?e
?e
Short Journey
?
?
W
??
??
?
?
W
??
??
7
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.
8
Let Us Assume Neutrino Masses and Leptonic Mixing

• Neutrino mass
• There is some spectrum of 3 or more neutrino mass
  eigenstates ?i

9
Leptonic mixing When W ? l? ?? , the
produced neutrino state ??gt is ?? gt ?
U?i ?igt . Neutrino of flavor ? Neutrino
of definite mass mi Leptonic
Mixing Matrix
e, ?, or ?
i
10
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 ?? gt produced together with
l?
is ?? gt ? U?i ?igt .
i
11
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 UU 1.

Some models include sterile neutrinos
neutrinos that experience none of the known
forces of nature except gravity. In such models,
there are N gt 3 ?i, and U is N x N, but still
unitary.
12
Just as each neutrino of definite flavor ?? is a
superposition of mass eigenstates ?i, so each
mass eigenstate is a superposition of flavors
. From ?? gt ?i U?i ?igt and the unitarity of
U, ?i gt ?? U?i ?? gt . The
flavor-??fraction of ?i is lt???igt2
U?i2 .
13
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
Taking mixing into account
14
Insert Explanation of Neutrino Oscillation
15
Experimental Evidence
16
Evidence For Flavor Change
Neutrinos Solar Reactor(L 180
km) Atmospheric Accelerator(L 250 and 735
km) Stopped ? Decay LSND L ? 30 m
Evidence of Flavor Change Compelling Compelling
Compelling Compelling Unconfirmed
)
(
17
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.
18
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 ?µ and ??.

19

• In the sun,
• At the center of the sun,
• v2GFNe 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.

?e ?x ?e ?x
For the (E 0.2MeV) pp neutrinos, HVac
dominates.
20
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) ProbSee ?e at earth sin2?sol.
Good to 91 (Nunokawa, Parke, Zukanovich-Funchal)