textures and flavour models g.g.ross, oxford, 21st june 2004 family? symmetries coherent picture of...
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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
???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