Neutrino Oscillations Flavor Mixing - Neutrino Masses - Neutrino Oscillations Harald Fritzsch IAS Princeton - LMU-MPI Munich

The Standard Model - - I II III I II III 3 families - 3 colors

1. SU(3) : c exact gauge symmetry 2. SU(2) x U(1): broken gauge symmetry

Further symmetries, beyond the SM ? (grand unfication? supersymmetry?...)

problem ===> 28 fundamental constants

4 fundamental constants G

14 fundamental constants G quarks leptons 4 4 flavor mixing

fermion masses 28 constants G

==> six fundamental constants m(fermions) ==>0 proton mass G ==> six fundamental constants

proton mass

dimensional transmutation Mass from no-mass 1 / QCD dimensional transmutation

( Brout - Englert - Higgs ) Masses of W-Bosons are generated by S.S.B. (B-E-H Mechanism) ( Brout - Englert - Higgs )

Mass and Symmetry Breaking Higgs particle Fermi constant

==========>>> Z + Z LHC muon Higgs particle ==========>>> Z + Z

The Dark Corner of HEP Fermion Masses: Arbitrary ???Higgs mech.??? R 246 GeV g L

Some constants might vary in time, e.g. the finestructure constant

Charged leptons and quarks (MeV) Masses - Charged leptons and quarks (MeV) tau: 1 777 muon: 105.7 electron: 0.51 - t: 174 000 c: 1 100 u: 5.3 b: 4 500 s: 170 d: 7.8 (u, d, c, s - quark masses at 1 GeV)

relations between quark masses? Observed: m(c) : m(t) = m(u):m(c) 1/207 1/207 m(s):m(b) = m(d):m(s) 1/23 1/23

ln m b s d

ln m b s d

ln m t b c s d ? u

175 GeV ln m t b c s d ? u FNAL: 1995 predicting t-mass (1987)

ln m 22 GeV tau muon - - 5 MeV e -

quark masses flavor mixing angles

- - III 2 families flavor mixing II I

mixing of mass eigenstates by weak interaction

(beyond Standard Model) Mass Matrices u,c - d,s texture zero Fritzsch, Weinberg (beyond Standard Model)

Reflection symmetries (~parity) texture zero: SU(2) x SU(2) L R Reflection symmetries (~parity) ===> Grand Unification -SO(10)

Relations between masses and mixing angles Quarks: Cabibbo angle: Exp.: angle 90 degrees ( symmetry ! )

data require rectangular triangle Cabibbo angle ====> data require rectangular triangle

both for up-type and down type quarks 0.049 0.044 + 0.005 = 0.049 Origin: both for up-type and down type quarks

- 3 families III flavor mixing II I

Mixing for three families CKM matrix (Fritzsch, Xing) Three angles + 1 phase

The angles and can be measured separately.

Theory: 3 texture zeros

agrees perfectly with experiment SLAC - DESY - CERN - KEK

-

unitarity triangle

(~rectangular triangle) Flavor-Symmetries, Flavor-Mixing, Neutrino Masses and Neutrino Mixing ad H. Fritzsch LMU / MPI Munich (~rectangular triangle)

- - - alpha: 86 ... 95

Cabibbo angle ====> Unitarity triangle ==> CP violation

CKM matrix -i phase 90 degrees Maximal CP violation

Neutrinos

speziell gegen dem Ende zu. Kamioka Ewigkeit ist lang, speziell gegen dem Ende zu. W.A. neutrinos from upper atmosphere

SNO Sudbury Canada 1000 t heavy water

SNO charged current and neutral current

neutrino mass differences Kamiokande, SNO neutrino mass differences

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

nearly degenerate neutrino masses. masses about 1 eV m(1) = 0 nearly degenerate neutrino masses? masses about 1 eV m(1) = 0.94 eV m(2) = 0.95 eV m(3) = 1 eV eV 1

hierarchical neutrino masses hierarchical neutrino masses? much smaller than 1 eV m(1) = 0 eV m(2) = 0.009 eV m(3) = 0.06 eV

reality 0.05 eV - - -

Gell-Mann, Ramond, Slansky See-saw mechanism: m: Dirac mass M: Majorana mass Minkowski Yanagida, Gell-Mann, Ramond, Slansky ==>

Ex.: tau-neutrino mass at about 1 eV: Dirac mass: t-quark new intermediate energy scale M

===> Grand Unification

( F., Minkowski; Georgi - 1975 ) SU(3)xSU(2)xU(1) ==>SO(10) ( F., Minkowski; Georgi - 1975 )

Neutrino Mixing Matrix: (like CKM Matrix)

(incl. righthanded neutrinos) SO(10) Fermions in 16-plet (incl. righthanded neutrinos)

SO(10) leptons and quarks in one multiplet O(10) Neutrinos are massive

Electroweak theory: SU(2) x SU(2) x U(1) In SO(10): lefthanded and righthanded neutrinos Electroweak theory: SU(2) x SU(2) x U(1) L R New energy scale for righthanded SU(2) related to neutrino masses? - consistent with LEP unlike SU(5)

Neutrino Mixing Neutrino Masses: Mass terms for charged leptons and neutrinos are not parallel  Neutrino Mixing ( Pontecorvo ... ==>)

Neutrino mixing V=UxP (not measured)

Kamiokande, SNO

Chooz

CHOOZ reactor

Mean values of angles

same pattern as for quarks:

Observation: weak mass hierarchy for neutrinos

==> neutrino masses fixed

relations between angles and masses

neutrino masses very small 0.0041 eV 0.0097 eV - 0.051 eV 0.01 eV - - neutrino masses very small

m(1) = 0.0036 … 0.0059 eV m(2) = 0.0085 … 0.0140 eV m(3) = 0.044 … 0.058 eV

Masses (relative)

Neutrino masses less hierarchical than the masses of the charged leptons

Reflection symmetry in mass matrices Leptons: Reflection symmetry in SO(10) theory

What is atm. angle? (ok with exp.)

The atm. angle is the sum of the two large angles (14 and 26 degrees). The atm. angle is large, but not precisely 45 degrees The atm. angle is the sum of the two large angles (14 and 26 degrees).

limit: ==>

A mass matrix of this type does not work for the quarks. m(top) < 90 GeV

quarks c

Neutrino Mixing Matrix: <===== not 0

Prediction for mixing of reactor neutrinos:

Present limit: CHOOZ V(e3) < 0.1 New experiments: Double CHOOZ: =>0.01 Daya Bay (China) =>0.03 T 2 K: ==> 0.008 (J-PARC) (soon observed?)

neutrino = antineutrino Majorana masses: no fermion number neutrino = antineutrino

76 Ge ==>

Neutrinoless Double Beta Decay Present limit about 0.23 ev Cuoricino Exp.: Te (130) Gran Sasso Lab.

Improvement by about 100 necessary! expected: Improvement by about 100 necessary!

Neutrino mixing - Maximal CP-violation for leptons ?

Conclude: Fermion masses remain a mystery 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.

quarks _ leptons

This works also well for leptons 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

Neutrino masses

Atmospheric angle about 40 degrees Neutrinoless double beta decay: difficult Reactor neutrinos: V (3e) ~ 0.052 (Daya Bay exp. ==> 0.03)