neutrinos and flavour
DESCRIPTION
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 PresentationTRANSCRIPT
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