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23
Searches for - non-SUSY - new physics at ATLAS Tülay Çuhadar Dönszelmann University of Sheffield (On behalf of the ATLAS collaboration) 23 rd Rencontres de Blois
Transcript
Page 1: Searches for - non-SUSY - new physics at ATLASlss.fnal.gov/conf2/C110529/doenszelmann.pdfDi-jet Results Resonance Mass [GeV] 1000 2000 3000 A [pb]! m 10-1 1 10 102 103 104 q* MC09

Searches for - non-SUSY - new physics at ATLAS

Tülay Çuhadar Dönszelmann

University of Sheffield (On behalf of the ATLAS collaboration)

23rd Rencontres de Blois

Page 2: Searches for - non-SUSY - new physics at ATLASlss.fnal.gov/conf2/C110529/doenszelmann.pdfDi-jet Results Resonance Mass [GeV] 1000 2000 3000 A [pb]! m 10-1 1 10 102 103 104 q* MC09

Introduction §  Within the SM itself and based on calculations on SM:

§  Naturalness problem: Mass of yet-to-be-discovered Higgs boson Higgs? SUSY? �

§  CP violation in SM not enough: Why more matter than antimatter? " " " "Does CKM triangle close? New flavor?

§  Completely absent from SM: §  No unification of the 3 forces

" " " "Technicolor? E6? �§  Also where is gravity?

" " " "Extra dimensions?�§  Why three families?

4th generation?�§  Arbitrary “input” parameters. Why is md>mu? Why me<mn-mp?

[See talk on Monday by Rohini Godbole – “Review of SUSY and Extra Dimensions”]

01/06/2011 23rd Rencontres de Blois 2

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Outline

§  Di-jet resonance §  ttbar resonance §  Leptoquarks §  Fourth generation quarks §  New Heavy bosons §  Contact interaction §  Randall-Sundrum Graviton

01/06/2011 23rd Rencontres de Blois 3

Page 4: Searches for - non-SUSY - new physics at ATLASlss.fnal.gov/conf2/C110529/doenszelmann.pdfDi-jet Results Resonance Mass [GeV] 1000 2000 3000 A [pb]! m 10-1 1 10 102 103 104 q* MC09

New physics in di-jet events §  These ‘2 → 2’ scattering

processes are well described within SM §  sensitive to new phenomena

§  Observables : §  Di-jet invariant mass §  Di-jet angular distributions of

energetic jets relative to the beam axis

§  Events with two highest pT jets recoiling back to back with rapidities, y1 and y2

1000 2000 3000

Even

ts

-110

1

10

210

310

410 DataFit

(1000)q*(1700)q*(2500)q*

[GeV]jjReconstructed m1000 2000 3000

B(D

- B)

/

-202ATLAS

-1 = 36 pbdt L

= 7 TeVs

No evidence for a bump using : χ2 test ⟹ p-value 0.88 BumpHunter (Phys. Rev. D79: 011101)

Set exclusion limits

arxiv:1103.3864 J. Phys. 13 (2011) 053044

y*= 12ln1+ cos! *1! cos! *

"

#$$

%

&''=12y1 ! y2( )

01/06/2011 23rd Rencontres de Blois 4

Page 5: Searches for - non-SUSY - new physics at ATLASlss.fnal.gov/conf2/C110529/doenszelmann.pdfDi-jet Results Resonance Mass [GeV] 1000 2000 3000 A [pb]! m 10-1 1 10 102 103 104 q* MC09

Di-jet angular distribution

§  χ ≡ exp(|y1-y2|) distribution is relatively flat for QCD

§  Average of y1 & y2, |yB| < 1.10 and |y*|<1.70 ⟹ χ ~ 30

[GeV]jjm500 1000 1500 2000 2500 3000 3500

) jj(m

F

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

ATLAS

=7 TeVs, -1dt = 36 pbL

QCD Prediction Theoretical uncertainties Total Systematics

= 5 TeV data

|2

-y1

|y = e

1 10

/dev

)dN

ev(1

/N

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

ATLAS

<800 GeVjj520<m<1200 GeV (+0.04)jj800<m<1600 GeV (+0.08)jj1200<m<2000 GeV (+0.12)jj1600<m

>2000 GeV (+0.18)jjmQCD PredictionTheoretical UncertaintiesTotal Systematics

=7 TeVs, -1dt = 36 pbL

= 3 TeV) (+0.18)D

QBH(M

§  Fraction of di-jets produced centrally versus total number of di-jets :

!

F" m jjmin +m jj

max[ ] 2( ) #Nevents y * < 0.6,m jj

min,m jjmax( )

Nevents y * <1.7,m jjmin,m jj

max( )

01/06/2011 23rd Rencontres de Blois 5

Page 6: Searches for - non-SUSY - new physics at ATLASlss.fnal.gov/conf2/C110529/doenszelmann.pdfDi-jet Results Resonance Mass [GeV] 1000 2000 3000 A [pb]! m 10-1 1 10 102 103 104 q* MC09

Di-jet Results

Resonance Mass [GeV]1000 2000 3000

A [p

b]!

-110

1

10

210

310

410q* MC09q* Perugia0q* MC09’A (MRST)Observed 95% CL upper limitExpected 95% CL upper limitExpected limit 68% and 95% bands

ATLAS

-1 = 36 pbdt L = 7 TeVs

[TeV]5 6 7 8 9 10

)H

1 -

lnL

H0

Q =

-2(ln

L-8

-6

-4

-2

0

=7 TeVs, -1dt = 36 pbL

95% C.L. Quantile

Measured Q

QCD Prediction

Expected Limit variation (68%)

ATLAS

Observable Expected Observed

Exited quark q*

mjj 2.07 2.15

FΧ(mjj) 2.12 2.64

Randall-Meade quantum black hole for n=6

mjj 3.64 3.67

FΧ(mjj) 3.49 3.78

Axigluon

mjj 2.01 2.10

Contact interaction Λ

FΧ(mjj) 5.72 9.51

95% C.L. Limits (TeV)

Likelihood ratio defined by FΧ versus CI

01/06/2011 23rd Rencontres de Blois 6

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ttbar Resonances §  Signature : (At least one W reconstructed leptonically):

§  High pT isolated lepton (e,µ), at least four jets and large missing energy

§  Observable : §  Invariant mass of ttbar computed from the reconstructed objects in the final

state §  Objects are not assigned to either of the t (i.e. no t reconstruction)

§  Two methods to reconstruct ttbar: 4 hardest jets - four highest pT jets and dRmin method - as “4 hardest jet”, removes jet if ΔR(j,ℓ) > 2.5-0.015×mj

ATLAS-CONF-2011-070

](dRmin method)2) [GeV/cνM(4jl0 500 1000 1500 2000

Can

dida

te E

vent

s

0

20

40

60

80

](dRmin method)2) [GeV/cνM(4jl0 500 1000 1500 2000

Can

dida

te E

vent

s

0

20

40

60

80 @ 7 TeV-1 Preliminary 33 pbATLAS

MC

nor

mal

ized

to S

M p

redi

ctio

n

topW+JetsZ+JetsQCD muonQCD eleATLAS data

](dRmin method)2) [GeV/cνM(4jl0 500 1000 1500 2000

Can

dida

te E

vent

s

0

20

40

60

80

](dRmin method)2) [GeV/cνM(4jl0 500 1000 1500 2000

Even

t Fra

ctio

n

0

0.1

0.2

= 1000 GeVZ'm

= 700 GeVZ'm

= 500 GeVZ'm

= 7 TeVs Preliminary ATLAS

norm

aliz

ed to

uni

t are

a

](dRmin method)2) [GeV/cνM(4jl0 500 1000 1500 2000

Even

t Fra

ctio

n

0

0.1

0.2

Topcolor Z’ model

01/06/2011 23rd Rencontres de Blois 7

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Limits on ttbar Resonances

§  The observed cross section limits on σ×Br(Z’ → ttbar) ranges from 55 pb at M = 500 GeV to 2.2 pb at M=1000 GeV

§  Exclude MQBH < 2400 GeV @ 95% C.L.

]2QBH mass threshold [GeV/c

1000 1500 2000 2500

[pb]

QBH

σ

210

310

dRmin. Syst.+stat.Obs. 95% CL upper limitExp. 95% CL upper limit

uncertaintyσExp. 1 uncertaintyσExp. 2

Quantum Black Hole

dRmin. Syst.+stat.Obs. 95% CL upper limitExp. 95% CL upper limit

uncertaintyσExp. 1 uncertaintyσExp. 2

Quantum Black Hole

ATLAS Preliminary

-1 = 33 pbdt L ∫

= 7 TeVs

]2Z' mass [GeV/c

500 600 700 800 900 1000

) [pb

]t t

→ B

R(Z

Z'σ

1

10

210

310

dRmin. Syst.+stat.Obs. 95% CL upper limitExp. 95% CL upper limit

uncertaintyσExp. 1 uncertaintyσExp. 2

Leptophobic Z'

dRmin. Syst.+stat.Obs. 95% CL upper limitExp. 95% CL upper limit

uncertaintyσExp. 1 uncertaintyσExp. 2

Leptophobic Z'

ATLAS Preliminary

-1 = 33 pbdt L ∫

= 7 TeVs

01/06/2011 23rd Rencontres de Blois 8

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Leptoquarks searches

§  Leptoquarks – particles that carry both lepton and baryon quantum numbers

§  Many models predict leptoquarks §  Quark and lepton sub-structure §  Theories seek GUT §  Extended technicolor

§  LQ search - LQ pair production e/µ for 1st/2nd LQ generation through ℓℓjj and ℓνjj

Leptoquark production from qqbar annihilation or gluon fusion (hep-ph/9808413v1)

!

" pp# lljj( ) $"LQ % &2

" pp# l'jj( ) $"LQ % 2&(1( &)& $ Br(LQ# l + X)

arxiv:1104.4481 accepted by PRD

01/06/2011 23rd Rencontres de Blois 9

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Leptoquarks searches §  Observables:

§  For ℓℓjj : Transverse energy in the event or for ℓνjj : Transverse mass

§  Backgrounds : §  ℓℓljj : Z+jet and ttbar and ℓvjj : W+jets and ttbar

[GeV]!TS

600 800 1000 1200 1400 1600

Even

ts /

120

GeV

0

1

2

3

4

5

6

7

[GeV]!TS

600 800 1000 1200 1400 1600

Even

ts /

120

GeV

0

1

2

3

4

5

6

7=7 TeV) sData 2010 (

V+jetsTopDibosonLQ (m=300 GeV)LQ (m=350 GeV)LQ (m=400 GeV)

-1 L dt = 35 pb

ATLAS

[GeV]eTS

600 800 1000 1200 1400 1600

Even

ts /

120

GeV

0

1

2

3

4

5

6

[GeV]eTS

600 800 1000 1200 1400 1600

Even

ts /

120

GeV

0

1

2

3

4

5

6=7 TeV) sData 2010 (

V+jetsTopDibosonLQ (m=300 GeV)LQ (m=350 GeV)LQ (m=400 GeV)

-1 L dt = 35 pb

ATLAS

STl = pT

l1 + pTl2 + pT

j1 + pTj2

MLQT = 2pT

jETmiss (1! cos! j )

, jet) [GeV]µ LQ M(150 200 250 300 350 400 450 500 550 600

Even

ts /

50 G

eV

0

1

2

3

4

5

6

7

, jet) [GeV]µ LQ M(150 200 250 300 350 400 450 500 550 600

Even

ts /

50 G

eV

0

1

2

3

4

5

6

7 =7 TeV)sData 2010 (V+jetsTopDibosonLQ (m=250 GeV)LQ (m=300 GeV)LQ (m=350 GeV)

ATLAS-1 L dt = 35 pb

LQ M(e,jet) [GeV]150 200 250 300 350 400 450 500 550 600

Even

ts /

50 G

eV

0

1

2

3

4

5

6

7

8 =7 TeV)sData 2010 (V+jetsTopDibosonLQ(m=250GeV)LQ(m=300 GeV)LQ(m=350GeV)

ATLAS-1 L dt = 35 pb

150 200 250 300 350 400 450 500 550 6000

1

2

3

4

5

6

7

8

150 200 250 300 350 400 450 500 550 6000

1

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150 200 250 300 350 400 450 500 550 6000

1

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7

8

01/06/2011 23rd Rencontres de Blois 10

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Limits on Leptoquarks

[GeV]LQM200 250 300 350 400 450 500 550

eq)

B(L

Q

00.10.20.30.40.50.60.70.80.9

1

eejj

jje

jj (Exp.)eejj + ejj (Obs.)eejj + e)-1D0 (1 fb

)-1CMS (33 pb[hep-ex/1012.4031]

[GeV]LQM200 250 300 350 400 450 500 550

eq)

B(L

Q

00.10.20.30.40.50.60.70.80.9

1

= 7 TeVs

-1 Ldt = 35 pb

ATLAS

[GeV]LQM200 250 300 350 400 450 500 550

q)!

B(L

Q

00.10.20.30.40.50.60.70.80.9

1

jj!!

jj!

jj (Exp.)!jj + !!jj (Obs.)!jj + !!)-1D0 (1 fb

)-1CMS (34 pb[hep-ex/1012.4033]

[GeV]LQM200 250 300 350 400 450 500 550

q)!

B(L

Q

00.10.20.30.40.50.60.70.80.9

1

= 7 TeVs

-1 Ldt = 35 pb

ATLAS

95% C.L. Lower limit on LQ (Modified frequentist method)

1st generation 2nd generation

Type (β) Expected limit (GeV) Observed limit (GeV)

1st generation (1.0) 387 376

1st generation (0.5) 348 319

2nd generation (1.0) 393 422

2nd generation (0.5) 353 362

The most stringent results to date

01/06/2011 23rd Rencontres de Blois 11

Page 12: Searches for - non-SUSY - new physics at ATLASlss.fnal.gov/conf2/C110529/doenszelmann.pdfDi-jet Results Resonance Mass [GeV] 1000 2000 3000 A [pb]! m 10-1 1 10 102 103 104 q* MC09

Fourth generation quarks §  Fourth generation is not excluded with the EW fit §  Pair production of Q4

§  Ws decay leptonically §  Discriminating variables : HT and MQ4 (assignments of particles that makes Q4 mass difference minimum)

W

Q4

Q̄4W

q

!

"

!

"

q

g

g

ATLAS Preliminary Background Collinear Mass0 100 200 300 400 500 600 700

HT

[GeV

]

0

200

400

600

800

1000

1200

350 GeV Collinear Mass4

ATLAS Preliminary Q0 100 200 300 400 500 600 700

HT

[GeV

]

0

200

400

600

800

1000

1200

HT = ETl+ +ET

l! +ETq1 +ET

q2 +ETmiss

mQ4 > 270 GeV/c2 @ 95% C.L.

ATLAS-CONF-2011-022

ttbar

signal

HT > X-Y×Mcoll. remove significant background while sacrificing a small fraction of events

(95% C.L limits by CDF md4> 372 GeV and mu4> 356 GeV)

Q4Q4 !W +qW "q q=u,d,c,s or b

01/06/2011 23rd Rencontres de Blois 12

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Introduction for new heavy bosons

§  Many models predict additional new heavy gauge bosons beyond SM (W’(*),Z’(*)) §  Sequential Standard Model (SSM)

§  Same coupling to fermions as SM §  Width increases linearly with W’/Z’ mass

§  GUT E6 inspired Z’ §  Different model leads to specific Z’ states :

§  New Chiral boson spin 1 bosons - W*, Z* §  Excited bosons §  Different couplings to fermions (magnetic moment type)

§  Previous lower Limits [TeV]

arXiv:0801.4235v1

(Differential cross section for Z’ and Z* at 800GeV < Mℓℓ < 1200 GeV)

!

Z"' ,ZN

' ,Z#' ,ZI

' ,ZS' ,Z$

'

W’ Z’

CDF 1.12 1.071

D0 1.0 1.023

CMS 1.58 1.14

Z*

01/06/2011 23rd Rencontres de Blois 13

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W’ and W* searches §  Signature :

§  High pT isolated lepton (e,µ) and large missing energy

§  Observable : §  Transverse mass

§  Backgrounds §  W → ℓν (irreducible) Drell-Yan, ttbar, di-boson QCD multi-jet, Cosmic rays

(from data) §  Signal W’ (PYTHIA), W* (CompHep using CTEQ6L1)

!

mT = 2pT ETmiss 1" cos#lv( )

[GeV]Tm

210 310

Even

ts

-210

-110

1

10

210

310

410

510

610Data 2010W’(500)W’(1000)W’(1500)WZttbarDibosonQCD

Data 2010W’(500)W’(1000)W’(1500)WZttbarDibosonQCD

ATLAS ! W’

= 7 TeVs-1 L dt = 36 pb

[GeV]Tm

210 310

Even

ts

-210

-110

1

10

210

310

410

510

610Data 2010W’(500)W’(1000)W’(1500)WZttbarDibosonQCD

Data 2010W’(500)W’(1000)W’(1500)WZttbarDibosonQCD

ATLAS eW’

= 7 TeVs-1 L dt = 36 pb

arxiv:1103.1391 Accepted by PLB

01/06/2011 23rd Rencontres de Blois 14

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Results on W’ and W* e/µ combined result for W’ e/µ combined result for W*

§  No evidence for an excess found §  Lower limits on W’ and W* are set at 95% C.L. mW’ > 1490 GeV and mW* >1350 GeV (the most stringent to date)

[GeV]W*m500 1000 1500

B [p

b]

-210

-110

1

10 LO theoryObserved limitExpected limit

1!Expected 2!Expected

= 7 TeV,s -1 = 7 TeV, Ldt = 36 pbs lW*

ATLAS

[GeV]W’m500 1000 1500

B [p

b]

-210

-110

1

10 NNLO theoryObserved limitExpected limit

1!Expected 2!Expected

= 7 TeV,s -1 = 7 TeV, Ldt = 36 pbs lW’

ATLAS

01/06/2011 23rd Rencontres de Blois 15

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Di-lepton resonances §  Signature: Opposite charge, same flavor di-lepton (e+e-/µ+µ-) §  Observable : invariant mass of di-lepton §  Backgrounds: Z/γ* (Drell-Yan), QCD , ttbar, di-boson (WW/WZ and

ZZ), W+jets §  Signals : Z’ (PYTHIA), Z* (CompHEP using CTEQ6L1)

[GeV]eem80 100 200 300 1000 2000

Even

ts

-210

-110

1

10

210

310

410Data 2010

*Z/QCDDibosonW+Jetstt

Z’(750 GeV)Z’(1000 GeV)Z’(1250 GeV)

ATLAS

= 7 TeVs

-1 L dt = 39 pb

[GeV]!!m80 100 200 300 1000 2000

Even

ts-210

-110

1

10

210

310

410 Data 2010*Z/

Dibosontt

W+JetsQCDZ’(750 GeV)Z’(1000 GeV)Z’(1250 GeV)

ATLAS

= 7 TeVs

-1 L dt = 42 pb

arxiv:1103.6218 accepted by PLB

p-values for electron and muon are 5% and 22% - no statistically significant excess above the SM

01/06/2011 23rd Rencontres de Blois 16

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Results on Z’ and Z*

§  No evidence for resonance found

§  The e+e-/µ+µ- combined mass limits @95 C.L.

MZ’ (SSM) > 1.048 TeV MZ* > 1.152 TeV (first

limit on Z* mass)

M [TeV]0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

B [p

b]

-110

1

10Expected limit

1!Expected 2!Expected

Observed limitSSMZ’

Z’Z’

ATLAS

llZ’ = 7 TeVs

-1 L dt ~ 40 pb

E6 Z’Ψ Z’N Z’η Z’I Z’S Z’χ

Mass limit (TeV) 0.738 0.763 0.771 0.842 0.871 0.900

(Z’S and Z’I are the more stringent than previous results)

01/06/2011 23rd Rencontres de Blois 17

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§  CI model introduces hypothetical constituents of quarks and leptons that are bound together by a energy scale Λ

§  To estimate level of agreement data and MC

§  SM only pseudo experiments generated §  Deviation from the SM quantified

Contact Interactions in di-muon events

§  Use the same event selection as in heavy resonance searches §  Signal broad deviation from SM not a peak

95% C.L. Λ- >4.9 TeV Λ+ > 4.5 TeV

[GeV]!!m80 210 210"2 310 310"2

Even

ts /

bin

-210

-110

1

10

210

310

410

510Data 2010

!!DYDibosontt

W + jets = 3 TeV-

= 5 TeV-

= 5 TeV+

[GeV]!!m80 210 210"2 310 310"2

Even

ts /

bin

-210

-110

1

10

210

310

410

510ATLAS

-1 L dt = 42 pb

= 7 TeVs

[GeV]min!!m

80 210 210"2 310 310"2

min !

!Nu

mbe

r of e

vent

s ab

ove

m

-210

-110

1

10

210

310

410

510

610

[GeV]min!!m

80 210 210"2 310 310"2

min !

!Nu

mbe

r of e

vent

s ab

ove

m

-210

-110

1

10

210

310

410

510

610Data 2010

Standard Model = 3 TeV-

= 4 TeV-

= 5 TeV-

= 3 TeV+

= 4 TeV+

= 5 TeV+

ATLAS

-1 L dt = 42 pb

= 7 TeVs

L = g2!2 [!LL" L#µ"L" L#

µ"L+!RR" R#µ"R" R#µ"R+2!LR" L#µ"L" R#

µ"R ]

g2 /4$=1 and !LL, !LR,!RR=±1

arxiv:1104.4398 submitted to PRD

01/06/2011 23rd Rencontres de Blois 18

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§  RS introduces an extra spatial dimension to resolve hierarchy problem :

§  The only propagator : Gravitons and Graviton excitation (Kaluza-Klein tower) §  Search for G ⟶γγ ( G could also decay to pairs of fermions or bosons)

Randall-Sundrum Graviton in di-photon

[GeV]m200 400 600 800 1000 1200

Even

ts /

5 G

eV

-210

-110

1

10

210

Estimated bkgBkg extrapolation syst uncertainty

bkg uncertainty band (stat+syst)1 bkg uncertainty band (stat+syst)2

=0.11PlMk/1000 GeV G=0.05PlMk/

700 GeV G=0.03PlMk/550 GeVMC G

-1 L dt = 36 pb

= 7TeVsData

ATLAS Preliminary

[GeV]Gm400 600 800 1000 1200 1400

) [pb

] @ 9

5% C

L

B

r (G

!

-110

1

10

k/M = 0.02

k/M = 0.05

k/M = 0.1

Expected limit 1 "Expected

2 "Expected Observed limitLO*

-1 L dt = 36 pb

= 7 TeVs

ATLAS Preliminary

§  No evidence for narrow resonance (p-value, BumpHunter shows agreement between data and background only hypothesis)

mG > 545 (920) GeV for coupling k/MPI = 0.02 (0.1) @ 95 C.L. (mG limits for coupling 0.01 and 0.1 by D0 : 560 and 1050 GeV CDF : 459 and 963 GeV)

ATLAS-CONF-2011-044

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Conclusions

§  With the very successful LHC run in 2010, 45 pb-1 data were collected at 7 TeV

§  Many BSM scenarios studied

§  No deviations from the SM found so far §  We were able to set limits (some of the world’s best

limits) at TeV scale

2011 data taking is going very well and we are already exploring new regions ..

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BACKUP

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ttbar : Limits with “4-hardest jet”

]2Z' mass [GeV/c

500 600 700 800 900 1000

) [pb

]t t

→ B

R(Z

Z'σ

1

10

210

310

4 jets. Syst.+stat.Obs. 95% CL upper limitExp. 95% CL upper limit

uncertaintyσExp. 1 uncertaintyσExp. 2

Leptophobic Z'

4 jets. Syst.+stat.Obs. 95% CL upper limitExp. 95% CL upper limit

uncertaintyσExp. 1 uncertaintyσExp. 2

Leptophobic Z'

ATLAS Preliminary

-1 = 33 pbdt L ∫

= 7 TeVs

]2QBH mass threshold [GeV/c

1000 1500 2000 2500

[pb]

QBH

σ

210

310

4 jets. Syst.+stat.Obs. 95% CL upper limitExp. 95% CL upper limit

uncertaintyσExp. 1 uncertaintyσExp. 2

Quantum Black Hole

4 jets. Syst.+stat.Obs. 95% CL upper limitExp. 95% CL upper limit

uncertaintyσExp. 1 uncertaintyσExp. 2

Quantum Black Hole

ATLAS Preliminary

-1 = 33 pbdt L ∫

= 7 TeVs

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Di-electron candidate (Z’ search) Highest invariant mass di-electron event with 617 GeV: The highest momentum electron pT = 279 GeV η  = 1.22 φ  = 1.74 The trailing electron pT = 276 GeV η = 0.28 φ = -1.40

01/06/2011 23rd Rencontres de Blois 23


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