Neutrinos and Flavour

G.G.Ross, Coseners House, May 03

What is the origin of the Quark and lepton masses, mixing angles and CP violating phases?

?u GUTM M

?d lGUTM M

(2) (2) ?L RSU SU(2) (2) ?L RSU SU

Family?Family?

DATA :

iu

Mixing

1 0.218 0.224 0.002 0.005

0.218 0.224 1 0.032 0.048

0.004 0.015 0.03 0.048 1CKMV

?

1GeV

i id il

1210 910 610 310 310

Masses

0d dij ijM Y H 0u u

ij ijM Y H

, ,u i c j d i c jYukawa ij ijL Y Q u H Y Q d H

THEORY :

0.72 0.89 0.45 0.69 0.2

0.24 0.58 0.39 0.76 0.52 0.84

0.24 0.58 0.39 0.76 0.53 0.84MNSV

Data Theory ?

†u uL Diag RM V M V

†d dL Diag RM U M U

†CKM L LV V U

Underconstrained – need mixing angles but only VCKM measured.

2 22

2 2

1 2 1/ 2

1 1 21

a aa

a a

u dC

Hierarchy Democracy

4 3 3

2 2?

? ? 1

d

b

M

m

dm usV

cbV

sm

ubV

23

33 33

12

2

32

2

2 22

13 1

3

1

3

3 33

23

12

13

s

b

d

s

d

b

mm m

mm m

mm

mm

mm

m

m

mmm m

V

V

V

11 12 13

22 2321

31 3 32 3

m m

m mm

m

m

M

mm

Hierarchy

d

b

3 3

3 2 2

20

320 2

Mm

0 1.5 0.4

1.5 1.3 0.15

0.4 1.3 1

i

i

e

e

Symmetric fit

Asymmetric fit

d

b

3

3 2Mm

0 1.7 0

1.7 0 5

0 0.3 1

u

t

3

3Mm

0 2 0

0 2

0 0.6 1

u

t

3 3

3 2 2

3 2

Mm

0

0.05

1

?

?

? ?

RobertsRomaninoGGRVelasco Sevilla

Data Theory

3 3

2 23

2 2

0

?

3 ?

?

?

1

lM

m

( ) 1bX

mM

m

( ) ( ) |X

l dMDet M Det M

1( )

3s

X

mM

m

Georgi Jarlskog

( ) 3dX

e

mM

m

Extension to charged leptons – GUT?

Family symmetries

Hierarchical structure strongly suggests a broken symmetry

0 0 0

0 0 0

0 0 1

2

0 0 0

0 0

0 0 1

a

0

2(1),OM

a

MESSENGER SECTOR?

i X

j

H

Xij

H

Mm

FAMILY SYMMETRY? Froggatt, Nielsen

6Abelian, Non-Abelian (U(3))

Abelian Family symmetry (1)U

3 4

3 2

4

0

1

R

R

R

d

s

b

L L Ld s bdR L

b

M

m

-3 2 1

-3 2 1

8( )O

X X

H H

M M

-1 -11 -1

Ibanez GGR

3(40.4 1.8)10 d

s

mcb mV O

uM lM ?M

M Asymmetric charge assignment :

23

13

13

4 3 3

3 2 2

1 1

R

R

R

d

s

b

54 1

3 3 3

L L Ld s b

}

Large mixing… maximal?

3 3

3

3

0

(1) (1)

(1) (1)

2

1

1

eL

L

L

O O

O O

2 1 1

eL L L

effM

) 5(5

c

c

L

c

d

d

S dU

e

Ramond et al, Jack, Jones, …..

Non-Abelian family symmetry

Near Bi (-Tri) maximal mixing suggests Non-Abelian symmetrycapable of relating e

Candidate group?

63: ( )Kinetic c cL L L LL U

Numerous suggestions for the symmetries of effM C3, S3, A4…

Harrison, Scott, PerkinsBabu, Ma, ValleWetterich…

But can such structures be consistent with all quark and lepton masses?

U(2), U(3)Various attempts :Barbieri et al,Chkareuli, Froggattt, NielsenKing, GGR….

King, GGR

8 3 3

3 2 2

3 2 1

d

b

z zM

z w wm

z w

Coefficients equal due to SU(2)family symmetry d

s

mcb mV

(10) (3) familySO U

(4) (2) (2)L RSU SU SU

Maximal, large mixing, SUSY flavour problem

: d l uM M M MGUT q l

: ')(2) (d uR

lU M MS M M

form of from U(3) symmetryMSRHD M

?

?

23 23

1 ici j

j HM

23 (0, , )i x x

3

Possible with “see-saw”

Extension to neutrinos???

???dDM M

( ) / 2b ea

( ) / 2a

i1R

j

1iDM

1D j

M

1M

TD DM MM M

3 3

3 2 3 2 3

3 2 3

0

1

M ( ) ( )

( )D a a

a

z z

z

Majorana Mass1

2 1 2 3

3

M

M

M M M M

M

M

Dirac Mass

100

10-1

10

10-2

10-3

10-4

eV

King, GGR

SUMMARY

The measurement of neutrino properties is testing our ideas about the origin of flavour and raises interesting questions :

Is there a connection between quarks and leptons?

GUT?

Tests?

, [ ] [ ],d lb Xm m Det M Det M Seesaw M

Is there a family symmetry?

Abelian? Non-Abelian?

Origin of the hierarchy?

Froggatt Nielsen? Radiative corrections? New spatial dimensions?

Origin of CP violation?

Spontaneous?

b

texture zeros

...GUT relations,

Precision tests . ..

...m m

Flavour changing neutral currents Mass matrix structure

, ,u c t, ,u c t

, ,..g W

, ,..g W

d

d

s

s

Probes RH angles

e , ,e

W W2 2

2 2

312 10c u

c u

m m

m m

2 2

2 2

312 10e

e

m m

m

l

m

22 , , , , ,R Ri i R Rq u q l em

232 2 1,2 1,2 1,2 31,2 3

22 22 2 2 2 2 2 2 2 21 13 23 ,, ,

R R R RL

i ii i q l u d u dMM M

m m m m m m m

soft mass speSUSY ctrum

SUSY CP : If CP is spontaneously broken in flavon sector the

SUSY CP violating phases are natural

prob

ly s

em

l

l

mal

TESTS?

Vives, GGR, Velasco Sevilla

Neutrino texture zero ?

3 1,2 DRHD M M

*312 1 2

*1 2 1

2 213 12 det

. . Wm M mm M m W

W W

2

313 12 2sin sin emmm m

2/ 2 2 1n 1

2

210MM

Ibarra, GGR

2β decay,leptogenesis

† †. . . .D MNS lM mY D R D U U

Casas,Ibarra

0 cos sin

0 sin cos

1 0 0

z z

z z

}

†W

, ,D D D M1,1 1,1 0 ; 1, 2 2,1 (Y diagonal )l l l

DY Y Y Y

CHOOZ

13

1 2ln( / )M M

/ 2

max

1 2ln( / )M M

(1,2) 0l (1,1) 0l

(SUSY) Textures : FCNC, CP constraints

4 3 3

2

23

2

2

1

d

b

M

m

( , 0 0)dm S Q

0 0

( )

S Q

A

( )

CP

A

?Gauge mediat

SUGRA

ion

Vives, GGR

2 2

2 2

i j

i j

m

ij

m

m m