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Published bySara Adams Modified over 9 years ago
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Fermion Masses: Arbitrary L R
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Quark Masses: Observed: Observed: m(c) : m(t) = m(u):m(c) m(c) : m(t) = m(u):m(c) 1/207 1/207 1/207 1/207 m(s):m(b) = m(d):m(s) m(s):m(b) = m(d):m(s) 1/23 1/23 1/23 1/23
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III II I
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Relations between masses and mixing angles
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III II I
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Thus far neutrinos have been used as tools, like electrons, to study nuclear matter (quark distributions etc.) New focus now: What type of mass? How big or small are masses? How big are the mixing angles? Relations among angles and masses?
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Ewigkeit ist lang, speziell gegen dem Ende zu.W.A.Ewigkeit ist lang, speziell gegen dem Ende zu.W.A.
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Neutrino masses: A: masses about 1 eV m(1) = 0.94 eV m(2) = 0.95 eV m(3) = 1 eV (nearly degenerate) Neutrino masses: A: masses about 1 eV m(1) = 0.94 eV m(2) = 0.95 eV m(3) = 1 eV (nearly degenerate)
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Neutrino masses: B: masses much smaller than 1 eV m(1) = 0 eV m(2) = 0.009 eV m(3) = 0.06 eV (strong hierarchy)
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Neutrino masses: C: neither hierarchy nor degeneracy m(1) = 0.10 eV m(2) = 0.14 eV m(3) = 0.29 eV Neutrino masses: C: neither hierarchy nor degeneracy m(1) = 0.10 eV m(2) = 0.14 eV m(3) = 0.29 eV
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See-saw mechanism:
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Ex.: tau-neutrino mass at about 1 eV:
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SU(5) theory with supersymmetry ok
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Electroweak theory: SU(2) x SU(2) x U(1) U(1): (B-L)
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O(10)
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Neutrino Masses: Mass terms for charged leptons and neutrinos are not parallel Mass terms for charged leptons and neutrinos are not parallel Neutrino Mixing
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Neutrino mixing V=UxP
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Observation:
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Neutrino masses fixed, since the mass differences are given by the experiment, and the angles are fixed by the mass matrix
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Neutrino masses less hierarchical than the masses of the charged leptons
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Double Beta Decay
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The atm. angle is the sum of the two large angles (14 and 26 degrees). The atm. angle is the sum of the two large angles (14 and 26 degrees).
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Conclude: Fermion 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. Conclude: Fermion 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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This works also well for leptons. One finds, using the observed mass differences: 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(1): 0.0041 eV m(2): 0.0097 eV m(2): 0.0097 eV m(3): 0.051 eV m(3): 0.051 eV Atmospheric angle about 40 degrees Neutrinoless double beta decay: difficult Reactor neutrinos: V (3e) ~ 0.052
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