[PPT] - SUSY: new search channels and new search techniques Maurizio PowerPoint Presentation

SLIDE 1

SUSY: new search channels and new search techniques

Maurizio Pierini

1

Wednesday, November 9, 11

SLIDE 2

Disclaimer

I was asked to talk about new searches, so I will not

cover classic approaches

I will focus on hadronic searches, which I know better
I will not show results. There are specific talks for that
The talk is CMS-centric, because I am biased and

because results based on “new” approaches mainly come from CMS

Wednesday, November 9, 11

SLIDE 3

Outline

The lesson from Tevatron: the “classic” approach
αT: rejecting QCD
MT2: characterizing signal as two-missing-particles

signature

The Razor: merging the two in a consistent framework
A few considerations thunking at 2012

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Wednesday, November 9, 11

SLIDE 4

A “classic” SUSY search

The typical signature: a lot of energy seen in the detector, recoiling against a lot of MET Several variables to quantify this behavior:

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Wednesday, November 9, 11

SLIDE 5

A “classic” SUSY search

(GeV)

T

H

500 1000 1500 2000 2500 3000 3500

Events / 100 GeV

1

10 1 10

2

10

3

10 Data

Bkg. expectation from MC

)+Jets ν W(l )+Jets ν ν Z( +Jets t t QCD Susy LM4

= 7 TeV s ,

1

CMS Preliminary, L = 1.1 fb

(GeV)

T

H

500 1000 1500 2000 2500 3000 3500

Events / 100 GeV

1

10 1 10

2

10

3

10

(GeV)

T

H

500 1000 1500 2000 2500 3000 3500

Events / 100 GeV

1

10 1 10

2

10

3

10

(GeV)

T

H

500 1000 1500 2000 2500 3000 3500

Events / 100 GeV

1

10 1 10

2

10

3

10

A counting experiment is performed on the tail of the distribution An exclusion limit is set on some NP parameter space

(GeV) m

200 400 600 800 1000 1200 1400 1600 1800

(GeV)

1/2

m

200 300 400 500 600 700

CMS Preliminary

=0 >0, A µ =10, β tan <0 µ =5, β tan , q ~ , g ~ CDF <0 µ =3, β tan , q ~ , g ~ D0 ± 1 χ ∼ LEP2 ± l ~ LEP2

1

CMS 1.1 fb T α Observed 2010 L S P τ ∼ (500)GeV q ~ (750)GeV q ~ (1000)GeV q ~ (500)GeV g ~ (750)GeV g ~ (1000)GeV g ~

= 7 TeV s ,

1

= 1.1 fb

int

L Observed σ 1 ± Expected

CMS Preliminary

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Wednesday, November 9, 11

SLIDE 6

Backgrounds To Fight

mismeasured jet Fake MET mismeasured jet MET

QCD with fake MET related to pathological events require understanding of rare detector-related effects SM processes with real MET, e.g. Z(νν)+jets measurable from control samples defined

n data

ν ν

_

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Wednesday, November 9, 11

SLIDE 7

The New Ways

The “classic” approach is still pursued by CMS and

ATLAS, adapted to the new detectors

New approaches proposed to reduce the QCD to

negligible level and deal with the residual SM background through data-driven control samples

Different layers of extra assumptions give different

signal vs. background separation

αT: unbalanced events
MT2: MET coming from two particles
RAZOR variables: pair production of heavy
bjects producing two missing particles

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Wednesday, November 9, 11

SLIDE 8

αT: Rejecting QCD

αT = ETjet2 MT

=

ETjet2 r⇣ ∑2

i=1 ETjeti

⌘2

−

⇣ ∑2

i=1 pjeti x

⌘2

−

⇣ ∑2

i=1 pjeti y

⌘2 ,

T

α 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Events / 0.025

1

10 1 10

2

10

3

10

4

10 CMS Preliminary 2011 = 7 TeV s ,

1

L dt = 1.1 fb

∫

= 7 TeV s ,

1

L dt = 1.1 fb

∫

Data Standard Model QCD MultiJet , W, Z + Jets t t LM4 LM6

αT = 0.5 for perfectly balanced dijet events
αT<0.5 for dijet + mismeasurements
EW main bkg after αT cut
QCD events could leak to αT>0.5 because of

detector effects (rare)

large fraction of signal events removed

(efficiency vs purity)

After αT cut the signal looks similar to

bkg in αT

another variable needs to be used to

characterize the signal

Back to the “classic” paradigm”:

HT used by CMS

(GeV)

T

H 300 400 500 600 700 800 900 counts / bin

1

10 1 10

2

10

3

10

Data (hadronic sample) SM (QCD + EWK) ) ν ν → + W + Z t EWK (t ν ν → Z LM6 (LO)

= 7 TeV s

1

CMS Preliminary 2011 1.1 fb

α ≡ pT 2 mjj . Randall & Tucker-Smith

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Wednesday, November 9, 11

SLIDE 9

αT: BKG Estimate

EW bkg is estimated using the RαT (*) ratio
This is computed scaling the pT of the jets with the HT threshold, to event

topology

The ratio is found to be compatible with the flat hypothesis within the available

data and SM MC statistics

(GeV)

T

H

400 600 800

T

α

R

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

3

10 ×

SM+LM4 SM+LM6 SM Data CMS preliminary 2011 = 7 TeV s ,

1

L dt = 1.1 fb

∫

(GeV)

T

H

400 600 800

T

α

R

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

3

10 ×

SM (nominal) W (+15%) W (-15%) (+15%) ν ν → Z (-15%) ν ν → Z (+15%) t t (-15%) t t t (+15%) t (-15%) CMS simulation 2011 = 7 TeV s ,

1

L dt = 0.4 fb

∫

ratio RαT = NαT>θ/NαT<θ exhibits

f the ratio in all H bins

(*) Number of EW events with αT>θ / number of QCD events with αT<θ

This is used to predict the bkg expected in each bin of HT. Then a fit to the HT

shape is used

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Wednesday, November 9, 11

SLIDE 10

[GeV]

T

M

50 100 150

events / 2.5 GeV

0.5 1 1.5 2 2.5

3

10 ×

data ν µ → W non-top top

CMS

= 7 TeV s at

1

36 pb

+ 1 jet ν µ → W

MT2: two missing particles

We are looking for events with

two undetected neutral particles leaving the detector

We measure the sum of their pT

as MET

This is similar to the detection of

the W, for which the edge of the mT distribution is used

The presence of two missing

particles make the picture more

complicated. But the physics

intuition holds

χ+

1 → χ0 1π+.

χ+

1 → χ0 1π+.

{

pp→

~ ~

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Wednesday, November 9, 11

SLIDE 11

m2

T(pπ T, p χ0

1

T ; mχ0

1) ≡ m2

π+ + m2 χ0

1 + 2(Eπ

TE χ0

1

T − pπ T · p χ0

1

T )

(

m2

χ+

1 = m2

π + m2 χ0

1 + 2

Eπ

TE χ0

1

T cosh(∆η) − pπ T · p χ0

1

T

m2

T2(χ)

≡ min /

q(1)

T +/

q(2)

T =/

pT

max
m2

T(pπ(1) T

, / q(1)

T ; χ), m2 T(pπ(2) T

, / q(2)

T ; χ)

.

MT2: two missing particles

11

If we could see all the particles, we could compute
If we could measure pT(Χ0), but not pz(Χ0), the best we could do would be
Since cosh>1, mT≤m, the equality holding for both pz(Χ0)=0. This means that

max(mT) has an “edge” at m

For each event we have two values of mT (two copies of the same decay). Both

are such that mT<m. This means that max(mT(1), mT(2))<m

We only know pT(Χ01)+ pT(Χ02)=ETmiss. A wrong assignment of the missing

momenta brakes the mT<m condition. But the condition would hold for the correct assignment. This means that min(mT)<mT(true)<m.

This defined mT2 as

Wednesday, November 9, 11

SLIDE 12

MT2: two missing particles

The variable we have is a function
f the mass of the LSP
SUSY characterization:
SUSY search:
Scan the LSP mass and look for the

edge developing in your sample

f SUSY events (if you have one...)

(MT2)2 = 2AT = 2pvis(1)

T

pvis(2)

T

(1 + cosφ12),

12

Assume a mass value (eg mLSP=0)
Assume that the visible system in has 0 mass
An analytical expression for MT2 is found
The edge is lost but we have an αT-like

variable to kill the QCD

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

m[π] m[χ1

+] - m[χ1 0]

mT4 ee mT3 eπ mT2 ππ mTX(m[χ1

0]) - m[χ1 0] / GeV

Figure 3: Simulations of mTX(mχ0

1)−mχ0 1 for X = 2, 3, 4 using a

simple phase-space Monte-Carlo generator program for a pair of decays ˜ q → χ+

1 q followed by χ+ 1 → χ0 1 π or χ+ 1 → χ0 1 e νe. As the

number of invisible particles increases, the proportion of events near the upper limit decreases. Within the figure, subscripts are indicated by square brackets.

Wednesday, November 9, 11

SLIDE 13

MT2: two missing particles

MT2 is found to be useful for

searches, since it allows to reduce QCD to negligible level

Signal is searched on the tail
f MT2 in a counting

experiment

Other variables could be used

to characterize the signal, in case of a discovery. CMS would use √smin for that

200 400 600

1

10 1 10

2

10

3

10

4

10

5

10

QCD W+jets Z+jets Top LM6 data

1

= 7 TeV, L = 1.1 fb s Analysis CMS Preliminary,

T2

High M

Events

T2

M 1000 2000 3000 4000 5 10 15

QCD W+jets Z+jets Top Other LM5 x 1 data

1

= 7 TeV, L = 1.1 fb s Analysis CMS Preliminary,

T2

High M

Events

min

s

√

smin(Mmiss,min) = q M2

vis + P2 T,vis +

q M2

miss,min + ET

/ 2

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Wednesday, November 9, 11

SLIDE 14

The Razor Frame

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Two squarks decaying to quark and LSP

. In their rest frames, they are two copies of the same monochromatic decay. In this frame p(q) measures MΔ

In the rest frame of the two incoming partons, the

two squarks recoil one against each other.

M∆ ≡ M2

˜ q − M2 ˜ χ

M˜

q

= 2M ˜

χγ∆β∆ ,

In the lab frame, the two squarks are

boosted longitudinally. The LSPs escape detection and the quarks are detected as two jets

→

If we could see the LSPs, we could boost back by βL, βT, and βCM In this frame, we would then get |pj1| = |pj2| Too many missing degrees of freedom to do just this βL

→

βT

x y x y z y

Wednesday, November 9, 11

SLIDE 15

The Razor Frame

In reality, the best we can do is to compensate the missing degrees of

freedom with assumptions on the boost direction

15

The parton boost is forced to be

longitudinal

The squark boost in the CM frame is

assumed to be transverse

We can then determine the two

by requiring that the two jets have the same momentum after the transformation

The transformed momentum

defines the MR variable

pj1 pj2 p*j1 p*j2 pRj1 pRj2

βLR*

RAZOR CONDITION |pRj1|= |pRj2|

βTCM

βTCM MR ≡ q

(Ej1 + Ej2)2 − (pj1

z + pj2 z )2 ,

momentum p is determined from the massless

Wednesday, November 9, 11

SLIDE 16

The Razor Variable

MR is boost invariant, even if defined from

3D momenta

No information on the MET is used
The peak of the MR distribution provides

an estimate of MΔ

MΔ could be also estimated as the “edge”
f MTR
MTR is defined using transverse quantities

and it is MET

related
The Razor (aka R) is defined as the ratio
f the two variables

16

R ≡ MR

T

MR .

MR MΔ MTR

MR

T ≡

s Emiss

T

(pj1

T + pj2 T ) − ~

Emiss

T

·(~

p j1

T + ~

p j2

T )

2 .

Wednesday, November 9, 11

SLIDE 17

The Razor Analysis

The backgrounds are characterized

by a turn-on (they have their own MΔ), after which they decay ~ exponentially

The two variables exhibit a clear

correlation, regardless of the process under consideration

17

[GeV]

R

M

500 1000 1500 2000

R

0.2 0.4 0.6 0.8 1 1.2 1.4

Events / bin

5000 10000 15000 20000 25000

=7 TeV s CMS Simulation

1

L dt = 35 pb

∫

QCD

[GeV]

R

M

500 1000 1500 2000

R

0.2 0.4 0.6 0.8 1 1.2 1.4

Events / bin

2 4 6 8 10 12 14 16 18 20 22

=7 TeV s CMS Simulation

1

L dt = 35 pb

∫

W+jets

[GeV]

R

M

500 1000 1500 2000

R

0.2 0.4 0.6 0.8 1 1.2 1.4

Events / bin

0.5 1 1.5 2 2.5 3

=7 TeV s CMS Simulation

1

L dt = 35 pb

∫

+jets t t

[GeV]

R

M

500 1000 1500 2000

R

0.2 0.4 0.6 0.8 1 1.2 1.4

Events / bin

0.02 0.04 0.06 0.08 0.1

=7 TeV s CMS Simulation

1

L dt = 35 pb

∫

SUSY LM1

QCD W+jets tt SUSY LM1

[GeV]

R

M

100 200 300 400 500 600 700 800

Events / 50 GeV

1 10

2

10

3

10

4

10 DATA Total SM QCD W+jets Z+jets Top+X LM0 LM1

=7 TeV s CMS

1

L dt = 35 pb

!

HAD BOX

As a consequence of the

correlation, the shape of mR (exponential) depends on the cut applied on R

2

(R threshold)

0.05 0.1 0.15 0.2 0.25

Slope Parameter [1/GeV]

0.12
0.1
0.08
0.06
0.04
0.02

=7 TeV s CMS

1

L dt = 35 pb

ent values of the R threshold for data events in the

Wednesday, November 9, 11

SLIDE 18

From DiJet To MultiJets

The “new” variables rely on the dijet

+MET final state as a paradigm

All the analyses have been extended

to the case of multijet final states clustering jets in two hemispheres (aka mega-jets)

Several approaches used

minimizing the HT difference between the mega-jets (aT CMS)
minimizing the invariant masses of the two jets (Razor CMS)
minimizing the Lund distance (MT2 CMS)
...

(Ei − picosθik)

Ei

(Ei + Ek)2 ≤ (Ej − pjcosθjk)

Ej

(Ej + Ek)2 .

Is the ultimate hemisphere definition out there

(I am not aware of studies on this)?

Could this improve the signal sensitivity in a significant way?

18

Wednesday, November 9, 11

SLIDE 19

How Do These Approaches Compare?

A fair comparison is difficult,

because not all the results are provided with the same luminosity

A new variable/approach is

not the end of the story. The actual analysis is more than the variable it uses

The best limit is not the best
sensitivity. The best limit is not

the best analysis (particularly if the cuts are so tight that nothing is left and nothing is expected to be left)

The best I found are these

three CMS plot

19

)

2

(GeV/c m

200 400 600 800 1000

)

2

(GeV/c

1/2

m

200 300 400 500 600 700

(250)GeV q ~ (500)GeV q ~ (500)GeV g ~ (750)GeV q ~ (750)GeV g ~ ( 1 ) G e V q ~ (1000)GeV g ~ ( 1 2 5 ) G e V q ~ (1250)GeV g ~

T

α

Jets+MHT SS Dilepton OS Dilepton MT2 1 Lepton

1

= 7 TeV, Ldt = 1.1 fb s

∫

CMS Preliminary

> 0 µ = 0, = 10, A β tan

<0 µ =5, β tan

, q ~ , g ~ CDF

<0 µ =3, β tan

, q ~ , g ~ D0

± 1

χ ∼ LEP2

±

l ~ LEP2

= LSP τ ∼

2011 Limits 2010 Limits

)

2

(GeV/c m

200 400 600 800 1000

)

2

(GeV/c

1/2

m

200 300 400 500 600 700

)

2

(GeV/c m

200 400 600 800 1000

)

2

(GeV/c

1/2

m

200 300 400 500 600 700

( G e V )

s q u a r k

m

4 5 6 7 8 9 1

( G e V )

L S P

m

1 2 3 4 5 6 7 8 9

T

α J e t s + m i s s .

T

H R a z

r

N L O

Q

C D

σ =

p r

d

σ

N L O

Q

C D

σ = 3

p r

d

σ

N L O

Q

C D

σ = 1/3

p r

d

σ

C M S P r e l i m i n a r y = 7 T e V s

1

= 3 5 p b

i n t

L

H a d r

n

i c S e a r c h e s

(GeV)

gluino

m

400 500 600 700 800 900 1000

(GeV)

LSP

m

100 200 300 400 500 600 700 800 900

T

α Jets + miss.

T

H Razor

NLO-QCD

σ =

prod

σ

NLO-QCD

σ = 3

prod

σ

NLO-QCD

σ = 1/3

prod

σ

CMS Preliminary = 7 TeV s

1

= 35 pb

int

L

Hadronic Searches

Razor missing MT2 missing

Wednesday, November 9, 11

SLIDE 20

What’s Next

20

The expertise gained in hadronic

analyses could be used for SUSY searches in specific scenarios, e.g. the light-stop scenario

Analyses will have to be modified

(GeV) m

200 400 600 800 1000 1200 1400 1600 1800

(GeV)

1/2

m

200 300 400 500 600 700

=0 >0, A µ =10, β tan

<0 µ =5, β tan

, q ~ , g ~ CDF

<0 µ =3, β tan

, q ~ , g ~ D0

± 1

χ ∼ LEP2

±

l ~ LEP2

1

CMS 1.1 fb

T

α Observed 2010

LSP τ ∼ (500)GeV q ~ (750)GeV q ~ (1000)GeV q ~ (500)GeV g ~ (750)GeV g ~ (1000)GeV g ~

= 7 T eV s ,

1

= 1.1 fb

int

L Observed σ 1 ± Expected

In case of a negative result, the focus will move from the hadronic

to the leptonic analyses, as a probe of SUSY EW production

The current physics

program will be repeated as it is, with higher statistic

)

2

(GeV/c m

200 400 600 800 1000

)

2

(GeV/c

1/2

m

200 300 400 500 600 700

( 5 ) G e V q ~ (500)GeV g ~ (750)GeV q ~ (750)GeV g ~ (1000)GeV q ~ (1000)GeV g ~ (1250)GeV q ~ (1250)GeV g ~

T

α

Jets+MHT SS Dilepton OS Dilepton MT2 1 Lepton

= 7 TeV, Ldt = 1.1 fb s

∫

CMS Preliminary

> 0 µ = 0, = 10, A β tan

<0 µ =5, β tan

, q ~ , g ~ CDF

<0 µ =3, β tan

, q ~ , g ~ D0

± 1

χ ∼ LEP2

±

l ~ LEP2

= LSP τ ∼

2011 Limits 2010 Limits

)

2

(GeV/c m

200 400 600 800 1000

)

2

(GeV/c

1/2

m

200 300 400 500 600 700

)

2

(GeV/c m

200 400 600 800 1000

)

2

(GeV/c

1/2

m

200 300 400 500 600 700

Wednesday, November 9, 11

SLIDE 21

Stop production vs Megajets

21

t

Δm<mt Di-charm+MET final state

t

Δm>mt ~ ~ ~ ~ 6-jets final state (with two bjets)

t

Δm>>mt ~ ~ Top decay products merge

The “inclusive” hemisphere definition is inappropriate
One could inject already at this level specific

features of the considered topology

force three jets per side, one b-jet per side
consider two-heavy jets + jet substructure

Wednesday, November 9, 11

SLIDE 22

Stop production vs MET

reduce the role of MET
based variables

(aT, MET, R,MT2)

base the analysis on the visible part

(HT, MR, √smin)

reduce the bkg to manageable level by other

requirements (e.g. jet multiplicity and/or b- tagging)

if done at the trigger level, one can go looser
n the kinematic requirements

(GeV)

q ~

m 400 600 800 1000 1200 (GeV)

χ ∼

m 200 400 600 800 1000 1200 )

s

(pb) (CL σ 95% CL upper limit on

2

10

1

10 1 10

CMS Preliminary

1

= 7 TeV L=1.1 fb s

T

α ) q ~ )>>m( g ~ ; m( χ ∼ q → q ~ , q ~ q ~ → pp

NLO-QCD

σ =

prod

σ

NLO-QCD

σ × = 3

prod

σ

NLO-QCD

σ × = 1/3

prod

σ

αT analysis

2j+MET

(GeV)

g ~

m 400 600 800 1000 1200 (GeV)

χ ∼

m 200 400 600 800 1000 1200 )

s

(pb) (CL σ 95% CL upper limit on

2

10

1

10 1 10

CMS Preliminary

1

= 7 TeV L=1.1 fb s

T

α ) g ~ )>>m( q ~ ; m( χ ∼ q q → g ~ , g ~ g ~ → pp

NLO-QCD

σ =

prod

σ

NLO-QCD

σ × = 3

prod

σ

NLO-QCD

σ × = 1/3

prod

σ

αT analysis

4j+MET

Signal region 7j55 8j55 6j80 7j80 Jet pT > 55 GeV > 80 GeV Jet |⌘| < 2.8 ∆R jj > 0.6 for any pair of jets Number of jets ≥ 7 ≥ 8 ≥ 6 ≥ 7 Emiss

T

/ √HT > 3.5 GeV1/2

2 4 6 8 10 12 14 16

1

10 1 10

2

10

3

10

4

10

5

10

2 4 6 8 10 12 14 16

1

10 1 10

2

10

3

10

4

10

5

10 2 4 6 8 10 12 14 16 2 4 6 8 10 12 14 16

1/2

Events / 0.25 GeV

1

L dt ~ 1.34 fb

∫

> 55 GeV

T

7 jets p ≥ Signal Region ATLAS

= 7 TeV) s Data 2011 ( Total SM Prediction qq (Template) → t QCD+t ql,ll → t Alpgen t ν ) τ , µ (e, → Alpgen W ν ν → Alpgen Z SUSY Point (1220,180) 2 4 6 8 10 12 14 16

1

10 1 10

2

10

3

10

4

10

5

10 )

1/2

(GeV

T

H /

miss T

E

2 4 6 8 10 12 14 16 DATA / Prediction 0.5 1 1.5 2

)

1/2

(GeV

T

H /

miss T

E

2 4 6 8 10 12 14 16 DATA / Prediction 0.5 1 1.5 2 16 16

16 16

16

)

16

)

16

2 4 6 8 10 12 14 16

1

10 1 10

2

10

3

10

4

10

5

10

2 4 6 8 10 12 14 16

1

10 1 10

2

10

3

10

4

10

5

10 2 4 6 8 10 12 14 16 2 4 6 8 10 12 14 16

1/2

Events / 0.25 GeV

1

L dt ~ 1.34 fb

∫

> 80 GeV

T

6 jets p ≥ Signal Region ATLAS

= 7 TeV) s Data 2011 ( Total SM Prediction qq (Template) → t QCD+t ql,ll → t Alpgen t ν ) τ , µ (e, → Alpgen W ν ν → Alpgen Z SUSY Point (1220,180) 2 4 6 8 10 12 14 16

1

10 1 10

2

10

3

10

4

10

5

10 )

1/2

(GeV

T

H /

miss T

E

2 4 6 8 10 12 14 16

DATA / Prediction 0.5 1 1.5 2

)

1/2

(GeV

T

H /

miss T

E

2 4 6 8 10 12 14 16

DATA / Prediction 0.5 1 1.5 2

With increasing jet

multiplicity, the analyses based

n MET are less sensitive to a

signal

If objects are light the

situation gets worse (not enough phase space)

Analyses have to be modified

Wednesday, November 9, 11

SLIDE 23

Conclusion

Lesson from Tevatron taken: CMS and ATLAS fully

committed to “classic” Jet+MET searches

In parallel, new directions have been explored,

exploiting specific features of the signal under considerations

First results showed the power of the new methods.

More results are coming

Increasing luminosity and no excess seen moves to

interest to specific scenarios (eg light stop).

Classic analyses migrated already. The new approaches

should too

23

Wednesday, November 9, 11

SLIDE 24

Basic/Incomplete Bibliography

ATLAS SUSY results
CMS SUSY results
Other papers
Original paper on α
Modified αT paper

by CMS

MT2
√smin
Razor

https://twiki.cern.ch/twiki/bin/view/CMSPublic/PhysicsResultsSUS https://twiki.cern.ch/twiki/bin/view/AtlasPublic/SupersymmetryPublicResults http://arxiv.org/pdf/0806.1049 http://arXiv.org/pdf/hep-ph/0304226 http://arxiv.org/pdf/1006.2727 http://cdsweb.cern.ch/record/1149915/files/SUS-08-005-pas.pdf http://www.arxiv.org/pdf/1006.0653 http://arxiv.org/pdf/0810.5576v2

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Wednesday, November 9, 11