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
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
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
Hierarchical masses with Small mixing angles
Less hierarchical masses with Two Large Mixing Angles
quark lepton
23-large mixing
can it be explained
naturally ?
2323--large large mixing mixing
can it be explained can it be explained
naturallynaturally ??
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
≈
Simplest Scenario with Family Symmetry
based on the worksbased on the works
in collaboration within collaboration with T.T.KugoKugo
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
≈⇒
≈
†
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 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!
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 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
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….
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
Mixing angles
Mass Differencessolatm θθ 22 tan2sin
largeAlmost maximal
22
atm
2sol λλ≈
∆∆
mm
Now we know・・・・・