Transcript L Y Q u H Y Q d H

Fermion Masses
The Standard Model
LYukawa  Y Q u H  Y Q d
u
ij
M
u
i
c, j
 Yij  H 
u
ij
d
ij
0
M
i
d
c, j
0
 Yij  H 
d
ij
H
DATA :
Masses
? 

i

10 12
109
106

103
  li
  di



1
103
GeV
Mixing
VCKM
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

1


M
M
d
u
u
 VL† M Diag
VR
d
 U L† M Diag
UR
VCKM  VL† U L
ui
DATA :
Masses
? 
10 12


i
109
106

  li
  di



103
1
103
ui
GeV
Mixing
VCKM
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

1


10-1
10-2
10-3
10-4
eV
VMNS
 0.2 
 0.79  0.88 0.48  0.61


  0.27  0.49 0.45  0.71 0.52  0.82 
 0.28  0.5 0.51  0.65 0.57  0.81 




 



2
3
1
3
1
6
1
3
1
6
1
3
0

1
 2

1 
2 
Bi-Tri Maximal
Mixing …
Non Abelian
Structure?

Data

Theory
(Yij )
...underconstrained - need mixing angles but only VCKM  VL† U L measured

Hierarchy
a 2

 


1


Democracy
1  2  a 2

1  a 2

C   u   d
1  a 2
1  2  a 2

/2

Quark Textures
Hierarchical :
 m11 m12

M   m21 m22
m
 31 m32
m13 

m23 
m33 
Expansion parameter   0.15
Md
mb
 

 ?
 ?

m23
m33
 mm3233
ms
mb
V12 
m12
m22
 mm2221
md
ms
V13 
m13
m33

m31 md
m33 mb
Vub
Vus
md
4
V23 

2

3
?


2
1
3
Vcb





ms
Quark Textures
Hierarchical :
 m11 m12

M   m21 m22
m
 31 m32
m13 

m23 
m33 
Expansion parameter   0.15
 

3
  
 

Md
mb
m23
m33
 mm3233
ms
mb
V12 
m12
m22
 mm2221
md
ms
V13 
m13
m33

m31 md
m33 mb
Vub
Vus
md
4
V23 

2


1
1
3
Det[ M ]

2
3
Vcb





ms

Data
(Yij  M ij )
Theory
Symmetric fit
Md
mb

0

  1.5 3
 0.4ei 20 3

Mu
mt
 0

   3
 ?  3

1.5 3
2
1.3  2
 3
 2
?  2
?  3
?  2
1
0.4ei 20 3
1.3  2
1










  0.15
   0.05
Roberts
Romanino
GGR
Velasco Sevilla
Asymmetric fit
Md
mb
 0
1.7 3

 1.7 3
0
 0
0.3

0 

5 2 
1 
Mu
mt
 0

   3
 0

2  3
0 

0
2 
0.6   1 
Texture zero
 5
0 
M
 3
   2
mb 
? ?
3
d
symmetric
 
2 
 
1 
3
GATTO, SARTORI, TONIN
CP
/ SM phase
Vus 
md
mu
i
e
ms
mc
0.217  0.222 c. f . | (0.216  0.214)  (0.07  0.076)ei |
 0.213  0.223,   900
Fritzsch,
Weinberg
Roberts,
Romanino,
GGR,Velasco
Origin of M quark structure?
Symmetric fit
Md
mb

0

  1.5 3
 0.4ei 20 3

Mu
mt
 0

   3
 ?  3

1.5 3
2
1.3  2
 3
 2
?  2
?  3
?  2
1
0.4ei 20 3
1.3  2
1










  0.15
   0.05
Roberts
Romanino
GGR
Velasco Sevilla
Asymmetric fit
Md
mb
 0
1.7 3

 1.7 3
0
 0
0.3

0 

5 2 
1 
Mu
mt
 0

   3
 0

2  3
0 

0
2 
0.6   1 
Origin of M quark structure?

Third generation heavy
hb  h  (?)ht
ht ,b
g
OK
(specific string calculations + IRFP)
(GUT?)
Infra red fixed point
8
2
d ln( ght3 )
dt
(ht2 ) 
 Yt 
 
 3 
QFP

9
 g32  ht2
2
2 2
g3
9
( Yt3 )
( t ) B3
(1  ( ii (0)
) )
205  sinmt  210GeV
Pendleton, Ross
Hill
Kobayashi, Kubo, Mondragon, Zoupanos
Origin of M quark structure

Third generation heavy
ht ,b
g
OK
(GUT?)
hb  h  (?)ht

(specific string calculations + IRFP)
Hierarchy :
 spontaneously broken family symmetry - mass matrix elements ordered by :
0.2
… dimension of operator
  
 L R H 

M 
… order of radiative corrections
n
Froggatt-Nielsen
 (h2 /16 2 )n
 spatial separation
Yijk h qu


A ijk 
n
d n e

n H D
M ,a a ,ijk
2

2

e 2 iijk n. #
Textures and flavour models
Symmetries
Coherent picture of quark and lepton masses and mixing?
Family?
Mu
SU (2)L  SU (2)R ?
Family?
GUT ?

 M
SU (2)L  SU (2)R ?
Md
GUT ?

 Ml
Symmetries and textures
Hierarchical structure strongly suggests a broken symmetry
 0 0 0


0
0
0


 0 0 1


0 0

2
0
a


0 0

   0
a  O(1),  2 
 
M
MESSENGER SECTOR?
mij 
0

0
1 
   H 
MX
FAMILY SYMMETRY?
Abelian, Non-Abelian  (U(3))6
   H 
i

X

Froggatt, Nielsen
j
U (1)
Abelian Family symmetry
 CKM 
 R M d L
mb

-3
2
1
d
sL
bL 
L
-2
0
 3

 4

O ( 8 ) 
 3  4   dR 

 2    sR 
 1   bR 
H
-3
2
1
?
Vcb  (40.4  1.8)103  O
1


ms
mb

-1
   

MX
MX
Ibanez GGR
U (1)
Abelian Family symmetry
 CKM 
 R M d L
mb

-3
2
1
d
sL
bL 
L
-2
0
 3

 4

O ( 8 ) 
 3  4   dR 

 2  2  sR 
 1   bR 
H
-3
2
1
Vcb  (40.4  1.8)103  O

ms
mb

Non-Abelian symmetry?
1

-1
   

MX
MX
Ibanez GGR

Extension to charged leptons – GUT?
Det ( M l )  Det ( M d ) |M X
 0
l
M
 3
 
m  2
 ?
 3 ? 3 
2
2

? 
? 2
1 
?
mb
(M X )  1
m

Extension to charged leptons – GUT?
Det ( M l )  Det ( M d ) |M X
 0
l
M
 3
 
m  2
 ?
ms
1
(M X ) 
m
3
md
(M X )  3
me
Georgi Jarlskog
 3 ? 3 
2
2
3 ?  
? 2
1 
mb
(M X )  1
m

Extension to neutrinos???
i
m3 23i  i23j j  m2 123
 i123j  j
  23 i  (0,1, 1),  123 i  (1,1,1)
c. f . m 3i i3 j cj

  3 i  (0,0,1)
Vacuum alignment
3
q i , li
SU(3)  SU(2)  ..
450
i
33 13
0
SU(3)  SU(2)'  ..
23
123
???
 NonAbelian Discrete Family symmetry?

Z 3 Z 
3
Vacuum alignment
i
Z 3i
King, GGR,
Varzielas
Z3' i
1  2  1
2  3  2
3  1   23
Radiative breaking
V ( )  m  
2
†
SU (3) f symmetric
   (a, b, c), a 2  b2  c 2
2
m2 ( † )

  † 

Z 3 Z 
3
Vacuum alignment
i
Z 3i
King, GGR,
Varzielas
Z3' i
1  2  1
2  3  2
3  1   23
Radiative breaking
V ( )  m     m  i i
2
†
2
i†
 3  (0,0,1),   0
 123 

3
(1,1,1),   0
i†
m2 ( † )

i †
 ' m2123
23,i23j †123,i
  23 i  (0, 1,1)
  † 
Z 3 Z 
3  SO (10)  G


 ic ,  i  16, 3  No mass while SU(3) unbroken
Spontaneous symmetry breaking
c.f. Georgi-Jarskog
i
3,
i
i
 23 ,  123 , H 45
(1,3)
(1,3)
(1,3)
0
 
0
1
 

(G  R  U (1))
PY 
0
 
 1  M
1
 
 1
  2
 1  M
 1
 
 45,1
M
1 i
1 i
1 i
1 i
j c
j c
j
c




H





HH





H

   j c H
j
45
2 3 i 3
3 23 i 23 j
2 23 i 123 j
2 123 i 23 j
M
M
M
M
only terms allowed by G
Dirac mass structure
MD
m3
0 0 0


 0 0 0
0 0 1


0
3   0 
1
 
PY 
1 i
1 i
1 i
1 i
j c
j c
j
c




H





HH





H

   j c H
j
45
2 3 i 3
3 23 i 23 j
2 23 i 123 j
2 123 i 23 j
M
M
M
M
Dirac mass structure
MD
m3
0
0

  0 a 2
 0 a 2

0 

a 2 
1 
ad  1
a e  3
a  0
 H 45   ( B  L)  2 T3R
c. f .Georgi Jarlskog
123
PY 
1
 
 1
1
 
1 i
1 i
1 i
1 i
j c
j c
j
c




H





HH





H

   j c H
j
45
2 3 i 3
3 23 i 23 j
2 23 i 123 j
2 123 i 23 j
M
M
M
M
   H 
Dirac mass structure
i
MD
m3
 0

  3
  3

0
23   1 
 1
 
PY 
3
a 2   3
a 2   3
123
 3 

a 2   3 

1

 d   l  0.15
 u  0.05
   0.02

X

j
Messenger masses break SO(10)
1
 
 1
1
 
1 i
1 i
1 i
1 i
j c
j c
j
c




H





HH





H

   j c H
j
45
2 3 i 3
3 23 i 23 j
2 23 i 123 j
2 123 i 23 j
M
M
M
M
M  M D M M1 M DT
Neutrino masses
 0 3
 3
3

  3  3


MD
m3
PY 
3 

 3 
1 
MM
 M1




M2



M 3 
Structure determined from
symmetries too
M 1  M 2  M 3
1 i
1 i
1 i
1 i
j c
j c
j
c
j c




H





HH





H




3 i 3
j
23 i 23 j
45
23 i 123 j
123 i 23 j H
M2
M3
M2
M2
Actually cancelled by small off diagonal
Majorana terms
Small
6
1
6
6
2
2
2
(    )(     e )
L 
(  ) 
(     e ) 
(    ) 
M
M3
M2
M1
2

a

  
b

      e
Bi-Tri Maximal Mixing
Summary

Extraction of Yukawa couplings crucial to understanding fermion structure
Bounded off diagonal terms

Texture and texture zero hints at underlying structure
Family symmetry ?

(anti)symmetric, hermitian  SUSY data
GUT symmetry?
Due to the see-saw mechanism, the quark, charged lepton and neutrino
masses and mixing angles can be consistent with a similar structure for
their Dirac mass matrices.
Hints at an underlying (spontaneously broken) family symmetry?

SO(10)  G ?
Z 3 Z 
3
SU (3) family gives a new solution to the SUSY FCNC and CP problems
2
m i
1
M2
2
2
m 
i
i 3
  q, u R , d R , l , e R ,  R
2
,
1
M2
2
m 
i
i 23
2

m  M
2
q ,l
23
L

2
,  md2R   2 ,  mu2R   '2
12 
2
2
mc  mu
2
2
mc  mu
 10
 
3
l
12
2
2
m  me
2
2
m  me
d
 103
g , W ,..
u , c, t
u , c, t
s

s
g , W ,..
d
W

W
 e ,  , 
Probes RH angles
 SU (3) family gives a new solution to the flavour problem
2
m i
1
M2
2
2
  q, u R , d R , l , e R ,  R
2
m  i3i ,
1
M2
2
2
m  i23i 
 mq2,l 
  , m
23 2
ML
2
dR
  2 ,  mu2R   '2
 SUSY CP problem : If CP is spontaneously broken in flavon sector the
SUSY CP violating phases are naturally small
e
mQi  muc  md c  mH  m0
i
i
mQi3  muc  md c  mH  m0
i
i
mQ3  mQi 3 (1  0.2)
3 family symmetry breaking
Ramage,GGR