Flavor and CP violation
in SUSY seesaw models
The 12th International Conference
on Supersymmetry and Unification of Fundamental Interactions
June 17-23, 2004, Tsukuba, Japan
Junji Hisano (ICRR, Univ. of Tokyo)
Neutrino oscillation:
Finite, but small neutrino masses
( f h2 ) 2
m
MN
 0 ( M  )
Seesaw model
(Introduction of right-handed neutrinos  R )
L  fl eR Lh1  f  R Lh2  M N  R R
Unification of Matter
in SO(10) GUT:
uL , uR , d L , d R
(16)  (
)
eL , eR , L , R
Superheavy
Baryon in Universe:
Leptogenesis
(B-L violation
by Majorana mass M )
M : We need Supersymmetry (SUSY)
Charged Lepton-Flavor Violation in SUSY seesaw model
Non-vanishing LFV slepton masses by radiative correction
m 
2
L
1
8
ij
2

(3m  A ) f f
2
0
2
0
†

MN
ij log
M pl
(Borzumati&Masiero)
Then,
Br (li  l j  ) 10
6
( 
mL2
mL2
100GeV 4
) (
) tan 2 
mSUSY
ij 2
The charged LFV,    ,   e
be observed in near future experiments.
(These are reviewed by Dr. Illana.)
, may
SUSY GUT with right-handed neutrinos
Matter unification: GUT relation in flavor physics
( sR1 sR 2 sR 3 L   L )

( bR1 bR1 bR 3  L   L )
Flavor Higgs
m  / m 
2
dR
ij
*
2
L ij
e
 i (i  j )
Colored Higgs
M GUT
MN
(log
/ log
)
M pl
M pl
(  i :CP phase in GUT)
(moroi)
Flavor-violating right-handed current might predict deviation of
Bd0   K s and so on.
Contents of my talk
Introduction
CP and flavor violation in SUSY GUT model
JH and Shimizu, hep-ph/040691
JH, Kakizaki, Nagai, and shimizu, in preparation.
Summary
2, CP violation in SUSY SU(5) GUT
the neutrino Yukawa induces the flavor violating right-handed
currents, ex,
(m )  (m ) e
2
d R ij
2 *
lL ij
i (i  j )
(log
M pl
M GUT
) /(log
M pl
MN
)
Here,  i is the CP phase in colored Higgs interaction. CP and
flavor violation in the RH currents give rich hadron physics
1) K 0  K 0 and B 0  B 0mixing
2)CP asymmetry in the decay
CP asymmetry in Bd0  K S (Im((
m
) )d20)23 
R
(2.7 sigma deviation observed in Belle experiment.)
3) EDMs of neutron and atom.
(1,2) mixing and (2,3) and (1,3) mixings are constrained by  K
and hadronic EDMs, respectively.
Hadronic EDMs
Current bounds on Mercury and neutron EDMs constrain the
SUSY models.
| dHg | 2.11028 ecm,
| dn |  6.3 1026 ecm.
Choromoelectric dipole moments (CEDM) generate CP violating
hadron interaction, which generates
EDMs of Mercury and
C
dq
neutron.
LCP   i
qg s (G   ) 5 q
2
q
Strange quark component in necleon is not negligible. From
baryon mass and sigma term in chiral perturbation theory,
p | uu | p
4.8,
p | dd | p
4.1, p | ss | p
2.8
(Zhitnitsky)
Thus, hadronic EDMs depend on the strange quark CEDM
via K or eta meson interaction. Using the QCD sum rule, ex,
2
2 C
2
2
g CP


p
|
ss
|
p
m
d
,
(
m

0.8
GeV
). (Falk et al)
pp
0 s
0
3 3 f
Hg atom EDM
199
Hg is a diamagnetic atom, and the EDM is sensitive to CPviolating nuclear force induced by pion and eta exchange, which
generates T-odd EM potential (Shiff momentum).
Recent evaluation of Shiff momentum by Dmitriev and Sen’kov
reveals that contribution to EDM from isoscalar channel for meson
exchange is suppressed by 0.01 compared with previous estimate.
From it, it is found that the strange quark CEDM contribution
comes from pi-eta mixing.
dHg  8.7 103 e (duC  ddC  0.005dsC )
(JH, Shimizu)
 0  0 mixing
CP violating
2
C
C
C
Previous result: dHg  3.2 10 e (du  dd  0.012ds )
(Falk et al)
Neutron EDM
This evaluation is a difficult task. The QCD sum rule is useful for
evaluation of only contribution from valence quarks. Here, we
present our result by a traditional calculation of the loop diagrams.
CP violating
CP violating
d n  1.6e (duC  0.81d dC  0.16d sC )
(JH, Shimizu)
Strange quark contribution to neutron EDM is not suppressed
Compared with up and down quarks.
Here, Peccei-Quinn symmetry is assumed. Axion suppresses
strange quark CEDM contribution for valence quarks, while
above formula is not so changed even if no PQ symmetry.
C
C
Compare with the sum rule result: d n  0.55e (du  0.5d d )
(Pospelov&Ritz)
Deuteron EDM
Recently new technique for measurement of deuteron EDM by
using storage ring is proposed and the sensitivity may reach to
d D (1  3) 1027 e cm.
This system is relatively simple and the EDM is given as
dD  (d p  dn )  dNN
CP violating nuclear force
Each components are
(d p  d n )  e (5.1duC  2.1d dC  0.32d sC )
dNN
 e (11duC  11d dC  0.063d sC )
27
New technique for deuteron EDM may reach to d D 10 e cm.
C
C
28
C
26
This corresponds to du d d 10 cm and d s 10 cm
Hadronic EDM constraint on
2
dR
(m )
in SUSY GUT
2
(
m
)
If the off-diagonal term in
d R has a CP phase, it contributes
to CEDM in the cooperation with the left-handed squark. The
off-diagonal terms are induced by the top quark Yukawa coupling
with CKM.
Enhanced by heavier
fermion mass
In typical models, the left-handed squark mixing induced by top
quark are
 23dL
 2 , 13dL
 3 , 13dL
Here,
 ijdR  (md2 )ij / md2
R
R
 5 ( ~ 0.2)
 ijdL  (md2 )ij / md2
L
L
Constraints on the flavor violation in squark mass term
From neutron (Hg atom) EDM
| Im( 32dR ) | 4.8(98) 103
| Im( 31dR ) | 4.7(2.5) 103
| Im( 2dR1 ) | 4.5(2.4)
for tan   10, mSUSY  500GeV
dL
Here,  23
 2 , 13dL
 3 , 13dL
 5 ( ~ 0.2) are assumed.
Constraints on (1-3) and (2-3) mixing for the right-handed squark
mixings are stringent. (1-2) mixing is constrained by  K .
| Im( ) | 2 10 ,
( K )
|
| 110 ,
(M Bd )
|
| 2,
(b  s )
4
dR
12
dR
13
dR
13
1
CEDMs in SUSY SU(5) GUT with right-handed neutrinos
For m0  500GeV , a0  0 mg  500GeV , tan   10
Deuteron EDM reach
d
C
s
(JH, Kakizaki, Nagai, Shimizu)
Deuteron EDM reach
d
C
d
Here, diagonal right-handed neutrino mass matrix is assumed, and
then parameters in neutrino sector are given by oscillation data.
New technique for deuteron EDM may reach to d D
C
This corresponds to d d
1028 cm and
d sC
1027 e cm.
1026 cm
CP asymmetry in Bd0   K S v.s. Strange quark CEDM
d
C8R
C
s
mb
dL R


 d 
(1
3)
Im

23 C8 
2

12
C
s
CP asymmetry in Bd0
strongly correlated.
  K S and strange quark CEDM are
Assuming d sC   mb 11 Im  23dLC8R  ,

4 2 21 
Belle
BaBar
(JH, Shimizu)
The neutron EDM bound is one or two orders of magnitude
stronger for a sizable deviation in Bd0   K S .
Summary
In the extension of SUSY GUT, right-handed squark mixings are
generated by the neutrino Yukawa interaction. The hadronic
EDMs have big potential to probe for (1-3) and (2-3) mixing of the
right-handed squark mixing, though they may suffer from
theoretical uncertainties.
The neutron EDM is more sensitive to strange quark CEDM, and
the constrain the deviation of CP asymmetry in Bd0   K S . .
New technique for the deuteron EDM measurement may give
more stringent constraints on them or find the signal.
It is important to take a correlation among various hadronic EDMs,
such as those of diamagnetic atom and neutron. The latter is
more sensitive to the strange quark CEDM.
1, Introduction
Lepton-flavor Violation (LFV) in neutrino sector
: Neutrino oscillation experiments
⇒ How large is LFV in charged lepton sector?
   ,  3 ,
  e ,   3e
However,
Tau LFV decays
( ⇔ Atmospheric neutrino ? )
Muon LFV decays
( ⇔ Solar neutrino ?)
Br (   e )  1048 (m /1eV ) 4
Charged LFV depends on the physics beyond the SM and
origin of the neutrino masses.
Other tau LFV processes:
Normal case
One-shell photon contribution is dominant,
since dipole operator contribution is proportional to tan 2  .
Furthermore, 3lepton processes is enhanced by log  m m 

Br (   ee(3e)) / Br (   (e) )
Br (  3 (e2 )) / Br (   (e) )
1/ 94,
1/ 440
If we find the LFV, we can examine non-trivial tests!
l

Even if the slepton is so heavy (ml  TeV ) ,
the anomalous LFV Yukawa coupling for Higgs boson may
be generated radiatively and not be suppressed by the
SUSY scale. In this case, the tau LFV processes may be
generated by Higgs mediation, and 3mu, mu eta, mu gamma
are comparable.
4
 tan    100GeV 
Br (   )  (8 10 )  

 
60
m

 
A

Br (   ) : Br (  3 ) : Br (   ) ~ 5 :1 : 0.5
6
7
(Babu&Kolda;Brignole&Rossi;JH&Shimizu)
2, Tau LFV in SUSY seesaw model
Non-vanishing LFV slepton masses by radiative correction
m 
2
L
and
1
ij
8
m 
2
eR
2
ij
(3m  A ) H ij
2
0
0
2
0
1
 Ae  ij
8
2
f e A0 H ij
 †

MN
where H ij   f log
f  ij


M
pl


Radiative decay processes:

l l, l ll l
'
Sizable effect
' '' ''
Belle’s new bounds and future
Belle
and BaBar experiments are improving the bounds on
.
Tau LFV processes significantly.
2000 PDG
Belle (current ) L  100 fb
    1.1106
 3.1107
  e  2.7 106
 3.6 107
    9.6 106
 4.4 107
  e  8.2 106
 6.9 107
  lll  a few 106  a few 107
1
L  3ab
107
108
107
108
1
107
108 109
107
108 109
107
108 109
Further improvements of one or two orders may be expected in
super B factory.
Bottom-up approach to seesaw model
Degrees of freedom of physical observables
In Seesaw model,
M:3+3, :6,CP:4(mixing)+2(Majorana)
 T h2 2 
(m )ij   f
f  ij


M
N


In light  mass matrix (m )ij
M:3, :3, CP:1(mixing)+ 2(Majorana)
 †

MN
H ij   f log
f  ij
MG


In H ij (Hermitian)
Real: 6,Phase:3
We can take (m )ij and H ij for parameterization of seesaw
model, and neutrino and charged lepton experiments give
independent information of seesaw model.
Br (   ) comes from H 23 , and Br (  e ) from H13 .
Question: How large they can be?
  e is generated if H12, and / or .H13 H 32  0.
We assume
* 0 0


H (1)   0 * * 
0 * *


Br (   )
(1)
H (2)
*

 0
*

Br (
(2)
0 *

* 0
0 * 
 e )
Model-building may favor with H , not H .
(Observed large mixings of neutrino come from Yukawa
coupling in a case of H (1), but Majorana mass in H (2).)
Bd0   K S in SUSY GUT
Observation of CP asymmetry in Bd0   K S :
S K  0.96  0.50 ( Belle),
S K  0.47  0.34 ( BaBar )
(SM prediction:S K  0.731  0.056 )
2
(
m
Non-negligible d R ) 23may lead to the deviation of CP
0
asymmetry Bd   K S since b  sss is a radiative processes.
The dominant contribution comes from the gluon penguin
diagram in the broad parameter space.
2
(
m
)
The effective operator for b  sg induced by
d R 23 :
R gs
H  C8
mb s ( G ) PLb
2
8
Normal ordering for neutrino mass
(mw  200GeV , A0  0GeV , tan   10 or 30, sign(  )  1)
The largest values are fixed by only validity of perturbation, and
they are larger than the experimental bound. These observations
give independent information about seesaw model of neutrino
oscillation. Even inverted ordering cases give similar results.
Br (  e )
Br (   )
H (1)
H (2)
BELLE result
BELLE result
H
(2)
(Ellis, JH,Raidal,Shimizu)
Slepton oscillation
If sleptons are produced in future collider experiments, LFV
slepton mass leads to slepton oscillation, and then
e e (     )  ll   (e)
The cross section behaves as    (m  m ) /   sin 2 2 
2




(Arkani-hamed et al)
Br (   )
.
e  e  collider
    collider
L  50 fb1 , s  500GeV
m  180GeV , tan   3
(JH, Nojiri, Shimizu, Tanaka)