The Neutrino World

1
Neutrino Phenomenology
Boris Kayser Scottish Summer School August 10,
2006
2
What We Have Learned
3
The (Mass)2 Spectrum
or
(Mass)2
?m2atm
Inverted
Normal
Are there more mass eigenstates, as LSND suggests?
4
Leptonic Mixing
This has the consequence that ?i gt ?
U?i ??gt . Flavor-? fraction of ?i U?i2
. When a ?i interacts and produces a charged
lepton, the probability that this charged lepton
will be of flavor ? is U?i2 .
?
5
The spectrum, showing its approximate flavor
content, is
Inverted
Normal
6
?3
?m2atm
(Mass)2
?2

?m2sol
?1
?? U?i2
?? U?i2
?e Uei2
7
The 3 X 3 Unitary Mixing Matrix
Caution We are assuming the mixing matrix U to
be 3 x 3 and unitary.
Phases in U will lead to CP violation, unless
they are removable by redefining the leptons.
8
W
U?i describes

?i
l?
When ??i? ? ?ei? ?i? , U?i ? ei? U?i When ?l?
? ? ?ei? l? ?, U?i ? ei? U?i


Thus, one may multiply any column, or any row, of
U by a complex phase factor without changing the
physics. Some phases may be removed from U in
this way.
9
Exception If the neutrino mass eigenstates are
their own antiparticles, then
Charge conjugate
One is no longer free to phase-redefine ?i
without consequences.
U can contain additional CP-violating phases.
10
Real parameters before constraints
18 Unitarity constraints Each row is a
vector of length unity 3 Each
two rows are orthogonal vectors
6 Rephase the three l?
3 Rephase two ?i , if ?i ? ?i
2 Total
physically-significant parameters
4 Additional (Majorana) CP phases if ?i ?i
2
11
How Many Of The Parameters Are Mixing Angles?
The mixing angles are the parameters in U when
it is real. U is then a three-dimensional
rotation matrix. Everyone knows such a matrix is
described in terms of 3 angles. Thus, U contains
3 mixing angles.
Summary
CP phases if ?i ?i
CP phases if ?i ? ?i
Mixing angles
3
3
1
12
The Mixing Matrix
Solar
Atmospheric
Cross-Mixing
cij ? cos ?ijsij ? sin ?ij
Majorana CP phases
?12 ?sol 34, ?23 ?atm 37-53, ?13 lt
10 ? would lead to P(??? ??) ? P(??? ??).
CP But note the crucial role of s13 ? sin ?13.

13
The Majorana CP Phases
The phase ?i is associated with neutrino mass
eigenstate ?i U?i U0?i exp(i?i/2) for all
flavors ?.
Amp(?????) ? U?i exp( imi2L/2E) U?i is
insensitive to the Majorana phases ?i. Only the
phase ? can cause CP violation in neutrino
oscillation.
i
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The Open Questions
15

• What is the absolute scale of neutrino mass?

• Are neutrinos their own antiparticles?

• Are there sterile neutrinos?

We must be alert to surprises!
16

• What is the pattern of mixing among the
  different types of neutrinos?
• What is ?13? Is ?23 maximal?

• Is the spectrum like or ?

• Do neutrinos violate the symmetry CP? Is P(?? ?
  ??) ? P(?? ? ??) ?

17

• What can neutrinos and the universe tell us about
  one another?
• Is CP violation by neutrinos the key to
  understanding the matter antimatter asymmetry
  of the universe?

• What physics is behind neutrino mass?

18
The Importance of the Questions, and How They May
Be Answered
19
What Is the Absolute Scale of Neutrino Mass?
How far above zero is the whole pattern?
20
A Cosmic Connection
Oscillation Data ? ??m2atm lt MassHeaviest ?i
Cosmological Data Cosmological Assumptions ? ?
mi lt (0.17 1.0) eV .
Mass(?i) If there are only 3 neutrinos, 0.04
eV lt MassHeaviest ?i lt (0.07 0.4) eV
??m2atm Cosmology
(
)
Seljak, Slosar, McDonald Pastor

21
Are Neutrinos Majorana Particles?
22
How Can the Standard Model be Modified to Include
Neutrino Masses?
23
Majorana Neutrinos or Dirac Neutrinos?

• The S(tandard) M(odel)
• and
• couplings conserve the Lepton Number L defined
  by
• L(?) L(l) L(?) L (l) 1.
• So do the Dirac charged-lepton mass terms
• mllLlR

l
?
W
Z
?
?


ml
24

• Original SM m? 0.
• Why not add a Dirac mass term,
• mD?L?R
• Then everything conserves L, so for each mass
  eigenstate ?i,
• ?i ? ?i (Dirac neutrinos)
• L(?i) L(?i)
• The SM contains no ?R field, only ?L.
• To add the Dirac mass term, we had to add ?R to
  the SM.

25

• Unlike ?L, ?R carries no Electroweak Isospin.
• Thus, no SM principle prevents the occurrence of
  the Majorana mass term
• mR?Rc ?R
• But this does not conserve L, so now
• ?i ?i (Majorana neutrinos)
• No conserved L to distinguish ?i from ?i
• We note that ?i ?i means
• ?i(h) ?i(h)
• helicity

26
The objects ?R and ?Rc in mR?Rc ?R are not the
mass eigenstates, but just the neutrinos in terms
of which the model is constructed. mR?Rc ?R
induces ?R ?Rc mixing. As a result of
K0 K0 mixing, the neutral K mass
eigenstates are KS,L ? (K0 ? K0)/?2 . As a
result of ?R ?Rc mixing, the neutrino
mass eigenstate is ?i ?R
?Rc ? ? .
27
Many Theorists Expect Majorana Masses
The Standard Model (SM) is defined by the fields
it contains, its symmetries (notably Electroweak
Isospin Invariance), and its renormalizability.
Leaving neutrino masses aside, anything allowed
by the SM symmetries occurs in nature. If this is
also true for neutrino masses, then neutrinos
have Majorana masses.
28

• The presence of Majorana masses
• ?i ?i (Majorana neutrinos)
• L not conserved

are all equivalent
Any one implies the other two.
29
Electromagnetic Properties of Majorana Neutrinos

• Majorana neutrinos are very neutral.
• No charge distribution

CPT

?



But for a Majorana neutrino,




?i
?i

CPT
30
No magnetic or electric dipole moment




?
?

e
e
But for a Majorana neutrino,
?i
?i

Therefore,
?i
?i
0

?
?
31
Transition dipole moments are possible, leading
to
One can look for the dipole moments this way. To
be visible, they would have to vastly exceed
Standard Model predictions.
32
How Can We Demonstrate That ?i ?i?
We assume neutrino interactions are correctly
described by the SM. Then the interactions
conserve L (? ? l ? ? l). An Idea that Does
Not Work and illustrates why most ideas do not
work Produce a ?i via
Spin
Pion Rest Frame
?
?i
?
?
Give the neutrino a Boost
??(Lab) gt ??(? Rest Frame)
33

• The SM weak interaction causes

?
?

?i
Target at rest
Recoil
?i ?i means that ?i(h) ?i(h).
helicity
?
?

??????i
,
????i
?
??????i
will make ? too.
34
Minor Technical Difficulties

• ??(Lab) gt ??(? Rest Frame)
• E?(Lab) E?(? Rest Frame) m? m?
• ? E?(Lab) gt 105 TeV if m? 0.05 eV
• Fraction of all ? decay ?i that get helicity
  flipped
• ? ( )2 10-18 if m??? 0.05 eV
• Since L-violation comes only from Majorana
  neutrino masses, any attempt to observe it will
  be at the mercy of the neutrino masses.
• (BK Stodolsky)

? gt
i

i
m? E?(? Rest Frame)
i
i
35
The Idea That Can Work Neutrinoless Double
Beta Decay 0???
By avoiding competition, this process can cope
with the small neutrino masses.
Observation would imply L and ?i ?i .
36
Whatever diagrams cause 0???, its observation
would imply the existence of a Majorana mass term
Schechter and Valle
37
In
SM vertex
e
e
?i
?
Mixing matrix
Uei
Uei
i
W
W
Nuclear Process
Nucl
Nucl
Mass (?i)
the ?i is emitted RH Omi/ELH. Thus, Amp ?i
contribution ? mi Amp0??? ? ?? miUei2?? m??
i
38
The proportionality of 0??? to mass is no
surprise. 0??? violates L. But the SM
interactions conserve L. The L violation in
0??? comes from underlying Majorana mass terms.
39
Backup Slides
40
How Large is m???

• How sensitive need an experiment be?
• Suppose there are only 3 neutrino mass
  eigenstates. (More might help.)
• Then the spectrum looks like

or
41
m?? ? ?? miUei2?
The e (top) row of U reads
?12 ?? 34, but s132 lt 0.032
42

• If the spectrum looks like
• then
• m?? ? m01 - sin22?? sin2()½ .
• Solar mixing angle
• m0 cos 2?? ? m?? ? m0
• At 90 CL,
• m0 gt 46 meV (MINOS) cos 2?? gt 0.28 (SNO),
• so
• m?? gt 13 meV .

m0
?2?1 2
43

• If the spectrum looks like
• then
• 0 lt m?? lt Present Bound (0.31.0) eV .
• (Petcov et al.)
• Analyses of m?? vs. Neutrino Parameters
• Barger, Bilenky, Farzan, Giunti, Glashow, Grimus,
  BK, Kim, Klapdor-Kleingrothaus, Langacker,
  Marfatia, Monteno, Murayama, Pascoli, Päs,
  Peña-Garay, Peres, Petcov, Rodejohann, Smirnov,
  Vissani, Whisnant, Wolfenstein,
• Review of ?? Decay Elliott Vogel

Evidence for 0??? with m?? (0.05 0.84)
eV? Klapdor-Kleingrothaus