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