1. カラーを持たない新粒粒⼦子を軸に
新しい物理理を探る
Takahiro Yoshinaga (Univ. of Tokyo)
Based on
T. Kitahara and T.Y JHEP 05 035 (2013)
M. Endo, K. Hamaguchi, S. Iwamoto, and T.Y JHEP 01 123 (2014)
M. Endo, K. Hamaguchi, T. Kitahara, and T.Y JHEP 11 013 (2013)
M. Endo, T. Kitahara, and T.Y JHEP 04 139 (2014)
33 Slides
2. 研究テーマ 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
Muon g-‐‑‒2 Motivated SUSY
mee
=
m eµ
=
m e⌧
m
ee =
m
eµ ⌧
m
e⌧
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.
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
γ
µR
γ
fW eH
≫1TeV
⇡
O(100)GeV
eg eq ···
eB fW eH e`
LHC
LHC & ILC
3. 研究での⾃自分の役割 3
「どのような切切り⼝口で物理理を引き出すか」
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
corresponds to such potential is given by
Hint = −〈−→µ 〉 ·
−→
B , (2.17)
where
〈−→µ 〉 = 2 F1(0) + F2(0) ×
eQℓ
2mℓ
ξ′†
−→σ
2
ξ. (2.18)
The factor ξ′†
(−→σ /2)ξ can be interpreted as the spin of the leptons,
−→
S . Comparing Eq. (2.18)
with Eqs. (2.3) and (2.4), the coefficient 2 F1(0) + F2(0) becomes
SUSY
超対称模型のMuon g-‐‑‒2への寄与
-‐‑‒ 全て考慮すると複雑、物理理が⾒見見えづらい
-‐‑‒ 加速器シミュレーションの計算が⼤大変
本質的に重要なセットアップに近似
1. Chargino-‐‑‒sneutrino 2. Neutralino-‐‑‒smuon
Multi-‐‑‒lepton signalが重要 真空の安定性が重要
7. 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 7
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
8. Muon g-‐‑‒2 8
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 =
素粒粒⼦子物理理学の⽂文化…不不⼀一致が3σ:兆候 5σ:発⾒見見
(標準模型)
11. Muon g-‐‑‒2 11
/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
-‐‑‒ 超対称模型(SUSY)を仮定
:新粒粒⼦子の質量量が加速器実験の探索索可能領領域に⼊入る
-‐‑‒ model-‐‑‒independent approachを採⽤用
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
本研究の⽴立立場
30. Neutralino-‐‑‒Smuon Contribution 30
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
38. Muon g-‐‑‒2 38
>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]
39. Muon g-‐‑‒2 39
(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…
40. Muon g-‐‑‒2 40
(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
41. Supersymmetry 41
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
50. Chargino-‐‑‒Sneutrino Contribution 50
Mass spectrum
⇡
≫1TeV
O(100)GeV
l 軽い(O(100)GeV)粒粒⼦子 : Bino, Wino, Higgsino, 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
eB fW eH e`
eg eq ···
46
µL µR
W±
νµ
γ
(a)
µL
µL
γ
fW eH
[Endo, Hamaguchi, Iwamoto, TY, ʼ’14]
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
51. Chargino-‐‑‒Sneutrino Contribution 51
Electroweak gaugino探索索
) [GeV]
2
0
χ∼(=m
1
±
χ∼m
100 200 300 400 500 600 700
[GeV]0
1
χ∼m
0
100
200
300
400
500
600
Expected limits
Observed limits
arXiv:1402.70293L,,ν∼/LL
~
via0
2
χ∼±
1
χ∼
arXiv:1403.52942l,,ν∼/LL
~
via−
1
χ∼+
1
χ∼
arXiv:1402.70293L,,τν∼/L
τ∼via0
2
χ∼±
1
χ∼
arXiv:1407.0350,τ2≥,τν∼/Lτ∼via0
2
χ∼±
1
χ∼
arXiv:1407.0350,τ2≥,τν∼/Lτ∼via
−
1
χ∼+
1
χ∼
arXiv:1403.52942l+3L,via WZ,0
2
χ∼±
1
χ∼
arXiv:1501.07110+3L,
±
l
±
+lγγlbb+lvia Wh,0
2
χ∼±
1
χ∼
arXiv:1403.52942l,via WW,
−
1
χ∼+
1
χ∼
All limits at 95% CL
=8 TeV Status: Feb 2015s,-1
Preliminary 20.3 fbATLAS
)
2
0
χ∼+ m
1
0
χ∼= 0.5(mν∼/L
τ∼/L
l
~m
τ/µL = e/
µl = e/
1
0
χ∼
=
m
2
0
χ∼
m
Z
+
m
1
0
χ∼
=
m
2
0
χ∼
m
h
+
m
1
0
χ∼
=
m
2
0
χ∼
m
1
0
χ∼
= 2m
2
0
χ∼m
Wino>slepton>Binoの場合はWino〜~数百GeVまで排除
52. Chargino-‐‑‒Sneutrino Contribution 52
Electroweak gaugino探索索(Future)
ATLAS
24 5 Discovery Potential: Supersymmetry
too massive and ˜c±
1 and ˜c0
2 are wino-like, which suppresses neutralino-pair production relative
to neutralino-chargino production.
The analysis is based on a three-lepton search, with electrons, muons, and at most one hadron-
ically decaying t lepton. In order to get an estimate for the sensitivity at 14 TeV two different
Scenarios (A and B) are considered, as discussed earlier. The results are shown in Fig. 21. The
chargino mass sensitivity can be increased to 500–600 GeV, while discovery potential for neu-
tralinos ranges from 150 to almost 300 GeV.
P1
P2
˜±
1
˜0
2
W
Z
˜0
1
˜0
1
(a)
[GeV]0
2
χ∼= m±
1
χ∼m
100 200 300 400 500 600 700
[GeV]0
1
χ∼m
0
50
100
150
200
250
300
350
400
450
500
-1
8 TeV, 20 fb
(scenario A)-1
14 TeV, 300 fb
(scenario B)-1
14 TeV, 300 fb
±
1
χ∼0
2
χ∼→pp
0
1
χ∼Z→
0
2
χ∼
0
1
χ∼W→
±
1
χ∼
CMS Preliminary
Based on SUS-13-006
discovery reachσEstimated 5
(b)
Figure 21: The simplified model topology for direct ˜c±
1 ˜c0
2 production decaying to the WZ+Emiss
T
final state (a), and the projected 5s discovery projections for this model (b).
assumptions and analysis strategies.
6.1 Direct Production of Weak Gauginos
Weak gauginos can be produced in decays of squarks and gluinos or directly in weak production.
For weak gaugino masses of several hundred GeV, as expected from naturalness arguments [20],
the weak production cross section is rather small, ranging from 10 2
to 10 pb, and a dataset
corresponding to high integrated luminosity is necessary to achieve sensitivity to high-mass
weak gaugino production. Results with the 2012 data exclude charginos masses of 300 to
600 GeV for small LSP masses, depending on whether sleptons are present in the decay chain.
For LSP masses greater than 100 GeV there are currently no constraints from the LHC if the
sleptons are heavy .
The weak gauginos can decay via ˜0
2 ! Z ˜0
1 or ˜±
1 ! W±
˜0
1, and both of these decays
lead to a final state with three leptons and large missing transverse momentum. SM back-
ground for this final state is dominated by the irreducible WZ process, even with a high missing
transverse momentum requirement of 150 GeV. Boosted decision trees can be trained to use
kinematic variables, such as the leptons0
transverse momenta, the pT of the Z-boson candidate,
the summed ET in the event, and the transverse mass mT of the lepton from the W and the
missing transverse momentum.
The expected sensitivity for the search is calculated using a simplified model in which the
˜0
2 and ˜±
1 are nearly degenerate in mass. With a ten-fold increase in integrated luminosity
from 300 to 3000 fb 1
, the discovery reach extends to chargino masses above 800 GeV, to be
compared with the reach of 350 GeV from the smaller dataset. The extended discovery reach
and comparison are shown in Fig. 10.
Mass (GeV)2
0
χ∼and1
±
χ∼
100 200 300 400 500 600 700 800
Mass(GeV)1
0
χ∼
100
200
300
400
500
600
700 ATLAS Simulation
, 95% exclusion limit-1
3000 fb
discovery reachσ, 5-1
3000 fb
, 95% exclusion limit-1
300 fb
discovery reachσ, 5-1
300 fb
=14 TeVs
Figure 10: Discovery reach (solid lines) and exclusion limits (dashed lines) for charginos and neutralinos
in ˜±
1 ˜0
2 ! W(?) ˜0
1Z(?) ˜0
1 decays. The results are shown for the 300 fb 1
and 3000 fb 1
datasets.
CMS
14TeV LHCでWino〜~1TeVまで探索索可能
[ATLAS-‐‑‒PHYS-‐‑‒PUB-‐‑‒2013-‐‑‒007]
[CMS-‐‑‒NOTE-‐‑‒13-‐‑‒002]
53. Neutralino-‐‑‒smuon contribution 53
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)
63. Universal Case 63
-‐‑‒ 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
64. Universal Case 64
-‐‑‒ 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
65. Universal Case 65
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
66. Universal Case 66
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]
67. Non-‐‑‒Universal Case 67
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]
70. Non-‐‑‒Universal Case 70
[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
71. Non-‐‑‒Universal Case 71
[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
81. 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 81
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
82. Stau 82
Stau contribution to κγ
[Endo, Kitahara, TY, ʻ‘14]
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
83. Stau 83
Stau mass region
[Endo, Kitahara, TY, ʻ‘14]
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
84. l 仮定
l Sample point
l Reconstruction (ILC at √s = 500GeV)
Stau 84
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‘14]
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
85. 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 85
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‘14]
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