1 neutrino phenomenology boris kayser scottish summer school august 10, 2006 +
TRANSCRIPT
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Neutrino Neutrino
PhenomenologPhenomenolog
yy Boris KayserScottish Summer
SchoolAugust 10, 2006 +
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What We What We Have LearnedHave Learned
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(Mass)2
12
3
or
123
}m2so
l
m2atm
}m2so
l
m2atm
m2sol = 8.0 x 10
–5 eV2, m2
atm = 2.7 x 10–3 eV2
~ ~
Normal
Inverted
Are there more mass eigenstates, as LSND suggests?
The (Mass)2 Spectrum
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This has the consequence that —
|i> = Ui |> .
Flavor- fraction of i = |Ui|2 .
When a i interacts and produces a charged lepton, the probability that this charged lepton will be of flavor is |Ui|2 .
Leptonic Mixing
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e [|Uei|2]
[|Ui|2] [|Ui|2]
Normal Inverted
m2atm
(Mass)2
m2sol}
m2atm
m2
sol}
or
sin213
sin213
The spectrum, showing its approximate flavor content, is
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m2atm
e [|Uei|2]
[|Ui|2]
[|Ui|2]
(Mass)2
m2sol}
Bounded by reactor exps. with L ~ 1 km
From max. atm. mixing,
€
3 ≅ν μ +ν τ
2
From (Up) oscillate but (Down) don’t{{
{
In LMA–MSW, Psol(ee) = e fraction of 2
From max. atm. mixing, includes (–)/√2
From distortion of e(solar) and e(reactor) spectra
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The 3 X 3 Unitary Mixing Matrix
€
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
∑
Caution: We are assuming the mixing matrix U to be
3 x 3 and unitary.
€
(CP) l Lα γ λ Uαiν LiWλ−
( )(CP)−1 = ν Liγλ Uαil LαWλ
+
Phases in U will lead to CP violation, unless they are removable by redefining the
leptons.
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Ui describes — i l
W+
–
Ui l W+Hi –
When i ei i , Ui ei Ui
When l ei l , Ui e–
i Ui
– –
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.
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Exception: If the neutrino mass eigenstates are their own antiparticles, then —Charge conjugate i = ic =
Ci
T
One is no longer free to phase-redefine
i without consequences.
U can contain additional CP-violating phases.
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How Many Mixing Angles and CP Phases Does U Contain?
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
€
Uαi*Uβi
i∑ = δαβ
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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
Mixing angles
CP phases if i i
CP phases if i = i
3 31
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The Mixing Matrix
€
U =
1 0 0
0 c23 s23
0 −s23 c23
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥×
c13 0 s13e−iδ
0 1 0
−s13eiδ 0 c13
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥×
c12 s12 0
−s12 c12 0
0 0 1
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
×
eiα1 /2 0 0
0 eiα 2 /2 0
0 0 1
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
12 ≈ sol ≈ 34°, 23 ≈ atm ≈ 37-53°, 13 < 10°
would lead to P() ≠ P(). CP
But note the crucial role of s13 sin 13.
cij cos ijsij sin ij
Atmospheric
Cross-Mixing
Solar
Majorana CP phases~
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The Majorana CP Phases
The phase i is associated with neutrino mass eigenstate i:
Ui = U0i exp(ii/2) for all flavors
.
Amp() = Ui* exp(– imi2L/2E)
Ui
is insensitive to the Majorana phases i.
Only the phase can cause CP violation in neutrino
oscillation.
i
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QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.The Open The Open QuestionsQuestions
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•What is the absolute scale
of neutrino mass?
•Are neutrinos their own antiparticles?
•Are there “sterile” neutrinos?
We must be alert to surprises!
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•What is the pattern of mixing among
the different types of neutrinos?
What is 13? Is 23 maximal?
•Do neutrinos violate the symmetry CP? Is P( )
P( ) ?
•Is the spectrum like or ?
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• 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?
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QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
The The Importance of Importance of
the the Questions, Questions,
and How They and How They May Be May Be
AnsweredAnswered
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How far above zero is the whole pattern?
3
0
(Mass)2
m2atm
m2sol
??
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Flavor Change
Tritium Decay, Double DecayCosmology
}}
What Is the Absolute Scale of Neutrino Mass?
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A Cosmic Connection
Cosmological Data + Cosmological Assumptions
mi < (0.17 – 1.0) eV .
Mass(i)
If there are only 3 neutrinos,
0.04 eV < Mass[Heaviest i] < (0.07 – 0.4) eV
m2atm
Cosmology
~
Oscillation Data m2atm <
Mass[Heaviest i]
Seljak, Slosar, McDonald Pastor
( )
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Are Neutrinos Are Neutrinos Majorana Majorana Particles?Particles?
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How Can the How Can the Standard Model be Standard Model be
Modified to Include Modified to Include Neutrino Masses?Neutrino Masses?
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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
–
–
Wl–
Z
l +(—) l
+(—)
Xml
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• Original SM: m = 0.
• Why not add a Dirac mass term,
mDLR
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.
XmD
(—)
(—)
—
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Unlike L, R carries no Electroweak Isospin.
Thus, no SM principle prevents the occurrence of the Majorana mass term
mRRc 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
XmR
—
—
—
—
—
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The objects R and Rc in mRRc R are not the mass eigenstates, but just the neutrinos in terms of which the model is constructed.
mRRc 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 = “ + ” .
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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.
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• The presence of Majorana masses
• i = i (Majorana neutrinos)
• L not conserved— are all equivalent
Any one implies the other two.
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Electromagnetic Properties
of Majorana Neutrinos Majorana neutrinos are very neutral.No charge distribution:
CPT[ ] = ≠++
+–
––
But for a Majorana neutrino,
[ ]CPT i
[ ]i
=
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No magnetic or electric dipole moment:
[ ] [ ]e+ e– =
–
But for a Majorana neutrino,
i i=
Therefore, [i
]=[i
] =
0
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Transition dipole moments are possible, leading to —
e
e1
2
One can look for the dipole moments this way.
To be visible, they would have to vastly exceed Standard Model
predictions.
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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—
+i +
SpinPion Rest Frame
(Lab) > ( Rest Frame)
+ i
+Lab. Frame
Give the neutrino a Boost:
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The SM weak interaction causes—
i
+
Recoil
Target at rest
—
i i
— i
,
will make + too.
i = i means that i(h) = i(h).helicity
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Minor Technical Difficulties
(Lab) > ( Rest Frame)
E(Lab) E( Rest Frame) m m
E(Lab) > 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)
i
>
~ i
i
m
E( Rest Frame)
i
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The Idea That Can Work —
Neutrinoless Double Beta Decay [0]
Observation would imply L and i = i .
By avoiding competition, this process can cope with the small neutrino masses.
ii
W– W–
e– e–
Nuclear Process
Nucl Nucl’
i
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0e– e–
u d d u
()R L
W W
Whatever diagrams cause 0, its observation would imply the
existence of a Majorana mass term:Schechter and Valle
()R L : A Majorana mass term
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ii
W– W–
e– e–
Nuclear Process
Nucl Nucl’
In
the i is emitted [RH + O{mi/E}LH].
Thus, Amp [i contribution] mi
Amp[0] miUei2 m
Uei
Uei
i
SM vertex
i
Mixing matrix
Mass (i)
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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.
3939
Backup Backup SlidesSlides
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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 —
sol < 21
3atm
3
sol < 12
atmo
r
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m miUei2
€
U =
1 0 0
0 c23 s23
0 −s23 c23
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥×
c13 0 s13e−iδ
0 1 0
−s13eiδ 0 c13
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥×
c12 s12 0
−s12 c12 0
0 0 1
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
×
eiα1 /2 0 0
0 eiα 2 /2 0
0 0 1
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
The e (top) row of U reads —
€
(Ue1,Ue2,Ue3) = (c12c13eiα1 /2, s12c13eiα 2 /2, s13e−iδ )
12 ≈ ≈ 34°, but s132 < 0.032
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If the spectrum looks like—
then–
m ≅ m0[1 - sin22 sin2(–––––)]½ .Solar mixing angle
m0 cos 2 m m0
At 90% CL,m0 > 46 meV (MINOS); cos 2 > 0.28
(SNO),so
m > 13 meV .
2–12
Majorana CP phases
{
sol <atm
m0
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If the spectrum looks like
then —
0 < m < Present Bound [(0.3–1.0) 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
sol <
atm
Evidence for 0 with m = (0.05 – 0.84) eV?
Klapdor-Kleingrothaus