Flavor Mixing, Neutrino Masses, and Neutrino Oscillations
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Transcript of Flavor Mixing, Neutrino Masses, and Neutrino Oscillations
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G s
w
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G s
wu
d
wM
HM
sun
atm
choozl
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G
um
s
w
dm
tmbm
em
m
cm
u
d
sm
m
wM
HM2m
1m
3m
sun
atm
choozl
2
3
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GeV2462
v
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Fermion Masses: ArbitraryFermion Masses: Arbitrary
L
R
lbGeVMeVme30100002246000002105110 ...
GeVMEVm
GeVMeVm
_246...0072.0__1777
_24600043.0_66.105
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Quark Masses:Quark Masses:
Observed:Observed:
m(c) : m(t) = m(u):m(c) m(c) : m(t) = m(u):m(c) 1/207 1/2071/207 1/207
m(s):m(b) = m(d):m(s)m(s):m(b) = m(d):m(s) 1/23 1/231/23 1/23
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III
II
I
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ba
a0
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Relations between masses and Relations between masses and
mixing anglesmixing angles
c
uu m
marctan
s
dd m
marctan
c
ui
s
dc m
me
m
m
21.0s
d
m
m07.0
c
u
m
m
o13
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c
u
m
m
090sd mm /
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2sin / /c d s u cm m m m
0 a
a b
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III
II
I
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100
0
0
0
0
00
100
0
0
dd
ddi
uu
uu
cs
sc
cs
sc
e
cs
sc
V
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tan /d d sm m tan /u u cm m
0 0
0
A
A C B
B D
0 0
0
A
A C B
B D
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c
u
m
m
090sd mm /
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Thus far neutrinos have been used as tools, Thus far neutrinos have been used as tools, likelike
electrons, to study nuclear matterelectrons, to study nuclear matter(quark distributions etc.)(quark distributions etc.)
New focus now: New focus now: What type of mass? What type of mass? How big or small are masses?How big or small are masses?How big are the mixing angles?How big are the mixing angles?Relations among angles and masses?Relations among angles and masses?
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23322 105.2 eVm
25221 108 eVm
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Ewigkeit ist lang, speziell gegen dem Ende zu.W.A.
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Neutrino masses:Neutrino masses: A: masses about 1 eVA: masses about 1 eV m(1) = 0.94 eV m(1) = 0.94 eV m(2) = 0.95 eV m(2) = 0.95 eV m(3) = 1 eV (nearly m(3) = 1 eV (nearly degenerate)degenerate)
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Neutrino masses:Neutrino masses: B: masses much smaller than 1 eV B: masses much smaller than 1 eV m(1) = 0 eV m(1) = 0 eV m(2) = 0.009 eV m(2) = 0.009 eV m(3) = 0.06 eV (strong m(3) = 0.06 eV (strong hierarchy)hierarchy)
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Neutrino masses:Neutrino masses: C: neither hierarchy nor degeneracy C: neither hierarchy nor degeneracy m(1) = 0.10 eV m(1) = 0.10 eV m(2) = 0.14 eV m(2) = 0.14 eV m(3) = 0.29 eV m(3) = 0.29 eV
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See-saw mechanism:See-saw mechanism:
Mm
mM
0
Mm
Mmm
2
21 /
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Ex.: tau-neutrino mass at Ex.: tau-neutrino mass at about 1 eV:about 1 eV:
GeVM
eVMGeV9
2
1016.3
_1/)777,1(
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SU(5) theory SU(5) theory with with
supersymmetry supersymmetry okok
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Electroweak theory:Electroweak theory:
SU(2) x SU(2) x U(1)SU(2) x SU(2) x U(1)
U(1): (B-L)U(1): (B-L)
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Electroweak theory:Electroweak theory:
SU(2) x SU(2) x U(1)SU(2) x SU(2) x U(1)
U(1): (B-L)U(1): (B-L)
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O(10)
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Neutrino Masses: Neutrino Masses:
Mass terms for Mass terms for charged leptons and charged leptons and neutrinos are not neutrinos are not parallel parallel
Neutrino MixingNeutrino Mixing
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321 ......... e
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321
321
321
VVV
VVV
VVV
Veee
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332211 eeee VVV
332211 VVV
332211 VVV
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Neutrino mixingNeutrino mixing
V=UxPV=UxP
100
00
00
i
i
e
e
P
100
0
0
0
0
00
100
0
0
cs
sc
cs
sc
e
cs
sc
U
i
ll
ll
sun at anglereactorl
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oat
o
osun
o
2.538.36
2.3930
23322 105.2 eVm 252
21 108 eVm
70.060.038.0
70.060.038.0
05.054.084.0
V
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34.6
45
4.6
0.821 0.568 0.08
0.047 0.40 0.03 0.58 0.70
0.047 0.40 0.03 0.58 0.70
osun
oatm
ochooz
i i
i i
V e e
e e
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100
0
0
0
0
00
100
0
0
cs
sc
cs
sc
e
cs
sc
U
i
ll
ll
2
1tanm
m 0695.0tan
m
mel
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Observation:Observation:
oo 45__33
42.0/
:
21 mm
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Neutrino masses fixed, Neutrino masses fixed, sincesincethe mass differences are the mass differences are given by the experiment,given by the experiment,and the angles are fixed and the angles are fixed by the mass matrixby the mass matrix
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19.0/ 32
3
2
1
mm
m
m
m
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Neutrino masses less Neutrino masses less hierarchical than the hierarchical than the masses of the charged masses of the charged leptonsleptons
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Double Beta DecayDouble Beta Decay
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DB
BA
A
M
0
0
00
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1
2 2 3
2
/ 14
/ 26
40
sin 0.97
o
o
o
m m
m m
1 2
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The atm. angle is the sum of the two large The atm. angle is the sum of the two large angles (14 and 26 degrees).angles (14 and 26 degrees).
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321
321
321
VVV
VVV
VVV
Veee
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052.02
13
m
mV ee
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Conclude:Conclude:
Fermion masses remain a mystery.Fermion masses remain a mystery.Neutrino masses might be Dirac masses or Neutrino masses might be Dirac masses or Majorana masses.Majorana masses.
Mixing angles for quarks are fixed by ratios of Mixing angles for quarks are fixed by ratios of quark masses. Very good agreement with quark masses. Very good agreement with experiment.experiment.
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This works also well for leptons. One finds, This works also well for leptons. One finds, using the observed mass differences:using the observed mass differences:
m(1)/m(2)=0.42, m(2)/m(3)=0.19.m(1)/m(2)=0.42, m(2)/m(3)=0.19.
m(1): 0.0041 eV m(1): 0.0041 eV m(2): 0.0097 eVm(2): 0.0097 eV m(3): 0.051 eVm(3): 0.051 eV
Atmospheric angle about 40 degreesAtmospheric angle about 40 degreesNeutrinoless double beta decay: difficultNeutrinoless double beta decay: difficultReactor neutrinos: V (3e) ~ 0.052Reactor neutrinos: V (3e) ~ 0.052