Textures and flavour models

G.G.Ross, Oxford, 21st June 2004

?u GUTM M

?d lGUTM M

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

Family?Family?

Symmetries Coherent picture of quark and lepton masses and mixing?

DATA :

iu?

1GeV

i id il

1210 910 610 310 310

Masses

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

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

2 13 3

1 1 16 3 2

1 1 16 3 2

0

10-1

10-2

10-3

10-4

eV

Bi-Tri Maximal Mixing …Non AbelianStructure?

DATA :

iu?

1GeV

i id il

1210 910 610 310 310

Masses

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

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

† ††(3) familyGUT SU G Simple(?) flavourGroup restricting Yukawa couplings

Quark Textures

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

Hierarchical :11 12 13

22 2321

31 3 32 3

m m

m mm

m

m

M

mm

Expansion parameter 0.15

Quark Textures

4 3 3

2 23

11

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

Hierarchical :11 12 13

22 2321

31 3 32 3

m m

m mm

m

m

M

mm

Det[ ]M

Expansion parameter 0.15

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

( )ij ijTheory YDat Ma

u

t

3 3

3 2 2

3 2

Mm

0

0.05

1

?

?

? ?

RobertsRomaninoGGRVelasco Sevilla

Is one favoured?

4 3 3

2

23

2

2

1

d

b

M

m

( , 0 0)dm S Q

0 0

( )

S Q

A

( )

CP

A

?

SUGR

Gauge mediation

bad for unific

A

ation

Vives, GGR

( , )..

i j ci j aMP Q q H

Cannot align Yukawa and A terms

(3 ( , )) *c c

ij ij a ij ai j i jA Y Q q H i j P Y Q q H

Symmetric structure?

With similar structure for charged leptons Neutrino mixing not related to large RH mixing

Favours near symmetric structure

SUSY

id uus

s c

m mV e

m m

| (0.216 0.2140.217 0.2 ) (0.0722 0.076) |. . iec f 00.213 0.223, 90

Fritzsch,WeinbergRoberts, Romanino,GGR,Velasco

CP SM phase/

3

23

3

2

? ? 1

0d

b

M

m

5

GATTO, SARTORI, TONINsymmetric

Texture zero

3 3

2 23

2 2

0

?

3 ?

?

?

1

lM

m

( ) 1bX

mM

m

( ) ( ) |X

l dMDet M Det M

facto

1(

3

r

)sX

m

T

Mm

GU

Georgi Jarlskog

( ) 3dX

e

mM

m

Extension to charged leptons – GUT?

Possible with “see-saw”

Extension to neutrinos???

1M

TD DM MM M

100

10-1

10

10-2

10-3

10-4

eV2

1 2

0

1

i i

45

SU

(3) SU(2) ..

SU(3) SU(2)

' ..

q ,

l

' ' i

1 (0,0,1)

1' (0,1,1)

???

1

2 1 2 3

3

M

M

M M M

M

M M

SRHD King

3 1 suppresses contributionM King,GGRVives, Velasco-Sevilla, GGR

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 M

1,1 1,1 0

1,2 2,1 (Y diago nal)

lD

l l

Y Y

Y Y

CHOOZ

13

1 2ln( / )M M

/ 2

max

1 2ln( / )M M

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

2 Texture zeros – 2RHN

0.22

0.08

0.08

13sin

With charged lepton contribution 0

13 4.5 3

???dD DM M

b e a

D

3

d d

d e

8 3 4 3 4

3 4 2 3 2 3

3 4 2 3

Mm

0.15, 1

0.15,

1 0.05,

a

a 3

a 0

a a

a

D

3

3 31

3 3 32 1 2 3

3 33

Mm

0

1M

M

M M M M

M

M

King, GGRVives, Velasco-Sevilla, GGR

. . (3) " (10) "fe g SU SO G dD

b

3 3

3 2 2

3

20

20 2

Mm

0 1.5 0.4

1.5 1.3

0.4 1.3 1

i

i

e

e

{

1M

TD DM MM M

45 3( ) 2 RB L T

Quark lepton symmetry?

Vacuum alignment (3), S U(3)SO

D

3

3 31

3 3 32 1 2 3

3 33

Mm

0

1M

M

M M M M

M

M

3

0

0

1

123

1

1

1

23

0

1

1

1 i 3 3 2 i 23 23 3 i 123 23 4 i 23 123P= c c c ci i i i

2 2 2

3 2 1

1 1 1( ) ( ) ( )eL

M M M

2

1( )( )eM

4

3

2

1 @

1(( ) ( ))

m 1=

2 m 20eM

Bi- Tri- maximal mixingBarbieri,Hall,Kane, GGRKing, GGR

de Medeiros Varzielas, GGR

Summary

Due to the see-saw mechanism, the quark, charged lepton and neutrino masses and mixing angles can be consistent with a similar structure for their Dirac mass matrices.

Hints at an underlying (spontaneously broken) family symmetry? SO(10)XSU(3)?

) (3 familySU gives a new solution to the SUSY FCNC problem

Extraction of Yukawa couplings crucial to understanding fermion structure

Bounded off diagonal terms (anti)symmetric, hermitian SUSY data

Texture and texture zero hints at underlying structure

Family symmetry ? GUT symmetry?

A spontaneously broken family symmetry offers a simple solution to the SUSY CP problem