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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?. Family?. Family?. Masses. 1. GeV. THEORY :. DATA :. ?. Mixing. Data. Theory ?. Hierarchy. Democracy. - PowerPoint PPT Presentation
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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
