Flavor Mixing of Flavor Mixing of Quarks and Quarks and

NeutrinosNeutrinosH. Fritzsch H. Fritzsch LMU MunichLMU Munich

W. Pauli: 1930 Neutrino mass ~ m(e)

1956:1956:maximal parity maximal parity

violationviolation

neutrinos neutrinos masslessmassless

1998:

Y. Totsuka …(Kamioka)

neutrino oscillations

III

II

I

cccc sd

c

sd

u

cossinsincos

013c

ba

a0

ba

a0

c

u

m

m

ba

a

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m

c

ui

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dc m

me

m

m

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u

m

m22.0s

d

m

m

oo 169

c

u

m

m090

sd mm /

013:angleCabibbo

c

ui

s

dc m

me

m

m

o13

III

II

I

100

0

0

0

010

0

0

0

001

1212

1212

1313

1313

2323

2323 cs

sc

ces

esc

cs

scVi

i

132312 ,,: angles

New parametrization:New parametrization:

100

0

0

0

0

00

100

0

0

dd

ddi

uu

uu

cs

sc

cs

sc

e

cs

sc

V

0 0

0

A

A C B

B D

0 0

0

A

A C B

B D

tan /d d sm m

tan /u u cm m

u d

0 0

0

A

A C B

B D

tan /d d sm m

od 4.00.13

tan /u u cm m

oou 7.00.5

oo

oou

Exp 1.14.5:

7.00.5

oo

od

Exp 6.27.11:

4.00.13

tbtstu

cbcscu

ubusud

VVV

VVV

VVV

V

c

u

m

m

090sd mm /

025.0681.02sin:

663.02sin

sincos

cossintan

Exp

du

du

090

321

321

321

VVV

VVV

VVV

Veee

100

00

00

i

i

e

e

P

at sun

)(unknown

anglereactorl

100

00

00

i

i

e

e

P

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00

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i

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at sun

)(unknown

anglereactorl

at sun

)(unknown

anglereactorl

100

0cossin

0sincos

cossin0

sincos0

00

100

0cossin

0sincos

i

ll

ll e

U

osun

o 3.367.31

oat

o 5238

23232 104.2 eVm

25221 106.7 eVm

0 0

0

A

A C B

B D

0 0

0

A

A C B

B D

100

0cossin

0sincos

cossin0

sincos0

00

100

0cossin

0sincos

i

ll

ll e

U

12

2122tan

mm

mm

0695.02

2tan

e

e

l mm

mm

Observation:Observation:

oo 45__33

12.004.021 42.0/

mm

25221 108 eVm

23322 104.2 eVm

:

42.0/ 21 mm

m(1) = ( 0.004 +/- 0.0012 ) m(1) = ( 0.004 +/- 0.0012 ) eVeV

m(2) = ( 0.011 +/- 0.002 ) m(2) = ( 0.011 +/- 0.002 ) eVeV

m(3) = ( 0.051 +/- 0.007 )eV m(3) = ( 0.051 +/- 0.007 )eV

12

3

e

321

321

321

VVV

VVV

VVV

Veee

0695.0tan

m

mel

oat

o 5238

atleV sinsin3

006.0049.0sin 133 eV

0022.00096.02sin 132

0022.00096.02sin 132

Neutrinoless Double Beta Neutrinoless Double Beta DecayDecay

332211. mVmVmVm eeeeff

.........................................

012.00025.00064.00035.0

321

.

effm

0 0

0

A

A C B

B D

0 0

0

A

A C B

B D

neutrino masses:neutrino masses:

m(1)/m(2)=0.42, m(2)/m(3)=0.19m(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 eVm(3): 0.051 eVm(3): 0.051 eV

neutrinoless double neutrinoless double beta decay: beta decay:

improvement by factor improvement by factor 20 necessary20 necessary

05.03 eV