Presentation for my PhD thesis.

1. Prospects for Slepton Searches
in Future Experiments
（将来実験におけるスレプトン探索索の展望）
Presented by Takahiro Yoshinaga
博⼠士論論⽂文審査会
Based on
T. Kitahara and T.Y JHEP 05 035 (2013)
M. Endo, K. Hamaguchi, T. Kitahara, and T.Y JHEP 11 013 (2013)
M. Endo, T. Kitahara, and T.Y JHEP 04 139 (2014)
45 Slides

2. 博⼠士論論⽂文の概要 2
「Muon g-‐‑‒2を説明する超対称模型の現象論論」
Muon g-‐‑‒2
>3σ dev.
eB e`L
e`R
eg eq fW ···
⇡
≫1TeV
O(100)GeV
“Minimal” SUSY model
LHC
ILC
LFV
EDM
mee
=
m eµ
=
m e⌧
m
ee =
m
eµ ⌧
m
e⌧
① massに制限
② 相補的に探索索可能

3. 博⼠士論論⽂文の内容 3
1. Introduction
2. Foundation (Review)
3. Supersymmetric Standard Model (Review)
4. Prospects for Slepton Searches (Main)
5. Conclusion
4.1 Foundation : Model & Mass Bound
4.2 Selectron/Smuon
4.3 Stau

4. 本⽇日の内容 4
Intro.
Muon g-‐‑‒2
Supersymmetric Standard Model
Main
“Minimal” SUSY model
Slepton Mass Bound
Conc. Summary
mee = meµ = me⌧ mee = meµ ⌧ me⌧

5. 本⽇日の内容 5
Intro.
Muon g-‐‑‒2
Supersymmetric Standard Model
Main
“Minimal” SUSY model
Slepton Mass Bound
Conc. Summary
mee = meµ = me⌧ mee = meµ ⌧ me⌧

6. ミューオンの異異常磁気モーメント (Muon g-‐‑‒2)
Muon g-2
✓ g = 2 at tree level (Dirac equation)
✓ g ≠ 2 by radiative corrections
Magnetic moment
g-factor
Muon g-‐‑‒2 6
l ミューオンの磁気モーメント
l g-‐‑‒factor
H = !m ·
!
B , !m =
Ç
e
2mµ
å
!sg
-‐‑‒ g = 2 : Tree Level
-‐‑‒ g ≠ 2 : Radiative Correction
aµ ⌘
g 2
2

7. Muon g-‐‑‒2 7
SM Prediction
Contributions Value (10-‐‑‒10)
QED (O(α5)) 11658471.8951 (0.0080)
EW (NLO) 15.36 (0.1)
Hadronic
(LO)
[HLMNT] 694.91 (4.27)
[DHMZ] 692.3 (4.2)
Hadronic (HO) -‐‑‒9.84 (0.07)
Hadronic
(LbL)
[RdRV] 10.5 (2.6)
[NJN] 11.6 (3.9)
Total SM [HLMNT] 11659182.8 (4.9)
CHAPTER 2. FOUNDATION
µ µ
γ
(A)
µ
(B
Figure 2.1: (A) The Feynman diagram which c
of the muon. (B) The hadronic vacuum-polariz
hadronic light-by-light contributions to the mu
The amplitude can be interpreted as th
electron from a potential (For detail, see textb
corresponds to such potential is given by
Hint = −〈−→µ
where
〈−→µ 〉 = 2 F1(0) + F2(0
The factor ξ′†
(−→σ /2)ξ can be interpreted as the
with Eqs. (2.3) and (2.4), the coefficient 2 F1(
2 F1(0) + F2(0) =
It is just the g-value.
2.2.2 The Standard Model predictio
The SM prediction of the muon g − 2 has bee
several groups of theorists. Fig. 2.1 (A) shows
muon g − 2. The theoretical uncertainty reach
review the SM prediction of the muon g − 2.
QED Contribution
The quantum electromagnetic dynamics (QED
to the muon g − 2 (99.993%), and come from
CHAPTER 2. FOUNDATION
µ µ
γ
(A)
µ µ
γ
(B)
µ
Figure 2.1: (A) The Feynman diagram which contributes to the ano
of the muon. (B) The hadronic vacuum-polarization contributions to
hadronic light-by-light contributions to the muon g − 2.
The amplitude can be interpreted as the Born approximatio
electron from a potential (For detail, see textbook [19]). The intera
corresponds to such potential is given by
Hint = −〈−→µ 〉 ·
−→
B ,
where
〈−→µ 〉 = 2 F1(0) + F2(0) ×
eQℓ
2mℓ
ξ′†
−→σ
2
ξ.
CHAPTER 2. FOUNDATION 23
µ µ
γ
(A)
µ µ
γ
(B)
µ µ
γ
(C)
Figure 2.1: (A) The Feynman diagram which contributes to the anomalous magnetic moment
of the muon. (B) The hadronic vacuum-polarization contributions to the muon g −2. (C) The
hadronic light-by-light contributions to the muon g − 2.
The amplitude can be interpreted as the Born approximation to the scattering of the
electron from a potential (For detail, see textbook [19]). The interaction Hamiltonian which
had
QED, EW
had
Experiment
[E821 Muon g-‐‑‒2実験のHome pageより]
11659208.9 (6.3) × 10-‐‑‒10aexp
µ =
>3σの不不⼀一致が観測
26.1 (8.0) × 10-‐‑‒10aµ ⌘ aexp
µ ath
µ =

8. Muon g-‐‑‒2 8
>3σの不不⼀一致が観測
26.1 (8.0) × 10-‐‑‒10aµ ⌘ aexp
µ ath
µ =
Status of the muon g-2
SM Value
experiment
DHMZ (11)
The latest result of the muon g-2
[Hagiwara,Liao,Martin,Nomura,Teubner,J. Phys. G 38 (2011)085033]
[Davier,Hoecker,Malaescu,Zhang,Eur. Phys. J. C 71(2011)1515]
3.3 σ
3.6 σ
aμ × 1010 -‐‑‒ 11659000
SM
Exp
[Hagiwara, Liao, Martin, Nomura, Teubner, ʼ’11]

9. Muon g-‐‑‒2 9
Future
35
26
25
40
Fermilab & JPARC
Next 3-‐‑‒5 years
e+e-‐‑‒→hadrons実験
中⼼心値が変わらなければ
近い将来>5σの感度度が期待
[Snowmass white paperより]
SMXX
181.5±3.5

10. Muon g-‐‑‒2 10
中⼼心値が変わらなければ
近い将来>5σの感度度が期待
>3σの不不⼀一致が観測
26.1 (8.0) × 10-‐‑‒10aµ ⌘ aexp
µ ath
µ =
「今」Muon g-‐‑‒2の不不⼀一致の原因
を調べることは⾮非常に重要
博⼠士論論⽂文での⽴立立場

11. Muon g-‐‑‒2 11
博⼠士論論⽂文での⽴立立場
/21Dec 2, 2013 SUSY: Model-building and Phenomenology Teppei KITAHARA -The Univ. of Tokyo
Status of the muon g-2
SM Value
experiment
DHMZ (11)
The latest result of the muon g-2
[Hagiwara,Liao,Martin,Nomura,Teubner,J. Phys. G 38 (2011)085033]
[Davier,Hoecker,Malaescu,Zhang,Eur. Phys. J. C 71(2011)1515]
3.3 σ
3.6 σ
(possibly a signal of new physics)muon g-2 anomaly
3
SM+NP
Exp
Muon g-‐‑‒2の不不⼀一致は新しい物理理(NP)の寄与が原因
新しい物理理
-‐‑‒ 博⼠士論論⽂文では超対称模型を仮定
-‐‑‒ model-‐‑‒independentにSUSYの寄与を確かめる
CHAPTER 2. FOUNDATION
µ µ
γ
(A)
µ µ
γ
(B)
µ
Figure 2.1: (A) The Feynman diagram which contributes to the anom
of the muon. (B) The hadronic vacuum-polarization contributions to
hadronic light-by-light contributions to the muon g − 2.
The amplitude can be interpreted as the Born approximation
electron from a potential (For detail, see textbook [19]). The intera
corresponds to such potential is given by
Hint = −〈−→µ 〉 ·
−→
B ,
where
〈−→µ 〉 = 2 F1(0) + F2(0) ×
eQℓ
2mℓ
ξ′†
−→σ
2
ξ.
The factor ξ′†
(−→σ /2)ξ can be interpreted as the spin of the leptons,
−→
S
with Eqs. (2.3) and (2.4), the coefficient 2 F1(0) + F2(0) becomes
2 F1(0) + F2(0) = 2(1 + aℓ) = gℓ.
It is just the g-value.
2.2.2 The Standard Model prediction of the muon g −
The SM prediction of the muon g − 2 has been precisely evaluated
NP

12. 本⽇日の内容 12
Intro.
Muon g-‐‑‒2
Supersymmetric Standard Model
Main
“Minimal” SUSY model
Slepton Mass Bound
Conc. Summary
mee = meµ = me⌧ mee = meµ ⌧ me⌧

13. Supersymmetry 13
「BosonとFermionの間の対称性」
MSSM＝Minimal Supersymmetric Standard Model
SM粒粒⼦子のパートナー(superparticle)を予⾔言

14. Supersymmetry 14
SUSY contribution to the muon g-‐‑‒2
aSUSY
µ ⇠
↵2 tan
4⇡
m2
µ
m2
SUSY
46 Dissertation / Takahiro Yosh
µL µR
W±
νµ
γ
(a)
µL µR
µL µR
B
γ
(b)
µL µR
µL
W0
H0
d
γ
(c)
µL µR
µL
B H0
d
γ
(d)
µL µR
µR
H0
d
B
γ
(e)
Figure 3.4: The diagrams of the SUSY contributions to the muon g − 2 in gauge eigen
The diagram (a) comes from the chargino–muon sneutrino diagram, the diagrams (b)–(
from the neutralino–smuon diagram.
∆aχ0
µ
= −
mµ
48π2
6
X=1
4
A=1
1
m2
ℓX
mµ
4
N
L(e)
2AX
2
+ N
R(e)
2AX
2
FN
1
⎛
⎝
m2
χ0
A
m2
ℓX
⎞
⎠
+
mχ0
A
2
ℜ N
L(e)∗
2AX N
R(e)
2AX FN
2
⎛
⎝
m2
χ0
A
m2
ℓX
⎞
⎠ ,
where FC
1,2
and FN
1,2
are the loop functions.
FC
1
(x) =
2
(1 − x)4
2 + 2x − 6x2
+ x3
+ 6x log x ,
FC
(x) =
3
−3 + 4x − x2
− 2log x ,
fW eH
Chargino-‐‑‒sneutrino Neutralino-‐‑‒smuon
Ç
⇠ 150 ⇥ 10 10
⇥
✓
100GeV
mSUSY
◆2
⇥
✓
tan
10
◆å
mSUSY : 典型的なSUSY粒粒⼦子の質量量, tanβ : Higgsの真空期待値の⽐比
mSUSY = O(100)GeV, tanβ = O(10)のとき
超対称模型の寄与によりMuon g-‐‑‒2の不不⼀一致を説明可能
[Lopez, Nanopoulos, Wang, ʼ’93]
[Chattopadhyay, Nath, ʼ’95]
[Moroi, ʼ’95]
26.1 (8.0) × 10-‐‑‒10aµ ⌘ aexp
µ ath
µ =

15. Supersymmetry 15
Representative SUSY contributions
Contributions O(100)GeV particles Diagram
Chagino-‐‑‒
sneutrino
Wino, Higgsinos,
(Bino), smuons,
Neutralino-‐‑‒
smuon
Bino, smuons
46 Dissertation / Takah
µL µR
W±
νµ
γ
(a)
µL µR
µL µR
B
γ
(b)
µL
µL
W0
H
(c)
µL µR
µL
B H0
d
γ
µL µR
µR
H0
d
B
γ
fW eH
46
µL µR
W±
νµ
γ
(a)
µL
µL µR
B
(b)
µL µR
µL
B H0
d
γ
(d)
Figure 3.4: The diagrams of the SUSY contributio
The diagram (a) comes from the chargino–muon s
from the neutralino–smuon diagram.
6 4
fW eH
l Muon g-‐‑‒2を説明するminimalな解の⼀一つ
l 特徴的な性質を持つ

16. Supersymmetry 16
博⼠士論論⽂文での⽴立立場
/21Dec 2, 2013 SUSY: Model-building and Phenomenology Teppei KITAHARA -The Univ. of Tokyo
Status of the muon g-2
SM Value
experiment
DHMZ (11)
The latest result of the muon g-2
[Hagiwara,Liao,Martin,Nomura,Teubner,J. Phys. G 38 (2011)085033]
[Davier,Hoecker,Malaescu,Zhang,Eur. Phys. J. C 71(2011)1515]
3.3 σ
3.6 σ
(possibly a signal of new physics)muon g-2 anomaly
3
SM+SUSY
Exp
Muon g-‐‑‒2の不不⼀一致は の寄与が原因
知りたいこと
-‐‑‒ どのような性質を持つか
-‐‑‒ 実験で検証できるか
46 Dissertation / Takahiro Yoshinaga
µL µR
W±
νµ
γ
(a)
µL µR
µL µR
B
γ
(b)
µL µR
µL
W0
H0
d
γ
(c)
µL µR
µL
B H0
d
γ
(d)
µL µR
µR
H0
d
B
γ
(e)
Figure 3.4: The diagrams of the SUSY contributions to the muon g − 2 in gauge eigenstates.
The diagram (a) comes from the chargino–muon sneutrino diagram, the diagrams (b)–(e) are
from the neutralino–smuon diagram.
∆aχ0
µ
= −
mµ
48π2
6
X=1
4
A=1
1
m2
ℓX
mµ
4
N
L(e)
2AX
2
+ N
R(e)
2AX
2
FN
1
⎛
⎝
m2
χ0
A
m2
ℓX
⎞
⎠
+
mχ0
A
2
ℜ N
L(e)∗
2AX N
R(e)
2AX FN
2
⎛
⎝
m2
χ0
A
m2
ℓX
⎞
⎠ , (3.33)
where FC
1,2
and FN
1,2
are the loop functions.
fW eH
46 Dissertation / Takahiro Yoshinaga
µL µR
W±
νµ
γ
(a)
µL µR
µL µR
B
γ
(b)
µL µR
µL
W0
H0
d
γ
(c)
µL µR
µL
B H0
d
γ
(d)
µL µR
µR
H0
d
B
γ
(e)
Figure 3.4: The diagrams of the SUSY contributions to the muon g − 2 in gauge eigenstates.
The diagram (a) comes from the chargino–muon sneutrino diagram, the diagrams (b)–(e) are
from the neutralino–smuon diagram.
∆aχ0
µ
= −
mµ
48π2
6
X=1
4
A=1
1
m2
ℓX
mµ
4
N
L(e)
2AX
2
+ N
R(e)
2AX
2
FN
1
⎛
⎝
m2
χ0
A
m2
ℓX
⎞
⎠
+
mχ0
A
2
ℜ N
L(e)∗
2AX N
R(e)
2AX FN
2
⎛
⎝
m2
χ0
A
m2
ℓX
⎞
⎠ , (3.33)
where FC
1,2
and FN
1,2
are the loop functions.
FC
1
(x) =
2
(1 − x)4
2 + 2x − 6x2
+ x3
+ 6x log x , (3.34)
FC
2
(x) =
3
2(1 − x)3
−3 + 4x − x2
− 2log x , (3.35)
FN
1
(x) =
2
(1 − x)4
1 − 6x + 3x2
+ 2x3
− 6x2
log x , (3.36)
fW eH

17. 本⽇日の内容 17
Intro.
Muon g-‐‑‒2
Supersymmetric Standard Model
Main
“Minimal” SUSY model
Slepton Mass Bound
Conc. Summary
mee = meµ = me⌧ mee = meµ ⌧ me⌧

18. Minimal SUSY model 18
Mass spectrum
eB e`L
e`R
eg eq fW ···
⇡
≫1TeV
O(100)GeV
46 Dissertation /
µL µR
W±
νµ
γ
(a)
µL µR
µL µR
B
γ
(b)
µL W
µL
γ
µR
γ
fW eH
l 軽い(O(100)GeV)粒粒⼦子 : Bino, sleptons
l 他の超対称粒粒⼦子 : Decoupled*
* 現在のLHCの制限および126GeV Higgs massと無⽭矛盾

19. Minimal SUSY model 19
Mass spectrum
eB e`L
e`R
eg eq fW ···
⇡
≫1TeV
O(100)GeV
46 Dissertation / Takahiro Yos
µL µR
W±
νµ
γ
(a)
µL µR
µL µR
B
γ
(b)
µL µR
µL
W0
H0
d
γ
(c)
µL µR
µL
0
γ
µL µR
µR
0
γ
fW eH
l 軽い(O(100)GeV)粒粒⼦子 : Bino, sleptons
l 他の超対称粒粒⼦子 : Decoupled*
* 現在のLHCの制限および126GeV Higgs massと無⽭矛盾
[GeV]0m
0 1000 2000 3000 4000 5000 6000
[GeV]1/2m
300
400
500
600
700
800
900
1000
(2400GeV)q~
(1600GeV)
q~
(1000 GeV)
g
~
(1400 GeV)g
~
h(122GeV)
h(124GeV)
h(126GeV)
Expected
Observed
Expected
Observed
Expected
Observed
Expected
Observed
Expected
Observed
Expected
Observed
> 0µ,0= -2m
0
) = 30, AβMSUGRA/CMSSM: tan( Status: ICHEP 2014
ATLAS Preliminary
= 8 TeVs,
-1
L dt = 20.1 - 20.7 fb∫
τ∼
LSP
not included.theory
SUSY
σ95% CL limits.
0-lepton, 2-6 jets
0-lepton, 7-10 jets
0-1 lepton, 3 b-jets
1-lepton + jets + MET
1-2 taus + 0-1 lept. + jets + MET
3 b-jets≥2SS/3 leptons, 0 -
arXiv: 1405.7875
arXiv: 1308.1841
arXiv: 1407.0600
ATLAS-CONF-2013-062
arXiv: 1407.0603
arXiv: 1404.2500
[GeV]g~m
600 700 800 900 1000 1100 1200 1300 1400 1500 1600
[GeV]
1
0
χ∼m
200
400
600
800
1000
forbidden
1
0
χ∼tt
→g~
= 8 TeVs),g~) >> m(q~, m(1
0
χ∼tt→g~production,g~g~ ICHEP 2014
ATLAS
Preliminary
Expected
Observed
Expected
Observed
Observed
Expected
10 jets≥0-lepton, 7 -
3 b-jets≥0-1 lepton,
3 b-jets≥2SS/3 leptons, 0 -
arXiv: 1308.1841
arXiv: 1407.0600
arXiv: 1404.2500
]-1
= 20.3 fb
int
[L
]-1
= 20.1 fb
int
[L
]-1
= 20.3 fb
int
[L
not included.theory
SUSY
σ95% CL limits.
Colored superparticles > ~∼1TeV
[https://twiki.cern.ch/twiki/bin/view/AtlasPublic/SupersymmetryPublicResults#Summary_̲plots_̲status_̲July_̲2014]

20. Minimal SUSY model 20
Mass spectrum
eB e`L
e`R
eg eq fW ···
⇡
≫1TeV
O(100)GeV
46 Dissertation / Takahiro Yos
µL µR
W±
νµ
γ
(a)
µL µR
µL µR
B
γ
(b)
µL µR
µL
W0
H0
d
γ
(c)
µL µR
µL
0
γ
µL µR
µR
0
γ
fW eH
l 軽い(O(100)GeV)粒粒⼦子 : Bino, sleptons
l 他の超対称粒粒⼦子 : Decoupled*
* 現在のLHCの制限および126GeV Higgs massと無⽭矛盾
Scalar top >> 1TeV
[Hahn, Heinemeyer, Hollik, Rzehak, Weiglein, ʼ’13]
3
FD approach in the
e leading and sub-
her up to a certain
btained in the RGE
all terms of Eq. (4)
n terms of mt; the
ven by
3αt)/(16π))] (5)
e are no logarithmic
MMS
S and MOS
S .
beyond 2-loop order
tion MA ≫ MZ, to
ons can be incorpo-
he φ2φ2 self-energy
t 1/ sin2
β). In this
ons enter not only
other Higgs sector
nHiggs. The latest
0, which is available
roved predictions as
etical uncertainties
ns. Taking into ac-
garithmic contribu-
certainty of the re-
tions. Accordingly,
ng from corrections
p sector is adjusted
running top-quark
s evaluated only for
er than for the full
5000 10000 15000 20000
MS
[GeV]
115
120
125
130
135
140
145
150
155
Mh
[GeV]
FH295
3-loop
4-loop
5-loop
6-loop
7-loop
LL+NLL
FeynHiggs 2.10.0
Xt
= 0
Xt
/MS
= 2
5000 10000 15000 20000
MS
[GeV]
115
120
125
130
135
140
145
150
155
Mh
[GeV]
3-loop, O(αt
αs
2
)
3-loop full
LL+NLL
H3m
FeynHiggs 2.10.0
A0
= 0, tanβ = 10
FIG. 1. Upper plot: Mh as a function of MS for Xt = 0 (solid)
and Xt/MS = 2 (dashed). The full result (“LL+NLL”) is
compared with results containing the logarithmic contribu-
tions up to the 3-loop, . . . 7-loop level and with the fixed-order
FD result (“FH295”). Lower plot: comparison of FeynHiggs
(red) with H3m (blue). In green we show the FeynHiggs 3-loop
2
Mh : Higgs mass
Ms : Scalar top mass

21. Minimal SUSY model 21
Mass spectrum
eB e`L
e`R
eg eq fW ···
⇡
≫1TeV
O(100)GeV
l 軽い(O(100)GeV)粒粒⼦子 : Bino, sleptons
l 他の超対称粒粒⼦子 : Decoupled*
* 現在のLHCの制限および126GeV Higgs massと無⽭矛盾
46 Dissertation /
µL µR
W±
νµ
γ
(a)
µL µR
µL µR
B
γ
(b)
µL W
µL
γ
µR
γ
fW eH

22. Minimal SUSY model 22
Dissertation / Takahi
µR
W±
νµ
γ
(a)
µL µR
µL µR
B
γ
(b)
µL
µL
W0
H0
d
(c)
µ µ
µL
0
γ
µ µ
µR
0
γ
fW eH eµL eµR
m2
e`LR
Neutralino-‐‑‒smuon contribution
右巻きと左巻きsleptonの混合に⽐比例例

23. Minimal SUSY model 23
右巻きと左巻きsmuonの混合に⽐比例例
-‐‑‒ Large μ×tanβ : enhanced
-‐‑‒ Large smuon mass : suppressed
46 Dis
µL µR
W±
νµ
γ
(a)
µL µR
µL µR
B
γ
(b)
µL µR
µL
B H0
d
γ
(d)
µL
µR
H0
d
(e)
Figure 3.4: The diagrams of the SUSY contributions to the mu
The diagram (a) comes from the chargino–muon sneutrino diag
from the neutralino–smuon diagram.
∆aχ0
µ
= −
mµ
2
6 4
1
2
mµ
N
L(e)
2AX
2
+ N
R
2
fW eH eµL eµR
m2
e`LR
SmuonがO(1)TeVでも極端に⼤大きな混合を
取ればMuon g-‐‑‒2の不不⼀一致を説明できてしまう
Muon g-‐‑‒2
1σ
2σ
加速器実験の探索索可能領領域を超えてしまう!？ [Endo, Hamaguchi, Kitahara, TY, ʻ‘13]
Neutralino-‐‑‒smuon contribution

24. Minimal SUSY model 24
右巻きと左巻きsmuonの混合に⽐比例例
-‐‑‒ Large μ×tanβ : enhanced
-‐‑‒ Large smuon mass : suppressed
46 Dis
µL µR
W±
νµ
γ
(a)
µL µR
µL µR
B
γ
(b)
µL µR
µL
B H0
d
γ
(d)
µL
µR
H0
d
(e)
Figure 3.4: The diagrams of the SUSY contributions to the mu
The diagram (a) comes from the chargino–muon sneutrino diag
from the neutralino–smuon diagram.
∆aχ0
µ
= −
mµ
2
6 4
1
2
mµ
N
L(e)
2AX
2
+ N
R
2
fW eH eµL eµR
m2
e`LR
SmuonがO(1)TeVでも極端に⼤大きな混合を
取ればMuon g-‐‑‒2の不不⼀一致を説明できてしまう
Muon g-‐‑‒2
1σ
2σ
加速器実験の探索索可能領領域を超えてしまう!？ [Endo, Hamaguchi, Kitahara, TY, ʻ‘13]
Neutralino-‐‑‒smuon contribution
スカラーポテンシャルの安定性条件
により上限が存在する

25. Minimal SUSY model 25
まとめとこれから議論論すること
SmuonがO(1)TeVでも極端に⼤大きな混合
を取ればMuon g-‐‑‒2の不不⼀一致を説明できてしまう
がMuon g-‐‑‒2の不不⼀一致の原因
46 Dissertation / Takahiro Yoshinaga
µL µR
W±
νµ
γ
(a)
µL µR
µL µR
B
γ
(b)
µL µR
µL
W0
H0
d
γ
(c)
µL µR
µL
B H0
d
γ
(d)
µL µR
µR
H0
d
B
γ
(e)
Figure 3.4: The diagrams of the SUSY contributions to the muon g − 2 in gauge eigenstates.
The diagram (a) comes from the chargino–muon sneutrino diagram, the diagrams (b)–(e) are
from the neutralino–smuon diagram.
∆aχ0
µ
= −
mµ
48π2
6
X=1
4
A=1
1
m2
ℓX
mµ
4
N
L(e)
2AX
2
+ N
R(e)
2AX
2
FN
1
⎛
⎝
m2
χ0
A
m2
ℓX
⎞
⎠
+
mχ0
A
2
ℜ N
L(e)∗
2AX N
R(e)
2AX FN
2
⎛
⎝
m2
χ0
A
m2
ℓX
⎞
⎠ , (3.33)
where FC
1,2
and FN
1,2
are the loop functions.
FC
1
(x) =
2
(1 − x)4
2 + 2x − 6x2
+ x3
+ 6x log x , (3.34)
FC
(x) =
3
−3 + 4x − x2
− 2log x , (3.35)
fW eH eµL eµR
m2
e`LR
極端に⼤大きな混合は
スカラーポテンシャルの安定性条件により制限
Muon g-‐‑‒2の不不⼀一致を説明するという
条件と合わせるとsmuonのmassに上限
[Endo, Hamaguchi, Kitahara, TY, ʻ‘13]

26. 本⽇日の内容 26
Intro.
Muon g-‐‑‒2
Supersymmetric Standard Model
Main
“Minimal” SUSY model
Slepton Mass Bound
Conc. Summary
mee = meµ = me⌧ mee = meµ ⌧ me⌧

27. Slepton Mass Bound 27
真空の安定性条件
-‐‑‒ SleptonとHiggsの3点結合
v : 真空期待値, h : SM Higgs, 混合はμ>0のときnegative
EW vacuumの寿命 > 宇宙年年齢とすると
混合の⼤大きさに上限が付く
EW vacuum Charge-‐‑‒breaking minima
⼤大きすぎる混合

28. Slepton Mass Bound 28
真空の安定性条件
-‐‑‒ 数値公式*
Slepton mass bound
[Kitahara, TY, ʻ‘13]
[Endo, Hamaguchi, Kitahara, TY, ʻ‘13]
* Calculated by CosmoTransitions
η~∼1, (leptonのフレーバーに弱く依存)
Muon g-‐‑‒2の不不⼀一致を説明するという
条件と合わせるとsmuonのmassに上限
(すべて縮退)のとき
Stau-‐‑‒Higgsポテンシャルで強く制限
Vacuum bound
〜～400GeV

29. Slepton Mass Bound 29
Stau mass dependence
Massの制限はstauとsmuonのmassの⽐比に依存
Vacuum bound
〜～400GeV 〜～600GeV
me⌧/meµ = 1 me⌧/meµ = 2 me⌧/meµ 1
stauによって制限
(3点結合はYukawaに⽐比例例)
meµ Æ 500GeV
smuonによって制限
(stauがdecoupleしたとき)
meµ Æ 2TeV
[Endo, Hamaguchi, Kitahara, TY, ʻ‘13]
stauが重くなると
制限が弱くなる

30. Slepton Mass Bound 30
まとめとこれから議論論すること
Universal Non-‐‑‒Universal
Spectrum
Vacuum Severe (stau) Mild (smuon)
Mass Bound Tight (<500GeV) Loose (<2TeV)
Collider LHC, ILC ✕
Flavor/CP GIM Sensitive
まとめ
これから
mee = meµ = me⌧ mee = meµ ⌧ me⌧

31. 本⽇日の内容 31
Intro.
Muon g-‐‑‒2
Supersymmetric Standard Model
Main
“Minimal” SUSY model
Slepton Mass Bound
Conc. Summary
mee = meµ = me⌧ mee = meµ ⌧ me⌧

32. Universal Case 32
-‐‑‒ Mass
-‐‑‒ 混合
-‐‑‒ LHC
mee = meµ = me⌧ (縮退)
真空の安定性条件を満たす
中で最⼤大の値を各点で選ぶ
LHC Status
e`e`
e0
1e0
1
` `
[Endo, Hamaguchi, Kitahara, TY, ʻ‘13]
Smuon mass < 500GeVに制限される
g-‐‑‒2
1σ
2σ
Excluded by
long-‐‑‒lived stau search
pp ! e`e`⇤
! `+
` + Emiss
T

33. Universal Case 33
-‐‑‒ Mass
-‐‑‒ 混合
-‐‑‒ LHC
mee = meµ = me⌧ (縮退)
真空の安定性条件を満たす
中で最⼤大の値を各点で選ぶ
LHC Status
e`e`
e0
1e0
1
` `
(Dilepton search)が有効
[ATLAS Collaboration, JHEP 05 (2014) 035]
[Endo, Hamaguchi, Kitahara, TY, ʻ‘13]
pp ! e`e`⇤
! `+
` + Emiss
T
pp ! e`e`⇤
! `+
` + Emiss
T

34. Universal Case 34
-‐‑‒ Mass
-‐‑‒ 混合
-‐‑‒ LHC
mee = meµ = me⌧ (縮退)
真空の安定性条件を満たす
中で最⼤大の値を各点で選ぶ
LHC Status
e`e`
e0
1e0
1
` `
Muon g-‐‑‒2を1σで説明できる領領域 (1σ Region)
のほとんどは現在のLHCのデータですでに排除
Excluded
[Endo, Hamaguchi, Kitahara, TY, ʻ‘13]
pp ! e`e`⇤
! `+
` + Emiss
T

35. Universal Case 35
-‐‑‒ Cross section (LO)
Future Prospects
Smuonの質量量がNeutralinoの質量量より
⼗十分⼤大きい領領域は14TeV LHCで探索索可能
[Endo, Hamaguchi, Kitahara, TY, ʻ‘13]
(eµ1 eµ1) =
8
>><
>>:
1fb (√s = 8TeV, のとき)meµ = 330GeV
meµ = 450GeV1fb (√s = 14TeV, のとき)
↔ 現在のLHCの制限
↔ (Naïveな)将来の感度度
LHC

36. Universal Case 36
Future Prospects
Smuonの質量量とNeutralinoの質量量が
近い領領域は1TeV ILCで探索索可能
[Endo, Hamaguchi, Kitahara, TY, ʻ‘13]
-‐‑‒ ILC
kinematicalに許される質量量領領域ならば探索索可能
Closing the loopholes
At the ILC, a systematic search for the NLSP is possible without leaving loopholes, covering even the cases
that may be very difficult to test at the LHC.
In the case of a very small mass difference between the LSP and the NLSP - less than a few GeV - the
clean environment at the ILC nevertheless allows for a good detection efficiency. If
√
s is much larger than
the threshold for the NLSP-pair production, the NLSPs themselves will be highly boosted in the detector
frame, and most of the spectrum of the decay products will be easily detected. In this case, the precise
knowledge of the initial state at the ILC is of paramount importance to recognize the signal, by the slight
discrepancy in energy, momentum and acolinearity between signal and background from pair production
of the NLSP’s SM partner. In the case the threshold is not much below
√
s, the background to fight is
γγ → f ¯f where the γ’s are virtual ones radiated off the beam-electrons. The beam-electrons themselves
are deflected so little that they leave the detector undetected through the outgoing beam-pipes. Under the
clean conditions at the ILC, this background can be kept under control by demanding that there is a visible
ISR photon accompanying the soft NLSP decay products. If such an ISR is present in a γγ event, the
beam-remnant will also be detected, and the event can be rejected.
If the LSP is unstable due to R-parity violation, the ILC reach would be better or equal to the R-
conserving case, both for long-lived and short-lived LSP’s and whether the LSP is charged or neutral.
Also in the case of an NLSP which is a mass-state mixed between the hyper-charge states, the procedure
is viable. One will have one more parameter - the mixing angle. However, as the couplings to the Z of both
states are known from the SUSY principle, so is the coupling with any mixed state. There will then be
one mixing-angle that represents a possible “worst case”, which allows to determine the reach whatever the
mixing is - namely the reach in this “worst case”.
Finally, the case of “several” NLSPs– i.e. a group of near-degenerate sparticles– can be disentangled due
to the possibility to precisely choose the beam energy at the ILC. This will make it possible to study the
“real” NLSP below the threshold of its nearby partner.
0
50
100
150
200
250
0 50 100 150 200 250
Exclusion
Discovery
Excludable
at95%
C
L
NLSP : µ˜R
MNLSP [GeV]
MLSP[GeV]
0
50
100
150
200
250
240 242 244 246 248 250
Exclusion
Discovery
NLSP : µ˜R
MNLSP [GeV]
MLSP[GeV]
Figure 3: Discovery reach for a ˜µR NLSP after collecting 500 fb−1
at
√
s = 500 GeV. Left: full scale, Right:
zoom to last few GeV before the kinematic limit.
The strategy
At an e+
e−
-collider, the following typical features of NLSP production and decay can be exploited: missing
[Baer, et.al., ʻ‘13]
ex) √s = 500GeV
Δm=O(10-‐‑‒100)MeV
Massの差はO(10)GeV
ILCで探索索可能

37. Universal Case 37
Muon g-‐‑‒2を1σで説明できる領領域 (1σ Region)
のほとんどは現在のLHCのデータですでに排除
残りの質量量領領域も将来のLHC, ILC実験
で探索索可能な⾒見見通し*
Stau-‐‑‒Higgsポテンシャルの安定性条件から
slepton mass < 500GeVに制限される
まとめ
* ILCにおけるStau探索索に関して、HiggsとDiphotonの結合の情報も有効
[Kitahara, TY, ʻ‘13]
[Endo, Kitahara, TY, ʻ‘14]

38. 本⽇日の内容 38
Intro.
Muon g-‐‑‒2
Supersymmetric Standard Model
Main
“Minimal” SUSY model
Slepton Mass Bound
Conc. Summary
mee = meµ = me⌧ mee = meµ ⌧ me⌧

39. Non-‐‑‒Universal Case 39
Smuon mass bound
500 1000 1500 2000
500
1500
2500
3500
meµ < me0
1
Smuon-‐‑‒Higgsポテンシャルの安定性条件から
smuon mass < 2TeVに制限される
-‐‑‒ Mass
-‐‑‒ 混合
mee = meµ ⌧ me⌧ (stauはdecouple)
meµL
= meµR
, tan = 40
真空の安定性条件を満たす
中で最⼤大の値を各点で選ぶ
Smuon mass <2TeVは
加速器実験の探索索可能領領域を超えている
[Endo, Hamaguchi, Kitahara, TY, ʻ‘13]

40. Non-‐‑‒Universal Case 40
Fermionを対⾓角にする基底で
Slepton質量量⾏行行列列に⾮非対⾓角項が出現
Sleptonの質量量が縮退していない場合、
GIM機構が働かないため、LFV/CPVを誘発
LFV/CPV
(対⾓角) である模型でも
Fermionを対⾓角にする基底とは⼀一般に揃わない
⇣
m2
e`
⌘
i j
= diag
⇣
m2
ee , m2
eµ, m2
e⌧
⌘
LFV/CPVはSlepton質量量⾏行行列列の⾮非対⾓角項に敏感

41. Non-‐‑‒Universal Case 41
[Endo, Hamaguchi, Kitahara, TY, ʻ‘13]
ex) μ→eγ崩壊
Br(µ ! e )
⇣
aNeutralino
µ
⌘2
'
1
(µ ! all)
↵mµ
16
13 23
2
Ç
m⌧
mµ
å2
+ (higher order)
l Stauは1,2世代のSleptonより重い：
l SelectronとSmuonは縮退：1-‐‑‒2世代間の混合の寄与はsuppress
mee = meµ ⌧ me⌧
仮定
Stauが1,2世代のSleptonより⼗十分重い場合
μ→eγとMuon g-‐‑‒2の⽐比はBino, slepton massと独⽴立立
Flavor mixingの定義
46 Diss
µL µR
W±
νµ
γ
(a)
µL µR
µL µR
B
γ
(b)
µL µR
µL
B H0
γ
µL
µR
H0
fW eH eµL eµReeR
eR

42. Non-‐‑‒Universal Case 42
[Endo, Hamaguchi, Kitahara, TY, ʻ‘13]
ex) μ→eγ崩壊
SleptonがLHC, ILCで発⾒見見されなくても
レプトンフレーバー実験から⾼高感度度で探索索可能
＝Non-‐‑‒Universality
現在の
Bound
将来の
感度度
-‐‑‒ Mass
-‐‑‒ Formula
mee = meµ ⌧ me⌧
Br(µ ! e )
Br(µ ! e )
⇣
aNeutralino
µ
⌘2
'
1
(µ ! all)
↵mµ
16
13 23
2
Ç
m⌧
mµ
å2
+ (higher order)
Stauが⼗十分重い(R≫1)とき
L 13 R
⇤
23 Æ 3 ⇥ 10 6
L 13 R
⇤
23 Æ 10 7⇠8
(Current)
(Future)
VubVcb ⇠ 10 4
cf) CKM-‐‑‒like

43. Non-‐‑‒Universal Case 43
Sleptonのmassが縮退していない場合、
⼀一般に⼤大きなLFV/CPVを誘発
Smuon-‐‑‒Higgsポテンシャルの安定性条件から
smuon mass < 2TeVに制限される
まとめ
SleptonがLHC, ILCで発⾒見見されなくても
レプトンフレーバー実験から⾼高感度度で探索索可能

44. 本⽇日の内容 44
Intro.
Muon g-‐‑‒2
Supersymmetric Standard Model
Main
“Minimal” SUSY model
Slepton Mass Bound
Conc. Summary
mee = meµ = me⌧ mee = meµ ⌧ me⌧

45. まとめ 45
「Muon g-‐‑‒2を説明する超対称模型の現象論論」
Muon g-‐‑‒2
>3σ dev.
eB e`L
e`R
eg eq fW ···
⇡
≫1TeV
O(100)GeV
“Minimal” SUSY model
LHC
ILC
LFV
EDM
mee
=
m eµ
=
m e⌧
m
ee =
m
eµ ⌧
m
e⌧
① massに制限
② 相補的に探索索可能

46. 補⾜足パート 46
Backup

47. Muon g-‐‑‒2 47
測り⽅方
磁場中でのMuonの歳差運動の周波数から求める
① ⼀一様磁場中に偏極した(反)muonを⼊入れる
② サイクロトロン運動(磁場)&歳差運動(スピン)
③ g=2 : 歳差運動はサイクロトロン運動に追従
g≠2 : 歳差運動の⽅方がわずかに速くなる(異異常歳差運動)
④ 崩壊先の陽電⼦子の数の時間変動の測定から歳差運動の振動数を求める
⑤ 歳差運動の振動数からg-‐‑‒2を読み取る
!a '
e
mµ
aµ
!
B

48. Muon g-‐‑‒2 48
BNLとJPARCの違い*
l BNL：Magic momentum
l JPARC：電場ゼロ
電場速度度
Lorentz因⼦子
異異常歳差運動の振動数
γ=29.4 (p = 3.094GeV/c) のとき、第⼆二項が無視できる
* Fermilab (FNAL) はBNLと同じsetup
極冷冷muonを⽤用いることで、収束電場を不不要にする
EDMの観測も⽬目標
!a =
e
mµ
2
4aµ
!
B
✓
aµ
1
2 1
◆ !
⇥
!
E
c
⌘
2
⇣!
⇥
!
B
⌘
3
5
EDM(無視)

49. Muon g-‐‑‒2 49
(Naive) NP contribution
aNP
µ ⇠
↵NP
4⇡
mµ
m2
NP
✓ g = 2 at tree level (Dirac equation)
✓ g ≠ 2 by radiative corrections
Magnetic moment
g-factor
gNP gNP
mNP
条件：SM EW contributionと同程度度
26.1 (8.0) × 10-‐‑‒10aµ ⌘ aexp
µ ath
µ =
aSM EW
µ ⇠
↵2
4⇡
m2
µ
m2
W
= 15.36 (0.1) × 10-‐‑‒10
αNP, mNP ~∼ O(EWボソンの結合, 質量量)
そのような粒粒⼦子が存在したら既に発⾒見見されているはず…

50. Muon g-‐‑‒2 50
(Naive) NP contribution
aNP
µ ⇠
↵NP
4⇡
mµ
m2
NP
✓ g = 2 at tree level (Dirac equation)
✓ g ≠ 2 by radiative corrections
Magnetic moment
g-factor
gNP gNP
mNP
2種類の可能性
l αNP~∼ O(10-‐‑‒6) (weak), mNP~∼ O(100)MeV (small)
l αNP~∼ O(0.1-‐‑‒1) (strong), mNP~∼ O(100-‐‑‒1000)GeV (heavy)
e.g. Hidden Photon
e.g. Supersymmetry

51. Supersymmetry 51
Higgs mass
l Tree level :
l Large top-‐‑‒stop correction
mtree
h ' mZ
m2
h ⇠ m2
Z cos2
2 +
3
4⇡2
Y 2
t sin2
ñ
m2
t log
M2
S
m2
t
+
X2
t
M2
S
Ç
1
X2
t
12M2
S
å
+ ···
ô
Ms =
p
met1
met2
, Xt = At µcot
-‐‑‒ Heavy stop : Ms ≫ 1TeV, Xt = 0
-‐‑‒ Maximal mixing : Ms ~∼ 1TeV, Xt = √6Ms
Scalar top > 1TeV

52. Supersymmetry 52
CMSSM (mSUGRA)
m0
A0
m1/2
sgn(µ) tan
Scalar mass
Scalar coupling
m0
Masses of Hu,d
Gaugino mass
Other parameters :

53. Supersymmetry 53
Muon g-‐‑‒2 vs CMSSM
CMSSMの枠組では現在のLHCの制限とHiggs massと
Muon g-‐‑‒2を同時に説明することができない
[Endo, Hamaguchi, Iwamoto, Nakayama, Yokozaki ʻ‘11]
[GeV]0m
0 1000 2000 3000 4000 5000 6000
[GeV]1/2
m
300
400
500
600
700
800
900
1000
(2400GeV)q~
(1600GeV)
q~
(1000 GeV)
g
~
(1400 GeV)g
~
h(122GeV)
h(124GeV)
h(126GeV)
Expected
Observed
Expected
Observed
Expected
Observed
Expected
Observed
Expected
Observed
Expected
Observed
> 0µ,0= -2m
0
) = 30, AβMSUGRA/CMSSM: tan( Status: ICHEP 2014
ATLAS Preliminary
= 8 TeVs,
-1
L dt = 20.1 - 20.7 fb∫
τ∼
LSP
not included.theory
SUSY
σ95% CL limits.
0-lepton, 2-6 jets
0-lepton, 7-10 jets
0-1 lepton, 3 b-jets
1-lepton + jets + MET
1-2 taus + 0-1 lept. + jets + MET
3 b-jets≥2SS/3 leptons, 0 -
arXiv: 1405.7875
arXiv: 1308.1841
arXiv: 1407.0600
ATLAS-CONF-2013-062
arXiv: 1407.0603
arXiv: 1404.2500
mh ~∼126GeV*
g-‐‑‒2
tanβ=20
m0[GeV]
m1/2[GeV]
* Higgs massは (b→sγの制限を満たす範囲で) A-‐‑‒termを調節して説明

54. Supersymmetry 54
Muon g-‐‑‒2 vs Higgs mass and LHC (model)
l Messenger sectorを拡張
l Extra vector-‐‑‒like matterを加える
l 新しいgauge対称性を加える
[Endo, Hamaguchi, Iwamoto, Yokozaki, ʼ’11,12]
[Endo, Hamaguchi, Ishikawa, Iwamoto, Yokozaki, ʼ’12]
[Moroi, Sato, Yanagida, ʼ’12]
[Evans, Ibe, Yanagida, ʼ’11]
[Evans, Ibe, Shirai, Yanagida, ʼ’11]
[Ibe, Matsumoto, Yanagida, Yokozaki, ʼ’12]
[Bhattacharyya, Bhattacherjee, Yanagida, Yokozaki ʼ’13]
[Endo, Hamaguchi, Iwamoto, Nakayama, Yokozaki, ʼ’11]

55. Supersymmetry 55
Electron g-‐‑‒2
11596521807.3(2.8)×10-‐‑‒13
aexp
e =
ath
e = 11596521818.7(0.6)(0.4)(0.2)(7.6)(0.1)×10-‐‑‒13
ae = aexp
e ath
e = -‐‑‒11.4 (8.1) × 10-‐‑‒13
l 実験値と理理論論値はConsistent (1.4σ)
l 新しい物理理の寄与
ae =
✓
aµ
3 ⇥ 10 9
◆
0.7 ⇥ 10 13 (NaïveにYukawaでスケール)
-‐‑‒ SUSYでSleptonが縮退している場合はMuon g-‐‑‒2に⽐比べて感度度が弱い
-‐‑‒ Non-‐‑‒universalの場合はElectron, Muon g-‐‑‒2の両⽅方がenhanceし得る
(符号逆＆LFV/CPVを誘発するのでちと厳しいが…)
ae ⇠ 2 ⇥ 10 12
ex.) のときmee = 100GeV, tan = 30

56. Minimal SUSY model 56
Muon g-‐‑‒2 (Higher order corr. 1, ~∼10%)
l QEDのLeading Log correction
l Bino couplingに重い粒粒⼦子がdecoupleした効果
1 + 2loop
=
Ç
1
4↵
⇡
ln
msoft
mµ
å
1 +
1
4⇡
✓
2↵Y b +
9
4
↵2
◆
ln
Msoft
msoft
egL = gY + egL ' gY

1 +
1
4⇡
✓
↵Y b +
9
4
↵2
◆
ln
Msoft
msoft
egR = gY + egR ' gY

1 +
↵Y
4⇡
b ln
Msoft
msoft
aµ = (1 + 2loop
) ⇥ a1loop
µ
Leading Log Bino coupling
重い粒粒⼦子のスケール
軽い粒粒⼦子のスケール
b =
41
6
(# of the generations of light sleptons)

57. Minimal SUSY model 57
Muon g-‐‑‒2 (Higher order corr. 2, ~∼10%)
l Yukawaの補正 (Non-‐‑‒Holomorphic Yukawa)
-‐‑‒ MSSMのYukawaとSMのYukawaのmatchingの際に出現
m` =
`L
`R
+
hHdi hHui
`L
`R
SUSYSUSY
Y MSSM
` =
m`
v cos
1
1 + `
`

58. Minimal SUSY model 58
Bino coupling
SUSY limitではU(1)Y ゲージ結合と等しい
(重い粒粒⼦子の) SUSY breakingの効果でズレが発⽣生
Coupling
EnergyMsoftmsoft
egBino = gY
gY
egBino
egBino
重い粒粒⼦子
decouple
くりこみ群の
runが変化
Lint =
1
p
2
egL
eB`L
e`⇤
L +
p
2egR
eB`R
e`⇤
R + h.c.
-‐‑‒ Interaction
-‐‑‒ Bino coupling
egL = gY + egL ' gY

1 +
1
4⇡
✓
↵Y b +
9
4
↵2
◆
ln
Msoft
msoft
egR = gY + egR ' gY

1 +
↵Y
4⇡
b ln
Msoft
msoft
b =
41
6
(# of the generations of light sleptons)

59. Slepton Mass Bound 59
スカラーポテンシャル
l Up-‐‑‒type HiggsとSlepton
l Slepton-‐‑‒Higgsの3点相互作⽤用
l Sleptonの4点相互作⽤用
V = (m2
Hu
+ µ2
)|Hu|2
+ m2
e`L
|e`L|2
+ m2
e`R
|e`R|2
(Y`µH⇤
u
e`⇤
L
e`R + h.c.) + Y 2
` |e`⇤
L
e`R|2
+
g2
8
(|e`L|2
+ |Hu|2
)2
+
g2
Y
8
(|e`L|2
2|e`R|2
|Hu|2
)2
+
g2
+ g2
Y
8
H |Hu|4
mixing Flavor dep.
-‐‑‒ Sleptonの混合に⽐比例例
-‐‑‒ 極端に⼤大きいとEW vacuumが不不安定になる
-‐‑‒ LeptonのYukawaに⽐比例例 (＝tanβが⼤大きい極限でにtanβに⽐比例例)
-‐‑‒ tanβを⼤大きくすると真空の安定性条件をゆるくする⽅方向に働く
-‐‑‒ Stauの場合は若若⼲干依存、Selectron/Smuonは依存性無視できる

60. Slepton Mass Bound 60
真空崩壊
l Decay rate
/(Volume) = A· e B
~∼(100GeV)4
Bounce解から評価
-‐‑‒ 偽の真空の基底状態のエネルギーの虚部から出現
-‐‑‒ 境界条件
-‐‑‒ 境界条件のもとでの運動⽅方程式の解：Bounce解
= 2ImE0, E0 = lim
T!1
1
T
ln
ÇZ
[D ]exp( SE[ ])
å
Φ=Up-‐‑‒type Higgs, Sleptons, SE はユークリッド作⽤用
lim
T!1
✓
!x ,±
T
2
◆
= f
¯
B = SE[ ¯] SE[ f
]
偽の真空での場の配位
[Coleman, ʻ‘77]
[Callan, Coleman, ʻ‘77]

61. Slepton Mass Bound 61
真空崩壊
l Bounce解 (Path deformation method)
-‐‑‒ 運動⽅方程式 (O(4) symmetric, zero temp. : α = 3)
-‐‑‒ 最初にPathにあたりをつける
-‐‑‒ Pathを変形させて運動⽅方程式の解になるものを探す
!
guess =
!
(x),
d
!
dx
= 1 (仮定)
Figure 4: Path deformation in two dimensions. The normal force exerted on
path (blue straight line) pushes it in the direction of the true tunneling so
curved line).
[CosmoTransitions, ʻ‘11]
d2 !
d⇢2
+
↵
⇢
d
!
d⇢
= rV(
!
)
d2
x
d⇢2
+
↵
⇢
dx
d⇢
=
@
@ x
V(
!
)
d2 !
d⇢2
✓
dx
d⇢
◆2
= r?V(
!
)
(Path⽅方向)
(垂直⽅方向)
V
true
false
cf.) Overshoot/Undershoot method
Multi-‐‑‒dimensionだと⼀一意に求められない

62. Slepton Mass Bound 62
Fitting Formula
200 300 400 500 600
200
300
400
500
600
l Stauの場合
µtan , tan = 70
30
20TeV
40
50
60
70
90
80
[Kitahara, TY, ʻ‘13]
[Endo, Kitahara, TY, ʻ‘14]

63. Slepton Mass Bound 63
Fitting Formula
l tanβ依存性
20 40 60 80 100
0.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
-‐‑‒ スカラーの4点はYukawaに依存 ( )
-‐‑‒ tanβが⼤大きい極限で(tanβ)2に⽐比例例
-‐‑‒ tanβを⼤大きくするとVacuumの制限が若若⼲干改善*
[Kitahara, TY, ʻ‘13]
改善悪化
ここで1に規格化
* 1,2世代のsleptonの場合は、Yukawaが⼩小さいため、tanβ依存性は無視できる

64. Universal Case 64
ILC (smuon)
[Endo, Hamaguchi, Kitahara, TY, ʻ‘13]
Smuonにmassの差がある場合はILCが有効
偏極ビームを⽤用いることで断⾯面積がenhance
p
s = 1TeV
p
s = 1TeV
Polarization

65. Universal Case 65
ILC (selectron)
[Endo, Hamaguchi, Kitahara, TY, ʻ‘13]
t-‐‑‒channel Bino exchangeのため断⾯面積がenhance
Bino couplingの測定にも有効
p
s = 1TeV
-‐‑‒ Diagram (t-‐‑‒channel)
-‐‑‒ Bino coupling
eB
ee
ee⇤
e+
e
ü 重い粒粒⼦子の効果でO(%)変化
ü ⾼高精度度のCouplingの測定から重いスケールを探れるかも
[Nojiri, Fujii, Tsukamoto, ʻ‘96]
[Nojiri, Pierce, Yamada, ʼ’97]

66. Non-‐‑‒Universal Case 66
[Endo, Hamaguchi, Kitahara, TY, ʻ‘13]
Non-‐‑‒Universality
Smuonが重いほどMuon g-‐‑‒2の説明のために
⼤大きなNon-‐‑‒Universalityが要求される

67. Non-‐‑‒Universal Case 67
[Endo, Hamaguchi, Kitahara, TY, ʻ‘13]
Flavor mixingの定義
l SleptonがFlavor diagonalである基底でのYukawa：
l Fermion massを対⾓角にする基底でのYukawa：
l Mixing matrix：世代間の混合をparameterize
Mixing matrix : 基底間のズレ

68. Non-‐‑‒Universal Case 68
[Endo, Hamaguchi, Kitahara, TY, ʻ‘13]
ex) Lepton FCNCs
l Effective operator (双極⼦子型)
l Wilson係数
l Flavor mixing
Leff ⌘ e
m`i
2
`i µ⌫
⇣
AL
i j PL + AR
i j PR
⌘
`j Fµ⌫
+ h.c.
Higher-‐‑‒order
correction
Loop function
AL
i j = (1 + 2loop
)
↵Y
8⇡
M1µtan
m`j
X
a,b=1,2,3
h
UR
i
ib
h
M`
i
ba
h
U†
L
i
aj
Fa,b
AR
i j = (1 + 2loop
)
↵Y
8⇡
M1µtan
m`j
X
a,b=1,2,3
h
UL
i
ia
h
M†
`
i
ab
h
U†
R
i
bj
Fa,b
h
UL
i
1a
h
M†
`
i
ab
h
U†
R
i
b2
Fa,b =
mµ
1 + µ
( L)12
Ä
F1,2 F2,2
ä
+
m⌧
1 + ⌧
( L)13( R)⇤
23
Ä
F1,2 F1,3 F3,2 + F3,3
ä
SelectronとSmuonが縮退
していればキャンセル
Sleptonが全て縮退
していればキャンセル
46 Dissertation
µL µR
W±
νµ
γ
(a)
µL µR
µL µR
B
γ
(b)
µL W
µL µR
µL
B H0
d
γ
(d)
µL µR
µR
H0
d
B
γ
(e)
Figure 3.4: The diagrams of the SUSY contributions to the muon g − 2
The diagram (a) comes from the chargino–muon sneutrino diagram, the
from the neutralino–smuon diagram.
χ0 mµ
6 4
1 mµ L(e)
2
R(e)
2
N
fW eH eµL eµReeR
eR

69. Non-‐‑‒Universal Case 69
[Endo, Hamaguchi, Kitahara, TY, ʻ‘13]
ex) Lepton FCNCs
l μ→eγ崩壊
l 電⼦子の電気双極⼦子モーメント
l Muon g-‐‑‒2との相関
46 Dissertation
µL µR
W±
νµ
γ
(a)
µL µR
µL µR
B
γ
(b)
µL W
µL µR
µL
B H0
d
γ
(d)
µL µR
µR
H0
d
B
γ
(e)
Figure 3.4: The diagrams of the SUSY contributions to the muon g − 2
The diagram (a) comes from the chargino–muon sneutrino diagram, the
from the neutralino–smuon diagram.
χ0 mµ
6 4
1 mµ L(e)
2
R(e)
2
N
fW eH eµL eµReeR
eR
de
e
=
me
2
Im
î
AL
11 AR
11
ó
B(µ ! e ) '
48⇡3
↵
G2
F
Ä
|AL
12|2
+ |AR
12|2
ä
Br(µ ! e )
⇣
aNeutralino
µ
⌘2
'
1
(µ ! all)
↵mµ
16
13 23
2
Ç
m⌧
mµ
å2
+ (higher order)
de/e
aNeutralino
µ
'
1
2mµ
Im[( R)13( L)⇤
13]
m⌧
mµ
+ (higher order)
Stauが⼗十分重いとき、SUSY粒粒⼦子の質量量と独⽴立立

70. Non-‐‑‒Universal Case 70
[Endo, Hamaguchi, Kitahara, TY, ʻ‘13]
SleptonがLHC, ILCで発⾒見見されなくても
レプトンフレーバー実験から⾼高感度度で探索索可能
＝Non-‐‑‒Universality
現在の
Bound
将来の
感度度
-‐‑‒ Mass
-‐‑‒ Formula
mee = meµ ⌧ me⌧
Stauが⼗十分重い(R≫1)とき
(Current)
(Future)
ex) 電⼦子の電気双極⼦子モーメント
de/e
aNeutralino
µ
'
1
2mµ
Im[( R)13( L)⇤
13]
m⌧
mµ
+ (higher order)
Im L 13 R
⇤
13 Æ 6 ⇥ 10 8
Im L 13 R
⇤
13 Æ 6 ⇥ 10 9⇠10
de/e

71. Extra-‐‑‒Slides 71
Future Prospects
for Stau
博⼠士論論⽂文 Sec.4.3
Based on
T. Kitahara and T.Y JHEP 05 035 (2013)
M. Endo, T. Kitahara, and T.Y JHEP 04 139 (2014)

72. Stau 72
Higgs Oblique Correction
l Loop-‐‑‒induced Higgs coupling
l 新しい物理理にsensitive
-‐‑‒ Higgs to digluon, diphoton, Zγ
-‐‑‒ 間接的に新しい物理理を制限
-‐‑‒ SM：tree levelで出現しない
-‐‑‒ 新しい物理理の影響を受けやすい
NPh
V
V制限
予⾔言
実験 新しい物理理

73. Stau 73
Higgs coupling to diphoton κγ
l Current accuracy (LHC)
l Joint analysis
 ⌘
gh
gh (SM)
= 1 +  ,  ⇠ 15%
-‐‑‒ Br(h→γγ)/Br(h→ZZ)はHL-‐‑‒LHCで精密測定 (3.6%と仮定)
-‐‑‒ Br(h→ZZ)は初期ステージでのILCで精密測定 (sub% level)
-‐‑‒ 両者の結果を合わせると単体での測定よりもκγを精密に決定可能
 ⇠ 1 2%
[Peskin, ʻ‘13]
5%
4%
3%
2%
1%
γ
CMS-1
CMS-2
ILC
ILC +
LHC BR
ratio
CMS 250 500 500up 1000up1000
6%
7%

-‐‑‒ HL-‐‑‒LHC, ILC単体だとO(1-‐‑‒10)%
-‐‑‒ Joint analysis

74. Stau 74
Higgs coupling to diphoton κγ
l Loop-‐‑‒induced Higgs coupling
l 新しい物理理にsensitive
l HL-‐‑‒LHCと初期のILCから1-‐‑‒2%の決定精度度が期待
将来excessが⾒見見えた場合に分かる
新しい物理理の性質を考察しておくことは重要
l 博⼠士論論⽂文では超対称模型を仮定
l Muon g-‐‑‒2を考慮すると、軽いStauが予想
l 初期のILCまでで数％のexcessが観測されたと仮定
新しい物理理

75. l Stau : κγのみに⼤大きな寄与
l 3つのParameterでcontroll (mass, mixing angle)
l Stauが軽い＆⼤大きな混合を持つ場合にenhance (O(10)%)
l 極端に⼤大きな混合は真空の安定性条件により制限
Stau 75
Stau contribution to κγ
Dissertation / Takahiro Yoshinaga
τR
τL
h
γ
γ
gure 3.6: Feynman diagram of the stau contribution to the Higgs coupling to di-photon.
re OL,R are the unitary matrices, which diagonalize the chargino mass matrix, as seen in
3.3.1. δm2
fLL,RR
and δm2
fLR
are defined as
m2
e⌧LR
=
1
2
⇣
m2
e⌧1
m2
e⌧2
⌘
sin2✓e⌧
m2
e⌧1
, m2
e⌧2
, ✓e⌧
Ue⌧Me⌧U†
e⌧
= diag(m2
e⌧1
, me⌧2
)
Ue⌧ =
✓
cos✓e⌧ sin✓e⌧
sin✓e⌧ cos✓e⌧
◆
cf.) Stauの質量量⾏行行列列

76. Stau 76
Stau contribution to κγ
[Endo, Kitahara, TY, ʻ‘13]
真空の安定性条件からκγの⼤大きさは制限
10-‐‑‒15%が取りうるexcessの最⼤大値
Large mixing angle：真空の安定性条件で制限

77. Stau 77
Stau mass region
[Endo, Kitahara, TY, ʻ‘13]
δκγ>4%ならば、 250GeVに制限
√s =500GeV ILCまでで発⾒見見可能
me⌧1
<
Higgs coupling to diphoton
sin2✓e⌧ = 1
真空の安定性条件を満たす
なかで最⼤大の値を選択tan = 20

78. l 仮定
l Sample point
l Reconstruction (ILC at √s = 500GeV)
Stau 78
Stau searches (Reconstruction)
-‐‑‒ Stau1,2, mixing angle全てがILC (√s = 500GeV)で観測
-‐‑‒ κγは数%のexcessが観測、測定精度度は2%と仮定
88 Dissertation / Takahiro Yoshinaga
Table 4.3: Model parameters at our sample point. In addition, tanβ = 5 and Aτ = 0 are set,
though the results are almost independent of them.
Parameters mτ1
mτ2
sin2θτ mχ0
1
δκγ
Values 100 GeV 230 GeV 0.92 90 GeV 3.6%
4.3 Stau
So far, we studied the prospects for the selection/smuon searches. In this section, we discuss
the stau searches. If the staus have masses of (100)GeV and large left-right mixing, the
Higgs coupling to the di-photon κγ is deviated from the SM prediction. Such a large left-right
mixing is constrained by the vacuum meta-stability condition of the stau-Higgs potential, as
mentioned in Sec 4.1.3. Then, we discussed that once the deviation from the SM prediction of
κγ were observed, the mass region for the staus were determined by the condition in Sec. 4.1.4.
Once the stau is discovered at ILC, its properties including the mass are determined. Par-
ticularly, it is important to measure the mixing angle of the stau θτ. When sin2θτ is sizable,
[Endo, Kitahara, TY, ʻ‘13]
me⌧1
⇠ 0.1 GeV, me⌧2
⇠ 6 GeV,
sin2✓e⌧
sin2✓e⌧
⇠ 2%
 ⇠ 0.5%
excessがStau起源かcheck可能

79. l 仮定
l Sample point (stau2は√s = 500GeVでは未発⾒見見）
l Prediction for stau2 (ILC at √s = 1TeV)
Stau 79
Stau searches (Prediction)
-‐‑‒ Stau1, mixing angleがILC (√s = 500GeV)で観測、stau2は未発⾒見見
-‐‑‒ κγは数%のexcessが観測、測定精度度は2%と仮定
[Endo, Kitahara, TY, ʻ‘13]
Table 1: Model parameters at our sample point. In addition, tanβ = 5 and Aτ = 0 are set,
though the results are almost independent of them.
Parameters mτ1
mτ2
sin2θτ mχ0
1
δκγ
Values 150 GeV 400 GeV 0.91 140 GeV 5.6%
me⌧1
⇠ 0.1 GeV,
sin2✓e⌧
sin2✓e⌧
⇠ 2.5%,  ⇠ 2%
√s = 1TeV ILCで発⾒見見が期待、ビームエネルギーを調節するためのヒントを与える
me⌧2
= 400 ± 53 GeV