Download - Models of Neutrino Mass
Models of Neutrino Mass
G.G.Ross, IPPP December 2005
Origin of mass and mass hierarchy
What do we learn from the mixing angles?
Origin of Neutrino masses
Dirac or Majorana?
Origin of Neutrino masses
Dirac or Majorana?
0 2
0 0iji j ijij
f HH H M f
Weinberg 1979
0H 0H
RM
i j
( ) ( )A A
0H 0H
M
i j
( ) ( )D D
0H
i j
( ) ( )E F ( ) ( )B C
i j
0H
0H
(2) singletsLSU
0i iH l H 0 0[ ( ) 2 ]i i i iH H l H l H
i j i jl l [ ( ) 2 ]i j i j i j i jl l l l
0 01 2 1 2H H H H 0 0 0[ 2 ]H H H H H H
(2) tripletsLSU
(A)
(B)
(C)
(D)
(E)
(F)
0H
0 2
0 0iji j ijij
f HH H M f
Weinberg 1979
0 2
i
R
Hm
M
2013
210
10R
Hm GeV
GeV
(2) singletsLSU
0i iH l H 0 0[ ( ) 2 ]i i i iH H l H l H
i j i jl l [ ( ) 2 ]i j i j i j i jl l l l
0 01 2 1 2H H H H 0 0 0[ 2 ]H H H H H H
(2) tripletsLSU
(A)
(B)
(C)
(D)
(E)
(F)
0H 0H
RM
i j
( ) ( )A A
Minkowski mechanism
Origin of Neutrino masses
Dirac or Majorana?
0 2
0 0iji j ijij
f HH H M f
Weinberg 1979
M
i j
( ) ( )A A
0 2
i
R
Hm
M
2013
210
10R
Hm GeV
GeV
2
i
N
mM
2
3
110N GeV
MeM
V
/PRSUSYPRSUSY
(2) singletsLSU
0i iH l H 0 0[ ( ) 2 ]i i i iH H l H l H
i j i jl l [ ( ) 2 ]i j i j i j i jl l l l
0 01 2 1 2H H H H 0 0 0[ 2 ]H H H H H H
(2) tripletsLSU
(A)
(B)
(C)
(D)
(E)
(F)
Origin of Neutrino masses
Dirac or Majorana?
New space dimensions
Closed string 11D propagation
Graviton, Modulini
Open string
SM states
Right-handed in the bulks
4 ( ) ( ) ( , 0)L Rd x x H x x y }
*
/1,2
( ) iny RR nRM
n
x e
Flux spreading
* *4.10Planck
HM TeV
M Mm eV
Arkani Hamed, Dimopoulos, March RussellDienes,Farragi
In 4D small Dirac masses can arise through higher dimension operators * *
*( , ) '( , ). . u d
F Fe g K LH N LH N
M M
Abel, Dedes, Tamvakis3/ 2 16 7, 10 10Mm
eVH GmM
Dirac or Majorana? 12, ?: 10L Rh H m h H h
Neutrino mass and dark energy
3 4(3.10 ) neutrino sectorDE eV
Quintessence field3310m eV
Symmetry needed to keep it light
CP violating field of neutrino mass matrix? Barbieri, Hall, Oliver, Strumia
Mass varying neutrinos
0( ) ( ), ( )V m m n V m m f A
. . . 1DM
E OM
energy in A
22
0 0( ) ( ) ( )DD L L
mm N ANN V A V A see saw
A
L
At finite density :
2
0( ) ( )Deff
mV m n V A
A
Neutrino density dependent term
4 At false minimum 0, DA V m
At true minimum 0, 0 ( )A V fine tuned
drives 0A
Fardon, Nelson, Weiner
spontaneously broken family symmetry - mass matrix elements ordered : by
n
L RH M
spatial separ n atio
Yijk hqu n H2
DM , a a,ijk
dn e
Aijk n
2 e 2 i ijkn. #
Froggatt-Nielsen
Origin of mass structure
… dimension of operator
… order of radiative corrections2 2( /16 )nh
Hierarchy
Structure
Can get normal, inverted or degenerate structures
(NB Radiative corrections can split precise degeneracies unless protected by symmetry)
Unravelling the origin of mass…..
…difficult (impossible) unless we are lucky!
?Q L
100
10-1
10
10-2
10-3
10-4
eV
Mixing
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
Bi-Tri Maximal Mixing …
Harrison, Perkins, Scottansatz
Non AbelianStructure?
Many possibilities, many parameters…
Small in quark sector, large in lepton sector?
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
23 23 123 123i j i j
i j i ja b effL
23
0
1
1
123
1
1
1
3 3 ...l i c ji ja L
3
0
0
1
0 0
3
i i
23 123
45 35
SU(3) SU(2) ..
SU(
3) SU(2)' ..
q , l
i
???
Tri-Bi-Maximal mixing
Discrete non Abelian family symmetry
2. . ( ) :Ze g i e d d
M d a b
d b a
1
2
3
0 0
0 0
0 0
T
m
U M U m
m
cos sin 0
sin / 2 cos / 2 1/ 2
sin / 2 cos / 2 1/ 2
U
Bi-maximal
23 12 13/ 4, , 0
But what about the charged lepton sector ??
Need complete theory…
“See-saw” with sequential domination1
MT
D DM MM M
1
3 1
3
2 1 2 3 suppresses contributio nMM M
M
M
M M M M
SRHD King
Two ingredients :
(Discrete) Non-Abelian family symmetry
3 3 23 23 123 123l i c j i c j i c j
i j i j i j L
2 2
23 23 123
2
3 1231
3 32
( )i j i ji j i j
i ji jM M M
effL
small
23
0
1
1
123
1
1
1
3
0
0
1
Vacuum alignment
King, GGR, Varzielas
Vacuum alignment Altarelli,Feruglio
1 2 32 3i ii
M gP
1 2 3 2 1 3 3 1 21 2 3
0, 0, 0P P P
M g M g M g
(v,v,v), vM
g
2 3 4(12) ( , )Z Z A
2 3 1 3 1 21 2 3
' ' 0, ' ' 0, ' ' 0' ' '
P P Pg g g
' (v',0,0), v' driven by soft terms
1 2 3
'' ' ' '
3
gP
King,GGR,Varzielas
Summary
Origin of mass and mass hierarchy
- Many possibilities for both Majorana and Dirac masses :
Heavy see-saw, light see-saw, bare Dirac, radiative generation, radiative running, running masses…dark energy
- All patterns of mass possible :
normal, inverted, degenerate
What do we learn from the mixing angles?
-Hints at an underlying (spontaneously broken) family symmetry?
SO(10)XSU(3)? Unified theory of quark, charged lepton and neutrino masses with related textures
(10) (3) familySO SU G
3 23 123 45, , ,i i i H
, No mass while SU(3) unbrok3 e16, nci i
Spontaneous symmetry breaking
(1,3) (1,3) (1,3) 45,1
2
0 0 1
0 1 1
1 1 1
M M M
c.f. Georgi-Jarskog
(4) (2) (2)L RSU SU SU
3 3 23 23 45 23 123 123 232 3 2 2
1 1 1 1i j c i j c i j c i j cY i j i j i j i jP H HH H H
M M M M
only terms allowed by G
I de Medeiros, GGRKing, Vives, Velasco Sevilla…
(1) (1) 'G R U U
D
3
3 4 3 4
3 4 2 3 2 3
3 4 2 3
Mm
0
1
a a
a
Common texture zero
Summary
Origin of mass and mass hierarchy
- Many possibilities for both Majorana and Dirac masses :
Heavy see-saw, light see-saw, bare Dirac, radiative generation, radiative running, running masses…dark energy
- All patterns of mass possible :
normal, inverted, degenerate
What do we learn from the mixing angles?
-Hints at an underlying (spontaneously broken) family symmetry?
SO(10)XSU(3)? Unified theory of quark, charged lepton and neutrino masses with related textures
- A discrete non-Abelian subgroup can give vacuum alignment neededfor bi-tri-maximal mixing