Models of Neutrino Mass
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Models of Neutrino Mass
G.G.Ross, IPPP December 2005
Origin of mass and mass hierarchy
What do we learn from the mixing angles?
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Origin of Neutrino masses
Dirac or Majorana?
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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
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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?
![Page 5: Models of Neutrino Mass](https://reader035.fdocuments.in/reader035/viewer/2022062304/56812b73550346895d8f932f/html5/thumbnails/5.jpg)
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?
![Page 6: Models of Neutrino Mass](https://reader035.fdocuments.in/reader035/viewer/2022062304/56812b73550346895d8f932f/html5/thumbnails/6.jpg)
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
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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
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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)
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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
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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
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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…
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“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
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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
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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
![Page 15: Models of Neutrino Mass](https://reader035.fdocuments.in/reader035/viewer/2022062304/56812b73550346895d8f932f/html5/thumbnails/15.jpg)
(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
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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