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Flavor Mixing and Neutrino Masses
H. Fritzsch LMU Munich
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mixing of mass eigenstates by weak interaction
(Cabibbo angle)
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mass matrices
texture 0
u,c - d,s
F., Weinberg
(beyond Standard Model)
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texture zero
SU(2) x SU(2)
L
R
Reflection symmetries (parity)
gt Grand Unification -SO(10)
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-
-
III
2 families
flavor mixing
II
I
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Relations between masses and mixing angles
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Cabibbo angle
Exp. phase 90 degrees
( symmetry ! )
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gt
Cabibbo angle

exp. data rectangular
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-
3 families
III
flavor mixing
II
I
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Mixing for three families
CKM matrix
3 angles, 1 phase
F. and Xing
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The angles
and
can be measured separately.
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Theory
3 texture zeros
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agrees well with experiments
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theory
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theory
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unitarity triangle
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Flavor-Symmetries, Flavor-Mixing, Neutrino
Masses and Neutrino Mixing
H. Fritzsch LMU / MPI Munich
(rectangular triangle)
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-
-
-
0
0
alpha 86 ... 95
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Cabibbo angle
gt

Unitarity triangle
(rectangular)
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maximal CP-violation
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Neutrinos
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Kamioka
Ewigkeit ist lang, speziell gegen dem Ende
zu. W.A.
neutrinos from upper atmosphere
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SNO
Sudbury Neutrino Observatory
Canada
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S N O
charged current and neutral current
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Kamiokande, SNO
neutrino mass differences
( absolute masses unknown)
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neutrino masses

• What type of mass term?
• How big or small are masses?
• How big are the mixing angles?
• Relations among angles and masses?

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• Neutrino Masses
• Mass terms for charged leptons and neutrinos
  are not parallel ?
• Neutrino Mixing

( Pontecorvo ,1957... gt)
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B. Pontecorvo
(1913 - 1993)
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neutrino mixing matrix
(like CKM Matrix)
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Neutrino mixing

• VUxP

(not measured)
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Kamiokande, SNO
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same pattern as for quarks
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Observation
weak mass hierarchy for neutrinos
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gt neutrino masses fixed
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relations between angles and masses
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neutrino masses very small
0.05 eV
-
0.01 eV
0.01 eV
0.004 eV
-
-
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m(1) 0.0036 0.0059 eVm(2) 0.0085 0.0140
eVm(3) 0.044 0.058 eV
normal hierarchy (not inverted)
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Masses
(relative)
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Neutrino masses less hierarchical than the
masses of the charged leptons
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Leptons
( 4 texture 0 )
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gt atmospheric angle
(ok with exp.)
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Neutrino Mixing Matrix
lt
not 0
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prediction
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Chooz
Maas
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present limit from CHOOZ
V(e3) lt 0.1
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New experiments
Double CHOOZ 0.06 gt0.008
Daya Bay (China) gt0.03
T 2 K gt 0.008
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Daya Bay reactor
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Daya Bay experiment
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Daya Bay (China) gt0.03
prediction 0.052
(observation in 2 years?)
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Majorana masses
no fermion number neutrino antineutrino
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76
Ge gt
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Neutrinoless Double Beta Decay
Present limit about 0.23 ev
Cuoricino Exp. Te (130) Gran Sasso Lab.
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expected
improvement factor 10 !
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CP violation of leptons
maximal violation?
gt reactor neutrinos
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ConcludeFermion masses remain a
mystery.Neutrino masses might be Dirac masses or
Majorana masses.Mixing angles for quarks are
fixed by ratios of quark masses. Very good
agreement with experiment.
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mass matrices of quarks and leptons
Structure
3 texture zeros
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• This works also well for leptons. One
  finds, using the observed mass differences
  
• m(1)/m(2)0.42, m(2)/m(3)0.19.
• m(1) 0.0041 eV
• m(2) 0.0097 eV
• m(3) 0.051 eV

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• Atmospheric angle about 40 degrees
• Neutrinoless double beta decay difficult

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reactor neutrinos
V 0.052
3e
gt Daya Bay