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Desperately Seeking SUSY
Ben Allanacha (University of Cambridge)
Please ask questions while I’m talking
a BCA,
Outlook in Particle Physics, KCL, 2012
Gripaios, 1202.6616; BCA, Sridhar 1205.5170
B.C. Allanach – p
Supersymmetric Copies
H
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Supersymmetric Copies
H ×2
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H̃ × 2
B.C. Allanach – p
Review of R-Parity
The superpotential of the MSSM can be seperated
into two parts:
W Rp = heij Li H1 Ēj + hdij Qi H1 D̄j
W 6RP
+huij Qi H2 Ūj + µH1 H2 ,
1
= λijk Li Lj Ēk + λ′ijk Li Qj D̄k
2
1 ′′
+ λijk Ūi D̄j D̄k + κi Li H2 .
2
W Rp is what is usually meant by the MSSM.
Q: Why ban W 6RP ?
A: “Proton decay”
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Definition of R-Parity
Q: How is W 6RP normally banned?
A: By defining discrete symmetry Rp
Rp = (−1)3B+L+2S .
→ SM fields have Rp = +1 and superpartners have
Rp = −1. There are two important consequences:
• Because initial states in colliders are Rp EVEN,
we can only pair produce SUSY particles
• The lightest superpartner is stable
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Candidate Event: High ET (j)
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Natural SUSY
The particles coupling the most strongly to the higgs
are the stopsa . Minimising the MSSM Higgs potential,
MZ2
≈ |µ|2 + m2H2 ,
−
2
2
−3ht 2
ΛU V
2
mt̃ ln
δmH2 ≈
2
4π
mt̃
t̃
H2
a
H2
H2
t̃
g̃
H2
H2
t̃
H2
M. Papucci, J. T. Ruderman and A. Weiler, arXiv:1110.6926;
C. Brust, A. Katz, S. Lawrence and R. Sundrum, arXiv:1110.6670
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Natural SUSY
The particles coupling the most strongly to the higgs
are the stopsa . Minimising the MSSM Higgs potential,
MZ2
≈ |µ|2 + m2H2 ,
−
2
2
−3ht 2
ΛU V
2
mt̃ ln
δmH2 ≈
2
4π
mt̃
No cancellation⇒
<
<
mt̃ ∼ 700 GeV,
mg̃ ∼ 1000 GeV.
Experimental E
6 T searches⇒
mt̃ > 500 GeV,
mg̃ > 900 GeV.
a
M. Papucci, J. T. Ruderman and A. Weiler, arXiv:1110.6926;
C. Brust, A. Katz, S. Lawrence and R. Sundrum, arXiv:1110.6670
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g̃ t̃: E
6 T > 50/120 GeV, Nb ≥ 2,
#j ≥ 2, HT > 320 GeV
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Direct Stop Seach
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Jets Plus E
6 T Search
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Bottom Up Implications of 2012
Data
Naturalness is under pressure. Ways to get around it:
• First two generation squarks > 1.8 TeV,
mt̃ = 0.5 − 0.7 TeV, mg̃ = 0.9 − 1 TeV,
mχ01 < 0.5 TeV. Ruled out soon?
•
Compressed spectraa : ISR monojets/6E T searches
give you mg̃ > 500 GeV only.
•
RPV decreases/removes the E
6 T b.
• Explains why natural SUSY hasn’t been
found yet
• Like-sign dileptons is a generic signature, as
we’ll see
a
Dreiner, Kramer, Tattersall arxiv:1207.1613
b BCA, Gripaios arXiv:1202.6616
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RPV and Dark Matter
If one gives up R−parity, χ01 is no longer a good dark
matter candidate, since it decays. One then has to
have something else, eg:
• Gravitino - still decays, but lifetime may be much
longer than the age of the universe
• Hidden sector matter
• Axion/axino
The implications of each of these is that (in-)direct
dark matter searches shouldn’t find anything.
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Upper Bounds on
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′′
λijk
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Bottom up thinking
We are not assuming
• MSSM: don’t put higgs constraints - there might
be higher dimension operators coming from
heavier fields.
• Some specific (or even generic) string model.
• We only put in the particles important for our
analysis. Others may be decoupled, or light: it
shouldn’t matter.
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Gluino/stop
LHC7
1e+06
100000
production
at
gluino
stop
σprod
NLO
/pb
10000
1000
100
10
1
0.1
0.01
0.001
100 200 300 400 500 600 700 800 900 1000
mass/GeV
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Gluinos With Rp Violation
•
•
•
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We assume lightish g̃, t̃R . If one has lepton
number violating LLE or LH1 operators, the
gluinos decay producing various leptons. These
cases ought to be easy to find, and are good
candidates for searches. Get same-sign leptons.
With LQD operators, the stops will again decay
into leptons, easy to see. Flavour constraints
imply that L3 QD operators are likely to be the
largest. Get same-sign leptons in ∼ 79 of g̃g̃
events.
With U DD operators, the (right-handed) top
decays direcly into jets.
B.C. Allanach – p
Baryon Number Violating Example
t
g̃
b
dj
t̃∗
dj
t̃∗
g̃
t
Can lead to natural SUSY
with light stops and
gluinos that hasn’t been
excluded yet. A difficult
casea : W ⊃ λ′′ijk Ui Dj Dk .
a BCA
and Ben
arXiv:1202.6616
Gripaios,
b
g̃g̃ production dominates. Here, you can look for
like-sign di-leptons since gluinos decay into t and t̄
with equal branching ratios.
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Other Light States
How robust is the same-sign dilepton signature in the
case that other states are also light?
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Can we avoid SS dileptons?
•
For mH ± > mt + mb , H + → tb̄ dominates,
which again will yield same-sign dileptons.
•
H + → τ + ντ is also OK, since we’ll get like-sign
di-taus.
Only fly in the ointment comes from Fig. 1c:
when H + → cb̄ (but only happens when
tan β ≪ mt Vcb/mτ ∼ 3, which seems unlikely).
•
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Same-sign E
6 T Limits
CMSSll1a : HT > 400 GeV, |6E T | > 120 GeV
a CMS-PAS-SUS-010;
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ATLAS-CONF-2012-004
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AF B in the Standard Model
1.96 TeV pp̄ collisions at the Tevatron.
AF B
N (c > 0) − N (c < 0)
, c = cos θ.
=
N (c > 0) + N (c < 0)
SM Prediction: 0.066.
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Measurements of AF B
S Leone (CDF) talk at Electroweak session of Rencontres de Moriond
2012.
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Other Constraints
σtLHC7
= 173.4 ± 10.6 pb,
t̄
y
AC
σtSM
= 163 ± 10 pb
t̄
N (|yt | > |yt̄ |) − N (|yt̄ | > |yt |)
= −0.015±0.04,
=
N (|yt | > |yt̄ |) + N (|yt̄ | > |yt |)
where yi = 1/2 ln(Ei − pi z )/(Ei + pi z ) is the rapidity
SM
= 0.006 ± 0.002.
of particle i. AyC
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∆AF B
Many models of random particles have been
proposed, but most don’t fit all the data. However, this
one does:
λ′′313
tR dR bR
W =
2
λ′′ ∗313
dR (p1 ) tR (q1 )
b̃R
dR (p2 ) tR (q2 )
λ′′313
Figure 1: SUSY contribution to AF B a
a BCA,
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Sridhar arXiv:1205.5170
B.C. Allanach – p
New Physics Contribution
"
(βc − 1)
|λ′′313 |4 βŝ
d∆σ
=
dc
384π
ŝ(βc − 1) + 2m2t − 2m2b̃
R
#2
+
4m2t + ŝ(βc − 1)2
αs |λ′′313 |2 β
,
2
2
72ŝ
ŝ(βc − 1) + 2mt − 2mb̃
R
p
where β = 1 − 4m2t /ŝ, ŝ = (p1 + p2 )2 , αs is the
strong coupling constant and mt is the top quark mass.
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Calculate observables with
MadGraph arXiv:1205.5170
Allanach and Sridhar, 2012
∆AFB
5
0.25
0.2
4.5
Allanach and Sridhar, 2012
∆AyC
0.06
5
0.04
4.5
0.15
0.1 4
0
λ’’313
4
0.02
0.053.5
3.5
0
3
-0.02
3
-0.04
-0.05
2.5
-0.1
2
-0.15
2.5
2
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
msbottom/TeV
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-0.06
-0.08
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
msbottom/TeV
B.C. Allanach – p
Constraints and Predictions
0.037 < ∆AF B < 0.205
−0.65 < ∆σtTt̄ EV /pb < 1.51
−0.38 < ∆AlF B < 0.23
−19.2 < ∆σtLHC7
/pb < 39.2
t̄
y
−0.079 < ∆AC < 0.061
4 < ∆σtTt̄ EV (bin)/fb< 156
0.062 < ∆AhF B < 0.33
Table 1: 95% CL constraints
0.037 < ∆AF B < 0.09
0.02 < ∆AyC < 0.06
0 < ∆σtTt̄ EV /pb < 1.8 110 < ∆σtTt̄ EV (bin)/fb< 156
0.062 < ∆AhF B < 0.14
0.005 < ∆AlF B < 0.04
LHC8
8 < ∆σtLHC7
/pb
<
25
13
<
∆σ
/pb < 33
t̄
tt̄
Table 2: Predicted values in good fit region
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Summary
•
•
•
•
•
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Rp violation allows natural SUSY with lightish
gluinos and squarks that have not yet been ruled
out by searches.
Same-sign dilepton searches without huge E
6 T cut
will be interesting. It covers almost all possible
cases of RPV operator.
In case of Ui Dj Dk operators, current searches
⇒ mg̃ > 550 GeV.
Anomalous AF B measurements can also be
explained by Ui Dj Dk type operator - fits all data
Other models tend to fail one or more checks
B.C. Allanach – p
Backup
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Technical Hierarchy Problem
A problem with light, fundamental scalars. Their
mass receives quantum corrections from heavy
particles in the theory:
F
2 Z
n
cλ
d
k
h λ
h
λ
∼−
+ ...
2
2
2
16π
k − mF
F
Quantum correction to Higgs mass:
phys
mh
= mtree
+ O(mF /100).
h
mF ∼ 1019 GeV/c2 is heaviest mass scale present.
Higgs is eaten by W, Z to give O(MW,Z ) ∼ 90
2
tot <
GeV/c ⇒ mh ∼ 1 TeV/c2 .
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Symmetry
Standard model gauge symmetry is internal, but
supersymmetry (SUSY) is a space-time symmetry.
We call extra SUSY generators Q, Q̄.
Q|fermioni → |bosoni
Q|bosoni → |fermioni
In the simplest form of SUSY, we have multiplets
spin 0
spin 1/2
,
,
spin 1/2
spin 1
where each spin component in the multiplet should
have identical quantum numbers (except spin).
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Supersymmetric Solution
Exact supersymmetry adds 2 scalars f˜L,R for every
massive fermion with
mf˜L,R = mF
and they couple to h with the same strength:
F
f˜L,R
+ h λ
λ h =0
h λ2 h
F
Q: Where are the selectrons?
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Supersymmetric Solution
Exact supersymmetry adds 2 scalars f˜L,R for every
massive fermion with
mf˜L,R = mF
and they couple to h with the same strength:
F
f˜L,R
+ h λ
λ h =0
h λ2 h
F
Q: Where are the selectrons?
A: SUSY must be softly broken.
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Supersymmetric Solution
Exact supersymmetry adds 2 scalars f˜L,R for every
massive fermion with
mf˜L,R = mF
and they couple to h with the same strength:
F
f˜L,R
+ h λ
λ h =0
h λ2 h
F
When we break SUSY, we must make sure that we
don’t reintroduce the naturalness problem: “soft
breaking”.
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Soft breaking
Make scalar partners heavier than fermions:
mf2˜
L,R
= m2F + δ 2
Then we find a quantum correction to mh of (Drees)
2
2
λ
mF
2
2
2
4
4δ + 2δ ln 2 + O(δ ).
∆mh ∼
2
16π
µ
<
So, if δ ∼ O(1) TeV/c2 , there’s no fine tuning in mh .
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Soft breaking
Make scalar partners heavier than fermions:
mf2˜
L,R
= m2F + δ 2
Then we find a quantum correction to mh of (Drees)
2
2
λ
mF
2
2
2
4
4δ + 2δ ln 2 + O(δ ).
∆mh ∼
2
16π
µ
<
So, if δ ∼ O(1) TeV/c2 , there’s no fine tuning in mh .
We should see supersymmetric particles in the Large
Hadron Collider.
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Broken Symmetry
3 components of the Higgs particles are eaten by
W ± , Z 0 , leaving us with 5 physical states:
h0 , H 0 (CP+),
A0 (CP-),
H±
SUSY breaking and electroweak breaking imply
particles with identical quantum numbers mix:
(B̃, W̃3 , H̃10 , H̃20 ) → χ01,2,3,4
(t̃L , t̃R ) → t̃1,2
(b̃L , b̃R ) → b̃1,2
(τ̃L , τ̃R ) → τ̃ 1,2
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(W̃ ± , H̃ ± ) → χ±
1,2
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Electroweak Breaking
Both Higgs get vacuum expectation values:
0 +
H1
v1
H2
0
→
→
−
0
H1
0
H2
v2
and to get MW correct, match with vSM = 246 GeV:
vSM
β
v2
tan β =
v2
v1
v1
L = ht t̄L H20 tR + hb b̄L H10 bR + hτ τ̄L H10 τR
hb,τ vSM
mt
mb,τ
ht vSM
= √ ,
= √
⇒
.
sin β
cos β
2
2
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Hierarchy problem solved
The supersymmetric copies cancel the quantum
fluctuations. (This is a very difficult problem to solve).
Not only that, the model contains a dark matter
candidate the neutralino χ01 :
• Weakly interacting
• Stable
• Massive
To predict how much of it is around today, we must
make assumptions on our cosmology, and on the
particle physics. If we can measure the particle
physics, we have a handle on the cosmology.
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Sets of Cuts
Signal Region
mµµ /GeV
test
/fb
σSSµµ
A/10−3
95
/fb
σSSµµ
ATLASµµ1
>15
12
1.3
58
ATLASµµ2
>100
7.5
0.86
16
ATLASµµ3
>200
2.1
0.29
8.4
ATLASµµ4
>300
0.41
0.077
5.3
Table 3: The ATLAS same-sign di-muon analysis
search regions.
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Sets of Cuts
Signal Region
|~pmiss
T |/GeV
mT (l1 )/GeV
A/10−3
95
σSSll
/fb
ATLASll1
> 150
>0
1.0
1.6
ATLASll2
> 150
> 100
0.6
1.5
Table 4: ATLAS same sign-di lepton analysis search
regions.
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Sets of Cuts
Signal Region
HT /GeV
|~pmiss
T |/GeV
Nll /fb
A × ǫ/10−3
Nll95
CMSll1
>400
>120
2.4
3.5
<3.7
CMSll2
>400
> 50
4.6
6.8
<8.9
CMSll3
>200
>120
2.5
3.7
<7.3
Table 5: Number of events past cuts for the CMS same
sign-di lepton analysis Nll predicted by our test point
over SM backgrounds, and acceptance A times efficiency ǫ of the signal selection, for the test point.
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Test Point
mg̃ = 588 GeV, mt̃ = 581 GeV.
500
500
400
400
300
300
200
200
100
0
100
0
100
200
300
400
500
600
700
0
0
1000
2000
LH panel: E
6 T /GeV , RH panel: HT /GeV
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Test Point
mg̃ = 588 GeV, mt̃ = 581 GeV.
400
300
300
200
200
100
100
0
0
500
1000
0
0
100
200
300
LH panel: pT (j1 )/GeV , RH panel: pT (l1 )/GeV
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Test Point
mg̃ = 588 GeV, mt̃ = 581 GeV.
6000
5000
2000
4000
3000
1000
2000
1000
0
2.5
5
7.5
10
0
0
1
2
3
LH panel: NJ , RH panel: Nisol e,µ
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Efficiencies of CMSll6E T
mgluino/TeV
SUSY events past cuts
ǫ=
SUSY events
You pay for the di-leptonic tt branching ratio.
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.2
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ε/%
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Allanach and Gripaios, 2012
0.4 0.6 0.8
mstop/TeV
1
B.C. Allanach – p