SUSY-SUSY サブグループ

SUSY-SUSY サブグループ
岩本 蘭藤 伊部 今井 大河内 太田 角田 菅井 中野 中山 森田
Special Thanks : 浅井さん
SUSY-SUSY サブグループ
SUSY が見つかっていない現状をふまえ、それでも SUSY が本当で
あった際に想定され得る可能性について横断的に議論しました。
各項目のバランスは全然考えずに議論してしまいましたがご了承下さい。
また、文献や図の出所等全く記していませんがこちらも議論のための
スライドだということでご了承下さい。
Current Status of SUSY models
squark
mass
SUSY
higher
than
100TeV
DM ??
wino<3TeV
Higgsino
<2TeV
10-100TeV
DM ??
wino<3TeV
Higgsino
<2TeV
TeV
Light Stop,
Higgsino
縮退 ?
焦らずもう少し
待ちましょう
まずは gluino 1TeV
以下での軽い stop
search!
Same Sign Muon ?
LHC search
での穴
Higgs
番外色々？
もっと手の込ん
だ模型？
GUT
10 years from now?
備考
現段階で Higgs mass への制限か
much heavier
than 125GeV
何それ？
Gaugino が TeV scale なら
ら less favored.
もはや SUSY じゃな
unification は OK
もし stopping gluino なんかが見
い？
つかったら大騒ぎ。
125GeV
in MSSM
何それ？
素敵な
1%で済む領域が
残っているか？
something
or
low scale
Large A-term mediation が有利
素敵な
something
Gaugino が TeV scale なら
unification は OK
Gaugino searches.
Cosmic ray?
下でないと O(10)%
素敵な
something
素敵な
something?
TeV 以内で見つかれ
ば文句無し？
得に問題無い
づつ削られて行く
g-2 はまだ説明可
最終的には 10TeV scenario に
能！
合流?
stop を軽くする際の
Model Dependent...
stop direct production では何 fine-tuning に注意。
処まで行けるか？
せ？
g-2 はまだ説明可
能！
基本的に gaugino の GUT
ISR jet で何処までいけるか？
relation は邪魔。
ISR photon とか？
例外) Mirage Mediation
soft lepton とか？
見やすくて意外な模型なら
Little Higgs とか他の
模型との組み合わ
シンプル。やれるこ
いわゆる SUSY search で少し
Two-loop を考える
と gluino は 1TeV 以
High energy model は
とが少ないかも
は難しそう
LHC で見つか
らないように
Naturalness
Dual Unification とか？
Welcome!
SUSY を隠す模型を作り続け
る人が出てくるか？
縮退を実現する High
energy model はほとん
どない。
大穴の一つ？
Current Status of SUSY models
squark
mass
SUSY
higher
than
100TeV
DM ??
wino<3TeV
Higgsino
<2TeV
10-100TeV
DM ??
wino<3TeV
Higgsino
<2TeV
TeV
Light Stop,
Higgsino
縮退 ?
焦らずもう少し
待ちましょう
まずは gluino 1TeV
以下での軽い stop
search!
Same Sign Muon ?
LHC search
での穴
Higgs
番外色々？
もっと手の込ん
だ模型？
GUT
10 years from now?
備考
現段階で Higgs mass への制限か
much heavier
than 125GeV
何それ？
Gaugino が TeV scale なら
ら less favored.
もはや SUSY じゃな
unification は OK
もし stopping gluino なんかが見
い？
つかったら大騒ぎ。
125GeV
in MSSM
何それ？
素敵な
1%で済む領域が
残っているか？
something
or
low scale
Large A-term mediation が有利
素敵な
something
Gaugino が TeV scale なら
unification は OK
得に問題無い
Gaugino searches.
Cosmic ray?
下でないと O(10)%
素敵な
something
素敵な
something?
TeV 以内で見つかれ
ば文句無し？
g-2 はまだ説明可
づつ削られて行く
能！
最終的には 10TeV scenario に
Higgs グループにおま
合流?
かせ
stop を軽くする際の
Model Dependent...
stop direct production では何 fine-tuning に注意。
処まで行けるか？
せ？
g-2 はまだ説明可
能！
基本的に gaugino の GUT
ISR jet で何処までいけるか？
relation は邪魔。
ISR photon とか？
例外) Mirage Mediation
soft lepton とか？
見やすくて意外な模型なら
Little Higgs とか他の
模型との組み合わ
シンプル。やれるこ
いわゆる SUSY search で少し
Two-loop を考える
と gluino は 1TeV 以
High energy model は
とが少ないかも
は難しそう
LHC で見つか
らないように
Naturalness
Dual Unification とか？
Welcome!
SUSY を隠す模型を作り続け
る人が出てくるか？
縮退を実現する High
energy model はほとん
どない。
大穴の一つ？
through the radiative corrections [23]. The first contribution to deviates the SUSY relation
SUSY much heavier than
TeV
(いわゆる
SUSY)
is the100
radiative
correction
through thesplit
renormalization-group
equation.
At the one-loop
level, the renormalization-group equation is roughly given by
まだ LSP-DM を期待するなら LSP
dλ
12
∼
(λ2 + λyt2 − yt4 ) ,
2
はdtTeV16π
領域 (see next
topic)
(9)
yt denotes the top Yukawa coupling, and we have neglected gaugino couplings for
(DM search andwhere
Gaugino
search @ LHC は期待できる？)
illustrative purpose. By imposing the SUSY relation in Eq. (8) at the renormalization
scale Q = MSUSY , the renormalization-group equation can be approximately solved by,
130GeV
135GeV
140GeV
この領域は naive には12Higgs
が重い
M
SUSY
4
λ(mh ) ∼ λ(MSUSY ) +
y
ln
.
2 t
(4π)
m
Higgs Mass 125GeV が本当ならh less favored
(10)
Therefore, we expect that the physical Higgs mass receives a large positive correction for
125GeV
MSUSY = O(104−6 ) GeV.
10
tanΒ
The second簡単に軽くする方法？
contribution which deviates the SUSY relation comes from the finite cor-
rection to the Higgs quartic coupling from the trilinear couplings. At the one-loop level,
４点に負の寄与、large A-term or Hard Breaking etc.
120GeV
this contribution is given by,
δλ �
mh �114.4GeV
6 4
y
(4π)2 t
1
10
102
MSUSY �TeV
103
104
�
Xt2
m2t̃
−
1
12
Xt4
m4t̃
�
,
[わざわざ軽くしたいかどうかは疑問…]
6
our plot of the lightest Higgs boson mass. The bands for mh =
eV represent the effects of the theoretical uncertainty of the ratio
est Higgs boson mass. We have assumed that MSUSY /3 < µH < 3MSUSY .
ral values of the 1σ errors of the strong coupling constant and the top
SUSY much heavier than 100 TeV (いわゆる split SUSY)
4678*+9&%:*0*7;%%%
Stable gluino ?
/C/>9?%*;%9)D:1&9&%!=EFGH$%
@2A%;786:9%;781I%
4678*+9&%:*0*7;%%%
&*A9D7%JA2&1DK2+
!"#$%%&'(&)%%*+%,-%%.%!"/$%012+%345%%!,,$%
τgluino = 5 x10-9 sec x ( mgluino / TeV)5 x (104 TeV / msquark)4
Current limit
/C/>9?%*;%9)D:1&9&%!=EFGH$%
#<=#%>9?%@2A%;786:9%B:1*+2
@2A%;786:9%;781I%
&*A9D7%JA2&1DK2+
LMN8&A2+O%%LP
#<=#%>9?%@2A%;786:9%B:1*+2
LMN8&A2+O%%LP
Q786:9%LMN8&A2+
Q786:9%LMN8&A2+
もっと重い
gluino は難しそう
10-100TeV SUSY
理論的には極めてシンプル
Wino DMの場合
Fermi : mwino>400GeV
Gluino > 3TeV
WMAP, BBN : mwino>200GeV
Planck : mwino >500GeV
LHCで生成困難
但しAMSB relationを変更すればLHCで生成可能
Higgsino mass~Wino massの場合
XENON100 : mHiggsino >400GeV
2-3年後 : mHiggsino >800GeV
Wino DMでない場合
mwino ~200-300GeVでもOK
W̃ W̃ j
LHCで発見可能
charged track 200-20 event@14TeV, 100fb-1
10-100TeV SUSY
Indirect
Annihilation Cross Section (cm3 /s)
Direct
Win
10
ï25
10
tter
Planc
k
iïLAT
m
r
e
F
tiïp)
n
A
(
LA
E
PAM
ï26
10
100
iïp)
t
n
A
(
02
AMSï
200
400
300
Dark Matter Mass (GeV)
500
Figure 6: Constraints and future prospects of indirect detection experime
100 prediction of the neutral wino dark matter is also shown.
matter. Theoretical
pT > 170GeV
pT > 270GeV
10
pT > 370GeV
Cross Section [fb]
pp → W̃ + W̃ − j
√
s = 14TeV
rk M
a
ï24
ï27
LHC
W
o Da
10
Near future
constraint
BN
B
,
P
MA
ï23
10
one) above the constraint
in order to take the uncertainties into account
1
seen that the neutral wino should be, at least, heavier than 300 GeV.
0.1
Another interesting
indirect detection is the PAMELA experiment ob
At least one Wino
cosmic-ray p̄ (anti-proton)
flux [43]. Current constraint on the dark matte
0.01
cτ > 44.3cm
experiment is also shown in Fig. 6 as a blue-shaded region. Since the p̄ flu
0.001
on how p̄ propagates
the250
complicated
field of our galaxy
100 under
150 200
300 350 magnetic
400 450 500
mWino
[GeV]
dark matter profiles we adopt [44],
the
constraint has large uncertainties
SUSY ＠ TeV
SUSY Search @ LHC
の制限&&)78!79&2+&0%:;+2/ mg~ [GeV]
ector, as described in Ref. [1], result in an uncerGGM: bino-like neutralino, tan% = 2, c$NLSP < 0.1 mm
1200
of 3.9 % for the GGM and SPS8 signals and 3.7 %
ATLAS CL s expected 95% CL limit
ATLAS
1100
UED signal. The uncertainty from the photon isoATLAS CL s observed 95% CL limit
± 1&
was estimated by varying the energy leakage and
1000
ATLAS CL s observed 95% CL limit (36 pb -1)
e-up corrections independently, resulting in an unCMS observed 95% CL limit (35 pb -1)
900
ty of 0.6 % for GGM and SPS8 and 0.5 % for UED.
800
fluence of pile-up on the signal efficiency, evaluated
Ldt = 1.07 fb-1
#
paring GGM/SPS8 (UED) MC samples with dif700
s = 7 TeV
pile-up configurations, leads to a systematic uncer600
of 1.3 %(1.6 %). Systematic uncertainties due to the
~
500
g NLSP
econstruction, estimated by varying the cluster enmiss
within established ranges and the ET
resolution
400
200
400
600
800
1000
1200
n the measured performance and MC expectations,
m!" [GeV]
ute an uncertainty of 0.1 % to 12.4 % (GGM), 1.7 %
% (SPS8) and 0.5 % to 1.5 % (UED). A systematic
ainty was also assigned to account for temporary
Figure 4: Expected and observed 95 % CL lower limits on the gluino
of the LAr calorimeter readout during part of the
mass as a function of the neutralino mass in the GGM model with
king period,
which was notなスペクトラムでの
modelled in the MC
Conventional
1TeV 付近までの領域の多くが excluded.
(&)*+,-./&&&&&&&&&$0-12+&&3&!"#$%&'
a bino-like lightest neutralino NLSP (the grey area indicates the
s. Electrons and photons were removed from the
region where the NLSP is the gluino, which is not considered here).
(&&&&&&&&&&&&$0-12+4.5-"#6&3&()"'*%&
The other sparticle masses are fixed to ∼ 1.5 TeV. Further model
d area, but jets, being larger objects, were not. Jet
parameters are tan β = 2 and cτNLSP < 0.1 mm. The previous
corrections were therefore applied. Varying these
ATLAS [1] and CMS [50] limits are also shown.
ions over their range of uncertainty results in sysc uncertainties of 1.0 %, 0.7 %, and 0.4 % for GGM,
and UED, respectively. Added in quadrature, the
in the signal region using the profile likelihood and CLs
ystematic uncertainty on the signal yield varies bemethod [51]. The result is 7.1 events at 95 % CL.
6.3 % and 15 % (GGM), 6.2 % and 15 % (SPS8) and
Further, 95 % CL upper limits on the cross sections of
nd 6.0 % (UED).
SUSY ＠ TeV
SUSY Search @ LHC
の制限&&)78!79&2+&0%:;+2/ mg~ [GeV]
ector, as described in Ref. [1], result in an uncerGGM: bino-like neutralino, tan% = 2, c$NLSP < 0.1 mm
1200
of 3.9 % for the GGM and SPS8 signals and 3.7 %
ATLAS CL s expected 95% CL limit
ATLAS
1100
UED signal. The uncertainty from the photon isoATLAS CL s observed 95% CL limit
± 1&
was estimated by varying the energy leakage and
1000
ATLAS CL s observed 95% CL limit (36 pb -1)
e-up corrections independently, resulting in an unCMS observed 95% CL limit (35 pb -1)
900
ty of 0.6 % for GGM and SPS8 and 0.5 % for UED.
800
fluence of pile-up on the signal efficiency, evaluated
Ldt = 1.07 fb-1
#
paring GGM/SPS8 (UED) MC samples with dif700
s = 7 TeV
pile-up configurations, leads to a systematic uncer600
of 1.3 %(1.6 %). Systematic uncertainties due to the
~
500
g NLSP
econstruction, estimated by varying the cluster enmiss
within established ranges and the ET
resolution
400
200
400
600
800
1000
1200
n the measured performance and MC expectations,
m!" [GeV]
ute an uncertainty of 0.1 % to 12.4 % (GGM), 1.7 %
% (SPS8) and 0.5 % to 1.5 % (UED). A systematic
ainty was also assigned to account for temporary
Figure 4: Expected and observed 95 % CL lower limits on the gluino
of the LAr calorimeter readout during part of the
mass as a function of the neutralino mass in the GGM model with
king period,
which was notなスペクトラムでの
modelled in the MC
Conventional
1TeV 付近までの領域の多くが excluded.
(&)*+,-./&&&&&&&&&$0-12+&&3&!"#$%&'
a bino-like lightest neutralino NLSP (the grey area indicates the
s. Electrons and photons were removed from the
region where the NLSP is the gluino, which is not considered here).
(&&&&&&&&&&&&$0-12+4.5-"#6&3&()"'*%&
The other sparticle masses are fixed to ∼ 1.5 TeV. Further model
d area, but jets, being larger objects, were not. Jet
parameters
are tan β = 2 and cτNLSP < 0.1 mm. The previous
corrections were therefore applied. Varying these
-1
[updated May 24th]
ATLAS [1] and CMS [50] limits are also shown.
ions over their range of uncertainty results in sysc uncertainties of 1.0 %, 0.7 %, and 0.4 % for GGM,
and UED, respectively. Added in quadrature, the
in the signal region using the profile likelihood and CLs
ystematic uncertainty on the signal yield varies bemethod [51]. The result is 7.1 events at 95 % CL.
6.3 % and 15 % (GGM), 6.2 % and 15 % (SPS8) and
Further, 95 % CL upper limits on the cross sections of
nd 6.0 % (UED).
4.71 fb Result!
SUSY ＠ TeV
SUSY Search @ LHC
!"#$だと 断面積 %&''()*+),ぐらいのゲイン （少し）)
-.-/012探索など 3 4*5+0)6)倍 （大きく効く） 7#8)9:;(&<())今年も注目。 もう少しで見つかることを期待…
ただし、Higgs 125GeV が本当の場合、conventional な model / parameter
space ではないことが起こっていると考えられる。
Higgs 125GeV を実現する方法と照らし合わせて考えて行く必要がある。
SUSY-Higgs group のトーク
ass, mH also
includes
the softsee
mass
the Here
HiggsΛfield
coupled
theatup-type
current
discussion),
e.g.of[49].
denotes
the to
scale
which SUSY breaking effects
Naturalness
がやっぱり気になる…
. Whetherare
the
soft mass
down-type
Higgs,
soft terms inm2Q3 , m2u3 and At control
mediated
to for
thethe
Supersymmetric
SM. m
Since
theother
soft parameters
Hd , or
Higgs sector,
should
be as light
and mHu isthe
instead
a model-dependent
the stop
spectrum,
as itas
is µ
well-known,
requirement
of a natural Higgs potential sets an
Naturalness conditions
d a heavierupper
mHd bound
can even
to improvements
[48]. The one
key has
observation that
on lead
the stop
masses. In particular
�−1/2
� must be light
�
� � −1 �−1/2
or SUSY collider
higgsinos
because
their
� phenomenology is that sin
β
log (Λ/ TeV)
mh
∆
2
2 <
mt̃1 + mt̃2 ∼ 600 GeV
,
tly controlled by µ,
(1 + x2t )1/2
3
120 GeV
20%
�
�
(6)
�
−1/2
� 2 + m2 .�Eq. −1
where xt = At / m
6
imposes
a bound on the heaviest stop mass. Moreover,
m
∆
h t̃2
t̃1
<
µ ∼ 200 GeV
(4)
120
GeV
20%
for a fixed Higgs boson mass, a hierarchical stop spectrum induced by a large off-diagonal
term At tend to worsen the fine-tuning due to the direct presence of At in the r.h.s. of eq. 5.
forward to extend this discussion to include SM singlets that receive vevs, see for example [35].
where the µ-term
generated
the vev of
some other field,
is generically
Allisthe
other by
radiative
contributions
to its
theeffective
Higgs size
potential
from the other SM particles
of the order of the electroweak scale by naturalness arguments. For a proof in the NMSSM
pose much weaker bounds
on theStop
supersymmetric
spectrum. The only exception is the
1. Light
/ Light Higgsino
].
gluino, which induces a large correction to the top squark masses at 1-loop and therefore
2. Degenerate
spectrum
feeds into the Higgs potential
at two loops.SUSY
One finds,
in the LL approximation,
8
δm2Hu |gluino
�
�
2
αs
= − 2 yt2
|M3 |2 log2
π
π
�
Λ
TeV
�
,
(7)
where M3 is the gluino mass and we have neglected the mixed At M3 contributions that can
be relevant for large A-terms. From the previous equation, the gluino mass is bounded from
above by naturalness to satisfy,
�
log (Λ/ TeV)
<
M3 ∼ 900 GeV sin β
3
�−1 �
mh
120 GeV
��
−1
∆
20%
�−1/2
.
(8)
(1 + xt )
3
120 GeV
20%
�
Light
Stop
Building
where xt = At / m2Model
+ m2 . Eq.
6 imposes a bound on the heaviest stop mass.
t̃1
t̃2
Moreover,
for a fixed Higgs boson mass, a hierarchical stop spectrum induced by a large off-diagonal
今日のルール
term A tend to worsen the fine-tuning due to the direct presence of A
t
t
in the r.h.s. of eq. 5.
All the other radiative contributions to the Higgs potential from the other SM particles
1. Stop mass2 に複数の起源があって cancel させる模型は考えない
pose much weaker bounds on the supersymmetric spectrum. The only exception is the
( light stop tuning! )
gluino, which induces a large correction to the top squark masses at 1-loop and therefore
feeds into the Higgs potential at two loops. One finds, in the LL approximation,
� �
�
�
→ stop だけ違う性質（対称性、余剰次元中の局在性など）
2
α
Λ
δm2Hu |gluino = −
を持ってるはず
π
2
y
t
2
s
π
|M3 |2 log2
TeV
,
(7)
where M3 is the gluino mass and we have neglected the mixed At M3 contributions that can
be relevant
for large
the previous
equation, the gluino mass is bounded from
2. Gluino
massA-terms.
からのFrom
fine-tuning
にも注意する
above by naturalness to satisfy,
�
< 900 GeV sin β log (Λ/ TeV)
M3 ∼
3
�−1 �
mh
120 GeV
��
−1
∆
20%
�−1/2
.
(8)
In the case of Dirac gauginos [50] there is only one power of the logarithm4 in Eq. 7, amelio4
→ Low Scale Mediation が Favored
The other logarithm is traded for a logarithm of the ratio of soft masses. We assume that the new log is
O(1), but in principle it can be tuned to provide further suppression.
9
Light Stop I : anomalous U(1) model (Nakano, Ozeki and Watanabe ’99)
Anomalous U(1) symmetry
ex) charge assignment
Anomalous U(1) symmetry
U(1)
Φ
-1
Q1
q
Q2
q
Q3
0
→ Non-vanishing FI-term
ξ ~ O(1/10) x MPL
VU(1) = g2/2 ( ξ2 - |Φ|2 + q |Q1|2 +....)2
motivated by unsuppressed yt
W = yt <Φ>0HuQ3T3
Vsoft = mΦ2 |Φ|2
< ξ2
- |Φ|2 > = mΦ2
V
1, 2 世代だけ重く出来る
ΔmQ1,22 = g2 q mΦ2
後は gluino が 1TeV になる程度の Gauge Mediation 等と
o
o
0
2
ξ
2
|φ|
組み合わせれば出来上がり！
Light Stop 2 : Flavored Mediation
Gauged Flavor symmetry を使った Gauge Mediation 効果
Squark たちに新しい soft mass
GMSB by SM gauge.
+
GMSB by SU(2) gauged flavor sym.
1,2世代 squark だけ重い！
2
mSM
2
＋ mf lavor
例) Craig, McCullough and Thaler (2012.Jan)
SU(3)F
m2q1,2
SU(2) F
第３世代の
m2q3
第３世代のmassを担うgauge bosonが
massive ( m2V )に
2
mf lavor
→0
the top quark and the Higgs; and the constraints of naturalness, we charge the third
Dimopoulos, Gherghetta, 1203.0572
tion chiral superfields and Hu , Hd under GA , while charging the first two Craig,
generations
GB . The model is shown schematically in Fig. 1.
lavor
Light Stop 3 : Split family
1,2 世代への GMSB
Hu,Hd
�χ� ∼ 10TeV
101,51
GA
GB
103,53
GA × GB → GSM
102,52
1.0
Figure 1: The deconstructed model.
145
135
GMSB by GB gauge sym.
140
0.8
-group locality determines the structure of both fermionic and sfermionic flavor.
2
2
only the third generation superfields and the Higgs multiplets are charged under
1,2
3
0.6
nly the Yukawa interactions of the third generation are marginal operators. Yukawa
ngs involving fields of the first two generations may arise via irrelevant operators
nsertions of the link field vevs, as discussed in detail in [17] (see also [21]). Such
ant operators arise from integrating out massive matter at the scale M∗ ∼ M . 0.4
rucially, the matter representations required by a complete theory of flavor have
implications for the prospects of gauge coupling unification. First, consider the
m̃
� m̃
�
Stopを軽く出来る
130
125
Bonus: Extra D-termの寄与
0.2
act, important contributions arise at both two and three loops; as we will discuss below, the threentributions dominate when �χ�/M < 4π, as is typically the case here.
Higgsを重く出来る
110
105
115
0.0
200
–4–
120
400
600
m�t �GeV�
800
1000
Figure 3: The lightest Higgs mass as a function of mt̃ and ∆ (for ∆� = ∆), including D-term an
two-loop radiative corrections computed in FeynHiggs [24]. The blue region is excluded by curren
Light Stop 4 : Extra Dimension
Larsen, Nomura & Roberts; cf. N.Okada & T.Yamada
SUSY bulk RS model + SUSY breaking @UV brane
H,t はIR brane付近，
３世代目だけ軽い！
SUSY Breaking
W/Z in the bulk
他はUV brane付近
SUSY br. ＠UV brane ＋gaugino med.（？）
Warped XD: high scale ΛSUSY
low scale Λcomp 微妙なことは背景計量へ？
（Finite threshold corrections…） Light Stop 5: Strong Interaction
(Fukushima Kitano,Yamaguchi 11, Csaki, Randall, Terning ‘12)
CFT でも来そう！
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q = Q3 , H, Hd
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Light Stop q5:=Strong
(Fukushima Kitano,(3.5)
Yamaguchi 11, Csaki, Randall,
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q̄ = X, H̄, Hu
q̄ = X, H̄, Hu
Other Yukawa couplings
From
the q, q̄ charge
assignments
it follows
that thethe
meson
M contains
rge assignments
it follows
that the meson
M contains
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t, the right-handed t,
the
singlets
S andHiggses
P , two Φadditional
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transforming
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under
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nded
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
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V
U
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V
U
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- - - (3.6)
M =  E G + P Mφu= E G + P φu [Q
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R
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[Q1Q2Q4Q5]BR
Hd
arks,
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Y
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1
6
H, H̄ Hu Hd
0
1
2
Y
1
6
1
6
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0
Y
U
6
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1 3 H,
1 H̄ H1u H2d
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1
6
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6
1
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一応 Yukawa を Higher dimensional operator で書ける
Running で持ち上げる予定？
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the Light
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the
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11,
Csaki,
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AN/(F
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)
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in
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section
we
will
choose
Nwill
=
4not
and
F = SUSY
6.
n
composite
theory,
”magnetic”
transform
under
thewell.
dual
gauge
SU
(F
−N
)(2.12)
q→
e statesbreaking
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type
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the
singlet
obtain
breaking terms. How
which
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eanthe
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θ
compoWe can
alsodual
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spurions
in assumed
the composite
description
the structure
of
e group,
and
include
meson
and
q, q̄.
Due
the
operator
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−N
)quarks
gauge
mediation
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to
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above thesince
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The
leading
contribution
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soft
masses
are
controlled
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The
effects
of thethe
soft
breaking
for
thetoelementary
fields
are
incorporated
q̄SUSY
→MeAN/(F
q̄ terms
(2.13)
2 including
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−8π
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F axial
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is
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the
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N spurions
F −Nlog
2A
nto the
Lagrangian
by
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the
and
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Z
and
U
with
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θ
compo=
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θ̄ ) − U (1).
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θ θ̄ . axial
QQ̄ (Arkani-Hamed,
↔ Mmetry.
,
Q
↔eq words
, . Zwith
Q̄
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‘98)
M
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M
(2.14)
�
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In
other
and
U
are
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all
will
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for
it.
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fermionic par
µ
bg
bg
b
�
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ents
[14–17]:
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†
V
†
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α
where
the
rotation
parameter
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to a chiral
we have
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singlino)
ish.c.
model
dependent.
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can besuperfield
a singlinoA,
mass
from n
θ
Q
Ze
Q
+
Q̄
Ze
Q̄
+
d
θ
U
W
W
+
µ
Q̄Q
+
.
(2.3)
α
f
ave
the
following
axial
transformations
for
the
composite
states:
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This Λterms
theforinvariant
scale an
that
can
dimensional analysis once
al composite� theory
is in the weakly coupled
phase
we
write
approximately
thecan
elementary
fields
(Q̄6be
Q6used
)2 /ΛUfor
V giving a singlino mass of ord
�
�
�
�
A
4
†
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†
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e
Q̄
→
e
Q̄
(2.7)
AN/(F
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)
ähler potential.
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and
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L = d θ Requiring
Q Ze Qq +
Q̄e Zeand
Q̄ qaxial
+ There
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+
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.
(2.3)
αa+
f Q̄Qmass
be
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→
(2.12)
a soft squark mass mU V , a gaugino massInm
,
and
a
soft-breaking
B
term
†
λ
−A−A
2F/b
A
the
composite
theory,
”magnetic”
the dual
gau
AN/(F −N )
Z quite
→ e small.
,We
Λhnot
→
e states
Λhtransform
(2.8)
find
the
dual
Lagrangian
typically
will
be
making
a definite under
assumption
on
the
q̄
→
e
q̄
(2.13)
∼ B) we Taylor expand the spurionsgauge
in superspace
coordinates:
group,
and
includespectra
the �meson
M and
dual
quarks
q, q̄.
Duefor
to it.
the op
but mass
explore
both
with
small
and
sizeable
values
2AU V , a mass,
�
To introduce
a
soft
squark
mass
m
gaugino
m
,
and
a
soft-breaking
B
term
λ
M†→N/(F
etoM
.) Ṽ
(2.14)
�
It
is
convenient
introduce
a
redundant
scale
that
is
invariant
under
transformations
†
2
−N
†
N/(F
−N
)
Ṽ Bµ
Note
that
the
usual
problem
is simply
notaxial
present,
since
the poten
2
2
2
2
2
2
2
2
M
M
q θZ
e− qspurions
q̄) Z in superspace
e q̄
N
F −N
N
F −N
with mUZV ∼=mλ41 ∼
B)BZ
we
Taylor
expand
the
coordinates:
−
θ
−
θ̄
B
−
θ̄
(m
|B|
(2.4)
QQ̄ ↔ terms,
M , both
Q of↔which
q
, induced
Q̄ ↔asq̄ described in
U V trilinear
L =
d θ theory2is in the
+ weakly
+ we
and
tadpole
are
(4N
−2F
)/(F
−N
)
(4N
−2F
)/(F
−N
)
†
e the dual composite
coupled
phase
can
write
an
approximately
2
ΛθY M
Λ2 mλ 2
Λ
1
= Λhas
Z 2F/b
Λhin NMSSM-type models, an issue similar
(2.9) to
2 µ-problem
2 2 isΛ2solved
2usual
nical Kähler
Requiring
SUSY
and
axial
invariance
and
using
dimensional
U =potential.
−
i
+
θ
,
(2.5)
Z 2= 1 −2θ Bwe−have
θ̄ B the
− θfollowing
− |B|transformations
)
(2.4)
�θ̄ (mU V axial
for the composite
states:
� 2g 2 � 16π
g
why
the
parameter
f
is
close
to
the
electroweak
scale,
which
as we discus
ysis we find the dual
Lagrangian
y
M
q
q̄
1
θY M to be2 m
α�
λ
�
addressed
model
SUSY breaking.
+ d2 θ �U W
W
+
+
µ
M
+
h.c.with�a5more complete
(2.15)
AN/(F
−N of
) (2.5)
U
=
−
i
+
θ
,
α
f
b/(F
−N
)
→e
q
2
2
2 to be confused withq the
2g
16π
g
so included the �CP violating
θ
† 2 parameter
† N/(F
−N
) M
Ṽ (not
† message
N/(F −N ) from
Ṽ
Λ
The
the
general
discussion
of Section 2 is that soft b
Y
M Z M
q Zh
e q q̄ Z
e q̄
4
AN/(F −N )
L spurion
=
d θU is related
+ to(4Nthe
+ (4N −2F
q̄compared
→e
q̄ of the elementary field
the
are
suppressed
to those
nate). The
holomorphic
strong
Λh which
2
−2F )/(F
−N
) composites
)/(F
−Nscale
)
Λ
Λ
Λ
we soft
have
alsothat
included
the
CP
violating
parameter
θYfor
(notcomposites
toWe
bechoose
confused
2A with the
M the
tadpole
T
is
unsuppressed.
parameters
dhere
off the
masses
near
the
infrared
fixed
point
[16,17]
from
M
→
e
M . consistent with the hie
�
�
uperfield
spurion
is
also
an
RG
invariant:
�
uperspace
coordinate).
Theinspurion
the holomorphic
scalesection
Λh which
yUMisq q̄related
in the to
previous
explained in strong
the previous
of order
2
α�
term by Taylor
expanding
superspace:
�
+ d θ U −16π
W W
+
+
µ
M
+
h.c.
(2.15)
2U
α(µ)/b b/(F −N )
f
cts as a chiral superfield
that
is
also
an
RGcomposite
invariant:
Since
the
dual
theory
in(2.6)
the∼weakly
coupled phase we can write an
Λh = µ spurion
e
Λh
melis∼
M
few · TeV
3
3N − 2F 2
3N
− 2F potential.
canonical
Kähler
Requiring SUSY and axial invariance and usi
2
2
2
2 U (µ)/b
−16π
Λ ∼ 5 − 10 TeV
m
= soft
2 masses near
mU Vthe, infrared
m
=
−
m
(2.16)
M
q
U
V
Λ
=
µ
e
(2.6)
can
read
off
the
fixed
point
[16,17]
for
the
composites
from
h
analysis
we
find
the
dual
Lagrangian
e-loop β-function coefficient
b
=
3N
−
F
and
µ
is
the
RG
scale.
In
the
b
b
m2el
Kähler
Taylorwe
expanding
in superspace:
∼ M1 ∼ M2 ∼ A ∼ few · 100 GeV �
�mcomp ∼
n the term
next by
section
will choose
N = 4 and F = 6.
�
Λ
2 or
†scale.
N/(F −N
Ṽ
† N/(F −N ) Ṽ
here bresults
is2 the spell
one-loop
β-function
coefficient
b =some
3N −ofFthe
and
µM
is† Zthe
RGmeson
In) ethe
these
trouble
for
composite
models:
dual
quark
M
q
Z
q
q̄
Z
e q̄
4
nclude
these
spurions
in
the
composite
description
since
the
structure
of
f
∼
100
GeV
m
of
composites
are
vanishing
for
F
=
3/2
N!
3N
−
2F
3N
−
2F
IR
L
=
d
θ
+
+
2
model
presented
the
next section
wem
will
choose apply
Nm
=2U4V for
andthe
F =entire
6.Λ22 (2.16)
(4N −2F )/(F −N )
(4N −2F )/(F −N )
m2M in
= be
2 tachyonic,
m2U V , and
=−
ng
masses
should
this
would
multiplet.
Λ
Λ
q
3
7
eory [up
is constrained
symmetries
including an anomalous
axial TU (1)
4by
2b) correction...]
b
∼ f symmel ∼ few · 10 GeV
to
O(m
/Λ
�
We
can
also
include
these
spurions
in
the
composite
description
since
the
structure of �
r the case
when
F =also
3N/2,
that isofatthe
theanomalous
lower end axial
of theUconformal
window
these
� Under
words
Z
and
U
are
spurions
(1).
axial
F ∼or
few
· TeV
yUM
q q̄ symerically
these
results
spell
trouble
for
composite
models:
some
of
the
dual
quark
meson
2
α
he
low-energy
theory
is
constrained
by
symmetries
including
an
anomalous
axial
(1)
�
�
ulable
terms
vanish.
This
is
exactly
the
right
region
for
the
model
considered
+ d A,
θ we
U Whave
Wα + b/(F −N ) + µf M + h.c.
Stops
and
Higgs
can
be light!
where
themasses
rotation
parameter
is
promoted
to
a chiral
superfield
µ
=
y�S�
∼ AΛ
breaking
should
be
tachyonic,
and
this
would
apply
for
the
entire
multiplet.
eff
metry.
In (F
other
Z 6).
and U
spurions
of the terms
anomalous
axial U
(1).
Under
axial
s paper
= words
4, N =
In are
thisalso
case
the leading
will come
from
the
h
ever, for the case when F
= 3N/2, that is at
the lower end of the conformal tan
window
βsuperfield
∼ these
O(1)
A
A
ansformations,
where
the
rotation
parameter
is
promoted
to
a
chiral
A, we have
mngincalculable
(2.2) corresponding
to
the
fact
that
we
do
not
run
all
the
way
to
µ
=
0
but
Q
→
e
Q
,
Q̄
→
e
Q̄
(2.7)
terms vanish. This is exactly
region
themasses
model near
considered
Wethe
canright
read
offmthefor
soft
the
fixed
point
[16,17]
for gener
the c
2
2
4 breaking
2 infrared
Here
includes
the
soft
scalar
masses
of
the
first
two
†
el
ale
by (2.2)
∼
soAthe
that
the
corrections
are
(mUfrom
) superspace:
which
−A−A
A leading
in given
this paper
(F→
=µe4,
Nm
= U,6).
case
the
terms
willO
come
the
Aby
V µ/Λ,
V /Λ
term
Taylor
expanding
in
Z
Λthis
e2F/b
Λ
(2.8)
he→
h
QIn→
Q
, Kähler
Q̄
→
e
Q̄
right handed sbottom, b̃ and all sleptons, while(2.7)
m
includes m
an
ple, while the fields E, X will pair together to obtain a mass from the
quarks, right handed bottom and all leptons) are assumed to be elementary fields transformmental
H.
The
standard
(first Kitano,
two
generation
Light
Stopremaining
5: (3)
Strong
(Fukushima
Yamaguchi
Randall, Terning
‘12)
ing under
SU
(2)el × Umodel
(1)Y . fields
This
charge
assignment
will 11,
be Csaki,
automatically
anomaly
c × SUInteraction
bottomfree,
and and
all leptons)
areofassumed
to be
transformis capable
producing
theelementary
usual flavorfields
structure
and CKM mixing matrix.
U (2)el × U The
(1)Y .relevant
This charge
assignment
will be automatically
anomaly
part
of
the
superpotential
(3.3)
together
with the singlet tadpoles from (3.8)
Interesting
bonus
producing
the usual
flavorasstructure and CKM mixing matrix.
can then
be written
of the superpotential (3.3) together with the singlet tadpoles from (3.8)
s
W ⊃ yP (HH̄ − F 2 ) + yS(Hu Hd − f 2 ) + yQ3 Hu t̄ + yHu Hφu + yHd H̄φd .
(3.9)
2
− F 2) +
yS(H
−
f
)responsible
+ yQ3 Hu t̄ for
+ yH
. el × SU
(3.9)
The
firstu H
term
is
theu Hφ
breaking
SUd(2)
(2)mag to the diagonal group,
d
u + yHof
d H̄φ
the second term will trigger electroweak symmetry breaking, the third will give rise to the
onsibletfor
the breaking
SU the
(2)ellast
× SU
(2)terms
the rise
diagonal
group, of the Higgs with a heavy
mag togive
Yukawa
couplingofand
two
to a mixing
trigger Higgs
electroweak
symmetry
the third
will give
rise below
to thethe scale F (and assuming
φu,d . At
this pointbreaking,
the low-energy
effective
theory
d the last
to NMSSM
a mixingwith
of the
Higgs with
a heavy
that two
F �terms
f ) is give
that rise
of the
a composite
Higgs,
Q3 and t. As explained above
oint thethelow-energy
theoryare
below
the scale
(and assuming
rest of theeffective
SM particles
assumed
to beF elementary,
that is made of fields that do
Higgs
Masscoupled
be
upsimply
byabove
SHcarry
uHd the usual SM quantum
f the NMSSM
with aunder
composite
Higgs,
Qcan
t. raised
As
not transform
the
strongly
SU
(4).explained
They
3 and
articlesnumbers
are assumed
that
is Ymade
of fields that do
underto
SUbe
(2)elementary,
U (1)
.
el × SU (3)c ×
he strongly
SU (4).there
They
carry
usual the
SM
quantum
Atcoupled
high energies
aresimply
three sets
ofthe
Higgses:
composite
Hu,d from the dual quarks
2
2
†
2
Vh = SU
y /4
sin, 2β
( H H ) φ from the mesons transform×
SU
(3)
×
U
(1)
.
transforming
under
the
composite
(2)
the
composite
el
c
Y
mag
u,d
here areing
three
setsthe
of elementary
Higgses: theSU
composite
the dual quarks
under
(2)el , andHau,d
setfrom
of elementary
Higgses φ�u,d transforming under
the elementary
(2)composite
fields
need
to
be transformpresent
to remove φu,d from the spece composite
SU (2)magSU
, the
φu,d from
the
mesons
el . 2These latter
2
2
2
2
(v=174GeV)
mh = mh(MSSM)
y transforming
sinafter
2β duality
v under
superpotential
term,+
which
maps into a mass term. The
ary SUtrum
(2)el ,via
anda atrilinear
set of elementary
Higgses
φ�u,d
�
elementary
Higgses
also
have ordinary
Yukawa
couplings
with the light elementary SM
latter fields
needφto
present
to remove
φu,d from
the specel . These
u,d be
matter fields
addition
their mass
, After
integrating
out φu,d , φ�u,d effective
uperpotential
term, in
which
after to
duality
maps with
into aφu,d
mass
term.
The
Yukawa couplings between the remaining light composite Higgses Hu,d and the light SM
u,d also have ordinary Yukawa couplings with the light elementary SM
are with
generated.
For more
details see
ion tofermions
their mass
φu,d , After
integrating
out[11].
φu,dThe
, φ�u,dresulting
effectivetheory of the Higgses in the
potential
the necessary
couplings
andSM
as we will now see it also has
tween low
the energy
remaining
light has
composite
HiggsesYukawa
Hu,d and
the light
viable
and interesting
potential.
d. For amore
details
see [11]. The
resulting theory of the Higgses in the
has the necessary Yukawa couplings and as we will now see it also has
Light Stop 5: Strong Interaction
(Fukushima Kitano,Yamaguchi 11, Csaki, Randall, Terning ‘12)
!"##!$%&'()*+,-.%/0')1-,
gluino mass ~ 1.5 TeV
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Heavy First Two Generations
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nmatter, Hd, Hu = 0, 0.5, 1
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89!
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コメント : これらの例の様な縮退スペクトルはなかなか難しい
縮退させると Radiative EWSB が難しい → μ-term が小さく出易い
→ Higgsino が軽すぎて縮退 spectrum でなくなりがち
全体が軽すぎると b→s+γ 等で excluded.
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rpotential includes three Rp violating terms each parametrized by the Yukawa
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WR/p = is λ
ijk Li L j Ēk + λijk Li Q j D̄k +
ijk Ūi D̄ j D̄k ,
2
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er violating processes induced by the R-parity breaking couplings
k are generation
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Ē,
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SU
(
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)
re sufficiently
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The bound is roughly given 2000
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[3]Preliminary
L = 2.1 fb , s = 7 TeV L
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Not to wash
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2000
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lds. The third term violates baryon-number conservation, while the first and
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re lepton-number
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ijk � = 0
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1200
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600
800
1000
1200
1400
1600
1800
600
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600
800
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1600
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conserved
i for each lepton flavor is separatelyCMS
L = 2.1 fb , s = 7 TeV
Preliminary
odels is the bino. Values of λijk considered in this analysis correspond to decay
s. (Here, B denotes the baryon number and Li is the lepton flavor
m. Our results are independent
of the decay length.!
!
−7
!
ration.) For instance, if λ1jk ! 10
1800
1400
600
s = 7 TeV
int
m~g (GeV/c2)
m~g (GeV/c2)
int
s = 7 TeV
1400
1200
on λ is set by constraints from neutrino-mass values. We choose values for
give prompt decay and are consistent with neutrino mass values. In this paper
or
is notindices
conserved
in generic SUSY
of the mixings
in
ration
corresponding
to e,models
µ, andbecause
τ are sometimes
denoted
by 1, 2, and
Missing ET search
is no more optimal...
es. These slepton
mixings can then erase the asymmetry between the
( = the LSP is no more DM candidate)
m (GeV/c )
m (GeV/c )
est
SUSY
amongproduction
the superpartners
of the standard
particles. If
ns allow particle
for single
of SUSY
particlesmodel
(sparticles)
and for sparticle
s the LOSP. If not, LSP is the LOSP.
Figure
2: 95% C.L.
limitsresults
for RPV in
couplings
particles
only. The decay of the lightest SUSY
particle
(LSP)
extraλ122 , λ123 , λ233 and Hadronic-RPV scenarios as
a function of the squark and gluino masses for a SUSY topology described in the text. The
Leptonic
: multilepton
final state
o their
cleanRPV
final-state
multilepton
signatures,
processes with single-slepton
observed limits, along with limits expected in the absence of signal are shown, along with the
owed by decay to a 2pair of SM charged leptons
are promising
searchMasses
channels
uncertainty
in the expectation.
to the left of the curves are excluded. For the H-RPV
Hadronic RPV : a lot of jets
scenario gluino masses below ∼ 500 GeV/c2 are allowed for reasons explained in the text. The
particles [3]. Prior searches for RPV interactions
include those by the CDF and
previous limit on λ122 , obtained with 35 pb−1 , is shown as a dotted line on the left plot.
ents at the Tevatron [5, 6], which were recently superseded by the Compact
(CMS) experiment at Large Hadron Collider (LHC) using 35 pb−1 of integrated
SUSY が見えない場合でも H-PRV はしぶとく生き残りそう…
n 10−7ijk
.
1400
1200
1000
800
1000
95% C.L. Limits:
NLO observed: !233
NLO expected: !233
NLO expected ± 1"
NLO expected ± 2"
95% C.L. Limits:
NLO observed: HadronicRPV
800
NLO expected: HadronicRPV
NLO expected ± 1!
600
600
600
800
1000
1200
1400
1600
1800
~
q
2000
2
600
800
1000
1200
1400
1600
~
q
R
2
1800
Current Status of SUSY models
squark
mass
SUSY
higher
than
100TeV
DM ??
wino<3TeV
Higgsino
<2TeV
10-100TeV
DM ??
wino<3TeV
Higgsino
<2TeV
Higgs
Naturalness
GUT
10 years from now?
備考
現段階で Higgs mass への制限か
much heavier
than 125GeV
何それ？
Gaugino が TeV scale なら
ら less favored.
もはや SUSY じゃな
unification は OK
もし stopping gluino なんかが見
い？
つかったら大騒ぎ。
125GeV
in MSSM
何それ？
Gaugino が TeV scale なら
unification は OK
Gaugino searches.
Cosmic ray?
High energy model は
シンプル。やれるこ
とが少ないかも
もっと意外なことが起こっていてももちろん
素敵な
1%で済む領域が
TeV
Light Stop,
Higgsino
焦らずもう少し
残っているか？
something
or
low scale
Large A-term mediation が有利
Happy...
待ちましょう
まずは gluino 1TeV
素敵な
得に問題無い
いわゆる SUSY search で少し
g-2 はまだ説明可
づつ削られて行く
能！
最終的には 10TeV scenario に
Higgs グループにおま
合流?
かせ
stop を軽くする際の
Two-loop を考える
まずは
8TeV
something
stop direct production では何 fine-tuning に注意。
-1
15fb で何かが見えることを
以下での軽い stop
と gluino は 1TeV 以
search!
Same Sign Muon ?
下でないと O(10)%
Model Dependent...
処まで行けるか？
は難しそう
能！
期待しましょう
縮退 ?
LHC search
での穴
素敵な
something
LHC で見つか
らないように
番外色々？
もっと手の込ん
だ模型？
素敵な
something?
TeV 以内で見つかれ
ば文句無し？
基本的に gaugino の GUT
せ？
ISR jet で何処までいけるか？
relation は邪魔。
ISR photon とか？
例外) Mirage Mediation
soft lepton とか？
見やすくて意外な模型なら
Little Higgs とか他の
模型との組み合わ
g-2 はまだ説明可
Dual Unification とか？
Welcome!
SUSY を隠す模型を作り続け
る人が出てくるか？
縮退を実現する High
energy model はほとん
どない。
大穴の一つ？