See-saw Mechanism 　　and Neutrino Ｍass Matrix

in GUT

Masako　Bando　Aichi University

2004.2.２２-２５

based on the works

in collaboration with

T.Kugo, K.Yoshioka, N. Maekawa 　　　　　　　 　

S.Kaneko, M.Obara, M.Tanimoto

based on the worksbased on the works

in collaboration within collaboration with

T.T.KugoKugo, K.Yoshioka, N. , K.Yoshioka, N. Maekawa Maekawa 　　　　　　　　　　　　　　 　　

S.Kaneko, M.S.Kaneko, M.ObaraObara, M., M.TanimotoTanimoto

PrincipleNaturalness

no fine tuning

PrinciplePrincipleNaturalnessNaturalness

no fine tuningno fine tuning

Seesaw Mechanism

Why is neutrino mass so small ?

Existence of Right-handed neutrinos

Small mass can be derived

Naturallyby seesaw

Small mass Small mass can be derived can be derived

NaturallyNaturallyby by seesawseesaw

Bi-large mixing can it be explained

naturally ?

BiBi--large mixing large mixing can it be explained can it be explained

naturallynaturally ??

Hint of the origin of power Hierarchy ?

Hint of the Hint of the origin of origin of power power Hierarchy ?Hierarchy ?

Scale Hierarchy in GUT scenario

log scale

PMνM EWM

Strong hierarchy

Scale Hierarchy in GUT scenario

log scale

PMνM EWM

Mild hierarchy

Strong hierarchy

τ

µ

λ m

m2≈ tM

m8

u

λ≈ EWMm≈

t

Mnλ

Scale Hierarchy in GUT scenario

log scale

PMνM EWM

Mild hierarchy

Strong hierarchy

P6M

M

λ≈R

P3

GUT

M

M

λ≈ P0

p

M

M

λ≈Mnλ

Introduce …Family

Quantum number

Introduce Introduce ……Family Family

Quantum Quantum numbernumber

Horizontal Symmetry1979 Yanagida san

質量項(SUSY)階層的構造Froggatt-Nielsen U(1)

)(

)(eff

ij

)(

uj

Ri

L

y )1O(

HFF

hji

hjiijij

hjih

ij

yy

yW

++

++

++

Λ

=

≡→≈

Λ

×=

θλ

λ

θ

Hierarchical parameter

We use the same idea (F-N)higher dimensional Operators

Anomalous U(1) with SUSY

Then …Family Quantum numberTThen hen ……

Family Quantum numberFamily Quantum number

Common family number

members of a multiplet

Neutrino MNS Matrix

SeeSaw

Hierarchical masses with Small mixing angles

Less hierarchical masses with Two Large Mixing Angles

quark lepton

Hints of family structure?

　　

Big difference between quarks and leptons !

Problem

Standard model …SStandard model tandard model ……

Common family number

members of a multiplet

23-large mixing

can it be explained

naturally ?

2323--large large mixing mixing

can it be explained can it be explained

naturallynaturally ??

Rν

Minimal Matter contents

Lq

RdRu

ReRν

Le

LdLu

L

L

eν

L

L

du

SU(2)L

Standard Symmetry

RdRu

ReRν

LQ

L

×３　！Ｆａｍｉｌｙ

Ｓｉｍｐｌｅｓｔ　Ｓｃｅｎａｒｉｏ　　　　　　　　　　with Family Symmetry

based on the worksbased on the works

in collaboration within collaboration with　　　　　　　　　　　　T. T. KugoKugo

QuarkMasses and mixings

λ＝λｃ

≈

−

1******

M 4

76

u λλ

tm

≈1

11

U23

2

3

CKM

λλλλλλ

≈2

4

6

d

******

Mλ

λλ

tm

Ｕｐ Quark Masses

[ ]

t

L

m

Q

≈

−−

1023

M

u0243

23

245

3576

u

R

λλλλλλλλ

76

t

u

4

c

u

−≈

≈

λ

λ

mmmm

4,2,0)-(3)t,c,X(u introduce weIf

RRR =

Ｄｏｗｎ Quark Masses

2

t

b

2

b

s

4

b

d

λ

λ

λ

≈

≈

≈

mmmmmm

(3,2,2))t,c,X(u introduce weIf

RRR =

[ ]

t

L

m

dQ

2223

334

d

R

11023

M

223

λλ

λλλλλλ

≈

No relation between quarks and leptons

　　

　Standard symmetry

Ｓｉｍｐｌｅｓｔ　Ｓｃｅｎａｒｉｏ　　　　　　　　　　with Family Symmetry

based on the worksbased on the works

in collaboration within collaboration with　　　　　　　　　　　　T.T.KugoKugo

GUT　with

Family Quantum number

GUTGUT　　withwith

Family Family Quantum Quantum numbernumber

Relations?

GUTGUTRM

DM νlM

dMuM

νM

RdRu

ReRν

LQ

LSU(5)

105*

Quark Masses mixings

≈

≈≈

−

11

1U

UU

23

2

3

CKM

1010du LL

λλλλλλ

λ ji

(3,2,0)),10,10X(10 lautomatica isIt

321 =

Ｄｏｗｎ Quark charged leptons

(3,2,2)),5,5X(5 3*

2*

1* =

[ ]

tl

t

L

m

m

dQ

2223

334

2223

334

d

R

11M

11023

M

223

λλ

λλλλλλ

λλ

λλλλλλ

≈⇒

≈

†

Neutrino mass matrix

≈

≈+

1111

)(M2

55 **

λλ

λλλ

λνji

(3,2,2)),,X( 3L2L1L =ννν

SU(5)

lM†dM

νM

Thus simple Ｕ（１）ＦＮuniquely dictates the forms:

∝1111M

2

λλ

λλλ

νAlso

We have

≈1111U

2

λλ

λλλ

bl m

Possibly, (Maekawa version)N.Maekawa, PTP 106(2001)401, and others

3?

2

2223

334

d

1

1M

mM

mt

λλλ

λλλλλλλλ

λλλ

λλλλλλλλ

ν

≈

≈

Up to here 2-3 family

structurealmost

determined !

Up to here Up to here 22--3 family 3 family

structurestructurealmost almost

determined !determined !

Question 1Question 1Question 1

Question 1Two large mixing angles？　Mass ratio ？

1 Order of magnitude does not work !

2 naturally reproduced?

However note that once it is realized.....

≈1111M

2

λλ

λλλ

ν

This sub-matrix should haveIts Det of order of λ? Non-trivial!

1-2large mixing is

automatically realized!

Maekawa version (E6)

3?

2

2223

334

d

1

1M

mM

mt

λλλ

λλλλλλλλ

λλλ

λλλλλλλλ

ν

≈

≈

This submatrix Det =λ

Naturally we have order of λ!

lMνM

Without fine tuning

either or

Which reproduces large mixing angle?

Up-roadDown-road Up-Down

CHOOZ limit

Provable texture

Need Little tuning

SimpleU(1)FN

OK

llMTM

atm

1111

2

λλ

λλλνM

1111

2

λλ

λλλ

1

4

8

λλ

1λλλλ

≤

1

2

λλ

111111111

m m

mm

atm

atmatm

1111

2

λλ

λλλ

1111

2

λλ

λλλ

Can we reproduce the neutrino large mixing out of hierarchical Dirac Masses?

Impossible !!! Unless fine tuningNeeds Zero structure to relate Hierarchical Up

quark mass matrix for Neutrino Dirac Masses

mthen

mIf

mMmji

ij

T

∝

∝

= −

ν

ν

λλ

M

)(

M 1

Parallel Family Structure

Can survive !!!!

M.B,S.Kaneko, M.Obara and M.TanimotoP.L B580(2004) 229

In order to get such desirable

neutrino mass matrix

Needs Zero structure to relate Hierarchical Up quark mass matrix

to Neutrino DiracMasses→ seesaw enhancement can occur

Tanimoto san

Question 2Question 2Question 2

Question ２Origin of difference between 5*and 10 ?　

1 Higher dimension or higher GUT ?

2 naturally reproduced?

ＧＵＴ ⇔　charge quantizationgauge unificationanomaly free set

　　１ｓｔ　　１ｓｔRRL eu,Q L,d R Rν

RRL eu,Q L,d R Rν　　3rd　　3rd

RRL eu,Q L,d R Rν　　2nd　　2nd

Doubling ⇔　same family number

　　１ｓｔ　　　　　

　　１ｓｔ　　　　　

RRL eu,Q L,d R Rν

RRL eu,Q L,d R Rν　　3rd　　3rd

RRL eu,Q L,d R Rν　　2nd　　2nd

３

２

０

L,d R RνL,d R RνL,d R Rν

２７

RdRu

ReRν

LQ

LSO(10) 16

5*

1

10

LQ Rd

Ru ReRν

Rd L

L27

E6 Rd L

SU(5)SO(10)

　Quite naturally Natural scenario

to reproduce Family twisting　

　

E6

Non Parallel Family Structure

not a mere repetition

We need some new idea for family structure

Interesting to find the reason

Why the nature choose the world where

10s are governed by King 5*s live in democratic society

Anarchy model, Brane world….

Another Interesting fact is

Even if we start hierarchical Dirac mass, we can reproduce bi-large mixing.

SO(10) with antisymmetricYukawa, zero structure….

Nature chooses?

Family twisting structure

Or ?

Parallel Family structure

That is a question!

My History on Neutrino

• SI1995 post YKIS The first SI in JapanSmirnov Lecture

• SI1997 SI1Yanagida san talk family twisting

structure• SI1998 pre-SI

Takayama conf. Ramond san at Aspen Center

Pre-historyYanagida san at Yukawa Indstitute

目次1979　 Seesaw　1987 Super Nova data1996 SK data1997 Takayama Conf.19981999 K2K20002001 Solar Neutrino LMA2002 KamLand SNO2003 WMAP2004 Oscillation L/E dep.

seesaw

Solar Neutrino

data

Atmneutrino

data

Good Old

Yanagida san at Yukawa Institute

Only two physicists Were at the seminor

Yanagida san at SI 1997SK preliminary data

Atm Neutrino Mass and mixing

Ramond san at Aspen center

F-N family numberWorks well !

We should make Full use of E6 GUT

Mixing angles

Mass Differencessolatm θθ 22 tan2sin

largeAlmost maximal

22

atm

2sol λλ≈

∆∆

mm

Now we know・・・・・

Kugo san can manage exceptional group !

F-N family +Family twisting structure

We can make Full use of E6 GUT