Lepton Electric Dipole Moments in
Supersymmetric Type II Seesaw Model
Takayuki Kubo
(KEK, Graduate University for Advanced Studies)
Toru Goto, Takayuki Kubo and Yasuhiro Okada,
“Lepton electric dipole moments in supersymmetric type II seesaw model,”
[arXiv:1001.1417].
1
Outline






Introduction: electric dipole moment (EDM)
SUSY type II seesaw model
A new source of CP violation
Lepton EDMs: previous study
Lepton EDMs: our results
Summary
2
Introduction(1)
The electric dipole moments (EDMs) of leptons ,
nucleons and atoms are important probe for new
physics.

Until now no EDM has been observed.
de  1.6 1027 e cm
d   7 10 19 e cm

i



L


d




F
 EDM
5
 
2


Upper limits on EDMs strongly constrain CP
violating parameters.
3
Introduction(2)
The ratio of the muon EDM to electron EDM is
important in order to suggest necessary sensitivity for
future experiments of muon EDM.
 The previous study for lepton EDMs in SUSY type II
seesaw model (Chun, Masiero, Rossi and Vempati, phys. Lett. B 622
(2005) 112) suggest
d
de

 10 4
(for the normal hierarchy of neutrino masses)
This implies that if the electron EDM lies just below
the present limit, muon EDM is given by
d   1023 e cm
4
Introduction(3)


However we found additional contributions which
should be taken into account.
We will show that the ratio is given by
d
de


m
me
 200
in a wide region of parameter space.
The ratio does not depend on the neutrino
parameters or unknown parameters.
5
SUSY Type II Seesaw Model (1):
superpotential

Superpotential of the model
WT 
1
1
1
(YT )ij LTi i 2T1L j 
1H1T i 2T1H1 
2 H 2T i 2T2 H 2  M T tr (T1T2 )
2
2
2
 1 

T1  
 T1

T1   2
1 
 T0

T1 
 1
2



 1 

T20 
 T2

T2   2
1
 T

T2 
 2
2 

SU(3)c
SU(2)L
U(1)Y
T1
1
3
+1
T2
1
3
-1
Exchange of heavy SU(2)L triplets generates small
neutrino masses: the seesaw mechanism.
6
SUSY Type II Seesaw Model (2):
neutrino masses

Integrating out the heavy SU(2)L triplets, we obtain
neutrino masses as follows:
2  v2 
(m )ij 
  (YT )ij
MT  2 
2

The matrix mνis diagonalized by the MNS matrix and
we have
2 ik
jk*
2
2
(
m
)
U
U
2

 k MNS MNS
2




0
.
01
1

tan

M


k
T
 

(YT*YT )ij  


2
3
2
 1013 GeV

tan

10
eV


 2 

YT is directly related to mν and UMNS.
7
SUSY Type II Seesaw Model (3):
soft SUSY breaking terms and assumptions

Soft SUSY breaking terms of the model
Lsoft  



1
1
1
~
~
( AT )ij LiT i 2T1L j 
A1H1T i 2T1H1 
A2 H 2T i 2T2 H 2  M T BT tr (T1T2 )
2
2
2
Soft SUSY breaking squared-mass parameters are
universal (m02) at MG=2×1016GeV.
Gaugino masses are also universal (m1/2) at MG.
A-terms are proportional to corresponding Yukawa
couplings (AE=a0YE) at MG.
8
BT as a new source of CP violation(1)

There still remains three CP violating phases,
namely μ, a0 and BT.

Effects of μ and a0 have been studied very well.

Here we study the effects of BT as a new source of
CP violation and assume that μand a0 are real.
9
BT as a new source of CP violation(2)

The BT contribute to the scalar trilinear couplings
and the gaugino masses through the threshold
correction at MT.
1 ~~ 1
a ~b ~ *
~w
~  h.c.
Lsoft   ab ( AE )ij H1 Li eRj  M 1b b  M 2 w
2
2
10
BT as a new source of CP violation(3)

The BT contribute to the scalar trilinear couplings ,
the gaugino masses and soft squared-masses
through the threshold correction at MT.
AE 
3
*
B
Y
Y
YE
T
T
T
2
16
AE 
3
2
B

T
1 YE
2
16
M 1  
AE 


3
2
*
B
Y
Y


YE
T T T
1
16 2
6
2
g
'
BT
2
16
M 2  
4
g 2 BT
2
16
11
Lepton EDMs: previous study


In the previous study (Chun, Masiero, Rossi and Vempati, phys.
Lett. B 622 (2005) 112), the contributions from δM1 and
δM2 are missing.
They estimate lepton EDMs di as follows:
di  v1 Im(AE )ii   mei (YT*YT )ii Im BT
2 *
(mLR
)ii 
AE 
1
v1 ( AE )ii   *mei tan 
2


3
2
*
B
Y
Y


YE
T T T
1
16 2
12
Lepton EDMs: previous study


In the previous study (Chun, Masiero, Rossi and Vempati, phys.
Lett. B 622 (2005) 112), the contributions from δM1 and
δM2 are missing.
They estimate lepton EDMs di as follows:
di  v1 Im(AE )ii   mei (YT*YT )ii Im BT

Their result implies
d
de

m (YT*YT ) 22
me (YT*YT )11
 10 4
13
Lepton EDMs: previous study

But we must include contributions from δM1 and δM2.
M 1  

6
2
g
'
BT
16 2
M 2  
4
2
g
BT
16 2
ex) Diagram shown below contribute to EDMs:


2
 Im M 1 (mLR
) ii  d iIm M1  d iIm AE
diIm M1  mei g '2 tan  ImBT 

diIm AE  mei ReM1  YT YT*  1
2
 ImB 
T
14
Lepton EDMs: our results(1)
de
dtau
dμ
2
YT 
λ2 blows up
MT
2
YT blows up
1012
1013
1014
M T / GeV
15
Lepton EDMs: our results(2)
d
de

m
me
 200
We can see that the ratio
is around 200 except for
the lower end of λ2 .
16
Summary



We studied lepton EDMs in the SUSY type II seesaw
model.
All contributions generated by one-loop threshold
corrections at MT through the BT term are included.
We showed that the ratios of lepton EDMs are given
by those of the lepton masses:
d
de


m
me
 200
Since the upper bound of de is at the level of 10-27 ecm,
muon EDM search at the level of 10-24-10-25 are
important.
17
Note
18
Lepton EDMs: our results(2)
Next we fix the λ2 and MT.
 λ2=0.03
 MT=1012 GeV
Other parameters are fixed at
 λ1=0
 tanβ=3, 30
 a0=0 GeV
 m1/2=300, 600 GeV
 ReBT=ImBT=100 GeV
19
Lepton EDMs: our results(2-1)
de
dμ
dtau
20
Lepton EDMs: our results(2-2)
d
de

m
me
 200
We can see that the ratio is
around 200, independent of
the values of tanβ, m1/2 and
mass of the lightest charged
slepton.
We vary m0 with in
100GeV < m0 < 1000GeV.
The horizontal axis represents
mass of the lightest charged
slepton.
21
Lepton EDMs: our results(3)
d
m

 17
d  m
We can see that the ratio
is around 17 except for the
lower end of λ2 .
22
23
Lepton EDMs: our results(1)

In the numerical calculation, we evaluated the
following diagrams:
We fix the parameters as follows:
 tanβ= 3 , 30
 λ1= 0
 m0 = m1/2 = 300 GeV
 a0= 0 GeV
 ReBT= ImBT= 100 GeV
24
Comments on EDMs(1)
grow at
small values of λ2
(large valus of YT).
25
Comments on EDMs(2)
mass of the lightest
slepton which couples to
muon rather than electron
rapidly decrease due to
the large YT.
26
Comments on LFV decays

Branching ratios of LFV decays are given by
BR  i   j   

 3 m

2
~
L ij
8
GF2 mSUSY
2
tan 2   BR  i   j i j 
Ratio between the branching ratios is
BR  e  : BR  e  : BR   
2
*
T T 12
 (Y Y )
2
*
T T 13
: (Y Y )
2
*
T T 23
 0.18 : (Y Y )
 0.17  1 : 0.2 : 400
for s13=0, δ=0
27
Comparison with SUSY type I seesaw
type II
dj
di

type I
mj
dj
mi
di

m j (YN*YNT ) jj
mi (YN*YNT ) ii
BR  i   j  BR  i   j i j  (Y Y )


BR k   l   BR  k   l i j  (Y Y )
2
*
T
T , N T , N ij
*
T
T , N T , N kl
2
MT  2  *
  U MNS mdiagU†MNS
YT 
2  v2 
YNT  i
2
v2
M N R mdiag U†MNS
28
29
SUSY seesaw models

SUSY type I seesaw model
SU(3)c
1
W   ab (YN )ij H L N j  M ij N i N j  ...
2
a b
2 i

SUSY type II seesaw model
W

1
1
(YT )ij LTi i 2T1L j 
2 H 2T i 2T2 H 2  M T tr (T1T2 )  ...
2
2

1
SU(3)c
1
SU(2)L
U(1)Y
0
U(1)Y
T1
1
3
+1
T2
1
3
-1
SU(2)L
U(1)Y
U(1)B-L
U(1)B-L extended MSSM
W   ab (YN )ij H 2a Lbi N j 

Ni
SU(2)L
….
….
1
f ij 1 N i N j  ...
2
SU(3)c
Ni
1
1
0
+1
Δ1
1
1
0
-2
Δ2
1
1
0
+2
30
31
Electric dipole moments
as probes of new physics

Non-relativistic Hamiltonian for the interaction of an
electric dipole moment (EDM) with an electric field:
H EDM  d

S
E
S
The relativistic generalization:
i
LEDM  d     5 F
2


Until now no EDM has been observed.
ex) electron and muon EDM
27
de  1.6 10 e cm
d   7 1019 e cm
32
electron EDM
d Tl  585d e  ...
33
Motivation(2): seesaw mechanism
Seesaw mechanism explains the observed tiny
neutrino masses:
34