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Lepton Electric Dipole Moments in Supersymmetric Type II Seesaw Model
Toru Goto, Takayuki Kubo and Yasuhiro Okada,
“Lepton electric dipole moments in supersymmetric type II seesaw model,” [arXiv:1001.1417].
Takayuki Kubo
(KEK, Graduate University for Advanced Studies)
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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
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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.
Upper limits on EDMs strongly constrain CP violating parameters.
cmede27106.1
cmed 19107
Fi
dL 52EDM
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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 62
2 (2005) 112) suggest
This implies that if the electron EDM lies just below the present limit, muon EDM is given by
Introduction(2)
410ed
d (for the normal hierarchy of neutrino masses)
cmed 2310
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Introduction(3)
However we found additional contributions which should be taken into account.
We will show that the ratio is given by
in a wide region of parameter space. The ratio does not depend on the neutrino
parameters or unknown parameters.
200ee m
m
d
d
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Superpotential of the model
Exchange of heavy SU(2)L triplets generates small neutrino masses: the seesaw mechanism.
SUSY Type II Seesaw Model (1): superpotential
)(2
1
2
1)(
2
121222221121112 TTMHTiHHTiHLTiLYW T
TTj
TiijTT tr
10
1
11
1
2
12
1
TT
TTT
22
022
2
2
12
1
TT
TTT
SU(3)c SU(2)L U(1)Y
T1 1 3 +1
T2 1 3 -1
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Integrating out the heavy SU(2)L triplets, we obtain neutrino masses as follows:
The matrix mνis diagonalized by the MNS matrix and we have
YT is directly related to mν and UMNS.
SUSY Type II Seesaw Model (2): neutrino masses
ijTT
ij Yv
Mm )(
2)(
2
22
23
*22
13
2
2
22
2
*
10
)(
10tan
tan101.0)(
eVGeV
MNSMNS
k
jkikk
TijTT
UUmM
YY
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SUSY Type II Seesaw Model (3): soft SUSY breaking terms and assumptions
Soft SUSY breaking terms of the model
Soft SUSY breaking squared-mass parameters are universal (m0
2) 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.
)(2
1
2
1~~)(
2
121222221121112 TTBMHTiHAHTiHALTiLAL TT
TTj
TiijTsoft tr
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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.
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h.c. wwMbbMeLHAL Rjbi
aijEabsoft
~~2
1~~
2
1~~)( 21
*1
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.
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BT as a new source of CP violation(3)
ETTTE YYYBA *216
3
ETE YBA
2
1216
3
ETTTE YYYBA2
1*
216
3
TBgM 221 '
16
6
TBgM 222 16
4
The BT contribute to the scalar trilinear couplings , the gaugino masses and soft squared-masses through the threshold correction at MT.
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Lepton EDMs: previous study
In the previous study (Chun, Masiero, Rossi and Vempati, phys.
Lett. B 622 (2005) 112), the contributions from δM1 and δM
2 are missing.
They estimate lepton EDMs di as follows:
TiiTTeiiEi BYYmAvdi
Im)()(Im *1
tan)(2
1)( *
1*2
ieiiEiiLR mAvm
ETTTE YYYBA2
1*
216
3
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Lepton EDMs: previous study
In the previous study (Chun, Masiero, Rossi and Vempati, phys.
Lett. B 622 (2005) 112), the contributions from δM1 and δM
2 are missing.
They estimate lepton EDMs di as follows:
Their result implies
TiiTTeiiEi BYYmAvdi
Im)()(Im *1
4
11*
22*
10)(
)(
TTe
TT
e YYm
YYm
d
d
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EAi
MiiiLR ddmM ImIm2
11)(Im
TTTeA
i BYYMmdi
E ImRe2
1*
1Im
TeM
i Bgmdi
Imtan'2Im 1
Lepton EDMs: previous study
But we must include contributions from δM1 and δM2.
ex) Diagram shown below contribute to EDMs:
TBgM 221 '
16
6
TBgM 2
22 16
4
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Lepton EDMs: our results(1)
de dμ
dtau 2T
T
MY
GeV/TM
2
1210 1310 1410
λ2 blows up
YT blows up
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Lepton EDMs: our results(2)
200ee m
m
d
d
We can see that the ratio is around 200 except for the lower end of λ2 .
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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:
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.
200ee m
m
d
d
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Note
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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
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Lepton EDMs: our results(2-1)
de dμ
dtau
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Lepton EDMs: our results(2-2)
200ee m
m
d
d
We vary m0 with in 100GeV < m0 < 1000GeV. The horizontal axis represents mass of the lightest charged slepton.
We can see that the ratio is around 200, independent of the values of tanβ, m1/2 and mass of the lightest charged slepton.
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Lepton EDMs: our results(3)
17
m
m
d
d
We can see that the ratio is around 17 except for the lower end of λ2 .
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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
Lepton EDMs: our results(1)
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Comments on EDMs(1)
grow at small values of λ2 (large valus of YT).
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Comments on EDMs(2)
mass of the lightest slepton which couples to muon rather than electron rapidly decrease due to the large YT.
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Comments on LFV decays Branching ratios of LFV decays are given by
Ratio between the branching ratios is
BR:BR:BR ee
4002.0117.0)(18.0)()(2
23*2
13*2
12* :::: TTTTTT YYYYYY
jiji
ijL
Fji m
m
G BRBR
SUSY
28
22~
2
3
tan
for s13=0, δ=0
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Comparison with SUSY type I seesaw
iiTNNi
jjTNNj
i
j
YYm
YYm
d
d
)(
)(*
*
type II type I
i
j
i
j
m
m
d
d
2
,*,
,*,
)(
)(
klTNTNT
ijTNTNT
jilk
jiji
lk
ji
YY
YY
BR
BR
BR
BR
†MNS
diag*MNS UmU
v
MY TT
2
22
2
†MNS
diagUmRMviY N
TN
2
2
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SUSY seesaw models
SUSY type I seesaw model
SUSY type II seesaw model
U(1)B-L extended MSSM
…. ….
...)(2
1)(
2
1212222212 TTMHTiHLTiLYW T
Tj
TiijT tr
...2
1)( 2 jiijj
bi
aijNab NNMNLHYW
...2
1)( 12 jiijj
bi
aijNab NNfNLHYW
SU(3)c SU(2)L U(1)Y
Ni 1 1 0
SU(3)c SU(2)L U(1)Y U(1)B-L
Ni 1 1 0 +1
Δ1 1 1 0 -2
Δ2 1 1 0 +2
SU(3)c SU(2)L U(1)Y
T1 1 3 +1
T2 1 3 -1
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Electric dipole moments as probes of new physics
Non-relativistic Hamiltonian for the interaction of an electric dipole moment (EDM) with an electric field:
The relativistic generalization:
Until now no EDM has been observed. ex) electron and muon EDM
F
idL 52
EDM
cmede27106.1 cmed 19107
ES
SdHEDM
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electron EDM
...585 eddTl
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Motivation(2): seesaw mechanism
Seesaw mechanism explains the observed tiny neutrino masses: