Dark Matter at the LHC - mpi-hd.mpg.de · Dark Matter at the LHC Tilman Plehn ... 1 1.5 theoretical uncertainty ... dN/dM 10-1 1 10 102 103 mSUGRA LM1 Zinv+tt Zinv+tt+EWK

DM@LHC

Tilman Plehn

Spectrum

Production

Jets Signature

Masses

Spins

Boosted tops

GUT?Dark Matter at the LHC

Tilman Plehn

Universitat Heidelberg

MPI-K, 7/2011

DM@LHC

Tilman Plehn

Spectrum

Production

Jets Signature

Masses

Spins

Boosted tops

GUT?

Weak-scale massesI typical model with weakly and gravitationally interacting DM (WIMP)

I some kind of R parity

I light weakly interacting sector

I heavy strongly interacting sector

I simplified models

050100150200250300350400450500

ho ˜ 1o ˜ 2

o ˜ 3o ˜ 4

o ˜ 1+ ˜ 2

+ g t1 t2 q At µ B~W~

m[GeV]

100/150/300/4/+

DM@LHC

Tilman Plehn

Spectrum

Production

Jets Signature

Masses

Spins

Boosted tops

GUT?

SUSY cross sectionsI hadron collider processes

I parton densities

I pair production via strong coupling (Feynman diagrams)

I cascade decays (Feynman diagrams)

10-3

10-2

10-1

1

10

100 200 300 400 500 600 700 800 900

χ2oχ1

+

νeνe*

t1t1*

qq

qq*

gg

qg

χ2og

χ2oqLO

maverage [GeV]

σtot[pb]: pp → SUSY √S = 7 TeV

Prospino2.1

DM@LHC

Tilman Plehn

Spectrum

Production

Jets Signature

Masses

Spins

Boosted tops

GUT?

SUSY cross sectionsI hadron collider processes

I parton densities

I pair production via strong coupling (Feynman diagrams)

I cascade decays (Feynman diagrams)

10-4

10-3

10-2

10-1

1

10

200 400 600 800 1000 1200 1400 1600

χ2oχ1

+

νeνe*

t1t1*

qq

qq*gg qg

χ2og

χ2oqLO

maverage [GeV]

σtot[pb]: pp → SUSY

√S = 14 TeV

Prospino2.1

DM@LHC

Tilman Plehn

Spectrum

Production

Jets Signature

Masses

Spins

Boosted tops

GUT?

SM cross sectionsI compared toO(10 − 100) pb for SUSYI triggersI background rejection: DM particle, leptons

0.1 1 1010-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

104

105

106

107

108

109

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

104

105

106

107

108

109

WJS2009

σjet(ETjet > 100 GeV)

σjet(ETjet > √s/20)

σjet(ETjet > √s/4)

σHiggs(MH=120 GeV)

200 GeV

LHCTevatron

eve

nts

/ sec

for L

= 1

033 c

m-2s-1

σb

σtot

proton - (anti)proton cross sections

σW

σZ

σt

500 GeV

σ (nb

)

√s (TeV)

DM@LHC

Tilman Plehn

Spectrum

Production

Jets Signature

Masses

Spins

Boosted tops

GUT?

Jets plus missing energyI missing transverse energy (kinematics)

I SUSY as role model, but analysis inclusive

I typical short/long cascades (Feynman diagrams)

I constraints in squark-gluino mass plane (mSUGRA?)

I known from Tevatron

gluino mass [GeV]0 250 500 750 1000 1250 1500 1750 2000

squa

rk m

ass

[GeV

]

0

250

500

750

1000

1250

1500

1750

2000

= 10 pbSUSYσ

= 1 pbSUSYσ

= 0.1 pbSUSYσ

)1

0χ∼Squark-gluino-neutralino model (massless

=7 TeVs, -1 = 35 pbintL

0 lepton combined exclusion

ATLAS0 lepton combined exclusion

q~LEP 2

FNAL MSUGRA/CMSSM, Run I

D0 MSUGRA/CMSSM, Run II

CDF MSUGRA/CMSSM, Run II

Observed 95% C.L. limit

Median expected limit

σ1 ±Expected limit

DM@LHC

Tilman Plehn

Spectrum

Production

Jets Signature

Masses

Spins

Boosted tops

GUT?

Fake missing energyI sources of physical missing energy (W , Z , and t t)

I sources of fake missing energy (list)

I 0.4% of the ATLAS calorimeter missing?

(GeV) missTE

200 400 600 800 1000 1200 1400 1600

m

iss

TdN

/dE

-110

1

10

210

310

410

510

610

>2j all-QCD NmissTP

>40 GeVmissT 3 + E! QCD jets

DM@LHC

Tilman Plehn

Spectrum

Production

Jets Signature

Masses

Spins

Boosted tops

GUT?

BackgroundsI W with jets from QCD (transverse mass)I QED: Poisson scalingI QCD: staircase scalingI lepton veto against W+jetsI jet veto and lepton subtraction against top pairsI mergers: Sherpa, Alpgen, Madevent

jetsn2 3 4 5 6

jets

dndN

210

310

410

510

610

2≥ jn

> 50 GeVT, j

p

-1L = 1 fb

W+jets

µW+jets, 1/4

µW+jets, 4

2≥ jn

> 50 GeVT, j

p

-1L = 1 fb

W+jets

µW+jets, 1/4

µW+jets, 4

2≥ jn

> 50 GeVT, j

p

-1L = 1 fb

W+jets

µW+jets, 1/4

µW+jets, 4

2≥ jn

> 50 GeVT, j

p

-1L = 1 fb

W+jets

µW+jets, 1/4

µW+jets, 4

jetsn2 3 4 5 6

jets

dndN

210

310

410

510

610

jetsn2 3 4 5 6

var

iati

onsα

0.5

1

1.5 theoretical uncertainty

statistical uncertainty

jetsn2 3 4 5 6

var

iati

onsα

0.5

1

1.5

jetsn2 3 4 5 6

var

iati

onµ

1

10

jetsn2 3 4 5 6

var

iati

onµ

1

10

DM@LHC

Tilman Plehn

Spectrum

Production

Jets Signature

Masses

Spins

Boosted tops

GUT?

Inclusive observablesI targeted at heavy stuff in generalI scalar momentum sums (define)I background uncertainties huge

jetN2 3 4 5 6 7 8 9 10

je

tdN

/dN

10

210

310

mSUGRA LM1Zinv+ttZinv+tt+EWK+QCD




-1 + multijets, 1 fbmissTCMS E

(GeV) missTE

200 400 600 800 1000 1200 1400 1600

mis

s

TdN

/dE

-110

1

10

210

310 mSUGRA LM1Zinv+ttZinv+tt+EWK+QCD





(GeV) TH600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800

T

dN/d

H

-110

1

10

210

310 mSUGRA LM1Zinv+ttZinv+tt+EWK+QCD





(GeV)effM600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800

eff

dN/d

M

-110

1

10

210

310mSUGRA LM1Zinv+ttZinv+tt+EWK+QCD





DM@LHC

Tilman Plehn

Spectrum

Production

Jets Signature

Masses

Spins

Boosted tops

GUT?

Inclusive observablesI targeted at heavy stuff in general

I scalar momentum sums (define)

I background uncertainties huge

[GeV]effm200 400 600 800

[1/

100

GeV

]ef

fdmdN 310

410

510

2≥ jn

> 50 GeVT, j

p

-1L = 1 fb

W+jets

µW+jets, 1/4

µW+jets, 4

2≥ jn

> 50 GeVT, j

p

-1L = 1 fb

W+jets

µW+jets, 1/4

µW+jets, 4

2≥ jn

> 50 GeVT, j

p

-1L = 1 fb

W+jets

µW+jets, 1/4

µW+jets, 4

2≥ jn

> 50 GeVT, j

p

-1L = 1 fb

W+jets

µW+jets, 1/4

µW+jets, 4

[GeV]effm200 400 600 800

[1/

100

GeV

]ef

fdmdN 310

410

510

[GeV]effm200 400 600 800

var

iati

onsα 0.9

1

1.1 theoretical uncertainty

statistical uncertainty

[GeV]effm200 400 600 800

var

iati

onsα 0.9

1

1.1

[GeV]effm200 400 600 800

var

iati

onµ

1

10

[GeV]effm200 400 600 800

var

iati

onµ

1

10

DM@LHC

Tilman Plehn

Spectrum

Production

Jets Signature

Masses

Spins

Boosted tops

GUT?

Kinematic endpointsI no invariant mass reconstructionI no transverse massI thresholds and edges in cascade decaysI lepton-lepton edge and mass-squared differences (edge)

0

50

100

150

200

0 50 100 150

mll (GeV)

dσ/

dm

ll (E

ven

ts/1

00fb

-1/0

.375

GeV

)

(a)

0

100

200

300

0 200 400 600 800 1000

mllq (GeV)

dσ/

dm

llq (

Eve

nts

/100

fb-1

/5G

eV)

(b)

0

100

200

0 200 400 600 800 1000

High mlq (GeV)

dσ/

dm

lq (

Eve

nts

/100

fb-1

/5G

eV)

(c1)

0

100

200

300

400

0 200 400 600 800 1000

Low mlq (GeV)

dσ/

dm

lq (

Eve

nts

/100

fb-1

/5G

eV)

(c2)

0

20

40

60

0 200 400 600 800 1000

mllq (GeV)

dσ/

dm

llq (

Eve

nts

/100

fb-1

/5G

eV)

(d)

0

20

40

60

80

0 200 400 600 800 1000

mzq (GeV)

dσ/

dm

zq (

Eve

nts

/100

fb-1

/5G

eV)

(e)

DM@LHC

Tilman Plehn

Spectrum

Production

Jets Signature

Masses

Spins

Boosted tops

GUT?

SPS1a measurementsI systematic errors

I theory errors and higher orders

I combinatorics

I mass differences vs masses

type of nominal stat. LES JES theo.measurement value error

mh 108.99 0.01 0.25 2.0mt 171.40 0.01 1.0mlL− m

χ01

102.45 2.3 0.1 2.2

mg − mχ0

1511.57 2.3 6.0 18.3

mqR− m

χ01

446.62 10.0 4.3 16.3

mg − mb188.94 1.5 1.0 24.0

mg − mb262.96 2.5 0.7 24.5

mmaxll : three-particle edge(χ0

2,lR ,χ01) 80.94 0.042 0.08 2.4

mmaxllq : three-particle edge(qL ,χ0

2,χ01) 449.32 1.4 4.3 15.2

mlowlq : three-particle edge(qL ,χ0

2,lR ) 326.72 1.3 3.0 13.2

mmaxll (χ0

4): three-particle edge(χ04,lR ,χ0

1) 254.29 3.3 0.3 4.1

mmaxττ : three-particle edge(χ0

2,τ1,χ01) 83.27 5.0 0.8 2.1

mhighlq : four-particle edge(qL ,χ0

2,lR ,χ01) 390.28 1.4 3.8 13.9

mthresllq : threshold(qL ,χ0

2,lR ,χ01) 216.22 2.3 2.0 8.7

mthresllb : threshold(b1,χ0

2,lR ,χ01) 198.63 5.1 1.8 8.0

DM@LHC

Tilman Plehn

Spectrum

Production

Jets Signature

Masses

Spins

Boosted tops

GUT?

SPS1a measurementsI systematic errors

I theory errors and higher orders

I combinatorics

I mass differences vs masses

Sparticle masses and mass differences [GeV]0 100 200 300 400 500 600

10χ∼

mRl

~ m

20χ∼

m

1b~m

Lq~m

g~m

10χ∼

- mg~m

10χ∼

- mLq

~m

10χ∼

- m1b

~m

10 χ∼-

m20 χ∼

m

10 χ∼-

mR l~

m

1b~

- m

g~m

DM@LHC

Tilman Plehn

Spectrum

Production

Jets Signature

Masses

Spins

Boosted tops

GUT?

Mass relationsI endpoints only using fraction of events

I mass relation methods (set of eqs)

I backgrounds and mismeasurements

DM@LHC

Tilman Plehn

Spectrum

Production

Jets Signature

Masses

Spins

Boosted tops

GUT?

MT2 magicI construct stransverse mass with endpoint

I pair production and direct decay (Feynman diagrams)

I mT 2 algorithm (formula)

I Lorentz invariance

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 eemT3 eπmT2 ππ

mTX(m[χ10]) - m[χ1

0] / GeV

DM@LHC

Tilman Plehn

Spectrum

Production

Jets Signature

Masses

Spins

Boosted tops

GUT?

Squarks or KK quarks?

DM@LHC

Tilman Plehn

Spectrum

Production

Jets Signature

Masses

Spins

Boosted tops

GUT?

Squarks or KK quarks?I general approach impossible

I hypothesis test: SUSY (dashed) vs UED (solid) (cascades)

I hierarchical spectrum: SPS1a

DM@LHC

Tilman Plehn

Spectrum

Production

Jets Signature

Masses

Spins

Boosted tops

GUT?

Boosted topsI hadronic case: top tagging

I leptonic case: missing energy (neutrino) direction (Feynman diagram)

I testable in semileptonic tops

x-1 -0.5 0 0.5 1

x

-1

-0.5

0

0.5

1

0

1

2

= 200 - 300 GeVt

p

DM@LHC

Tilman Plehn

Spectrum

Production

Jets Signature

Masses

Spins

Boosted tops

GUT?




x-1 -0.5 0 0.5 1

x

-1

-0.5

0

0.5

1

0

1

2

3

4

= 400 - 500 GeVt

p

DM@LHC

Tilman Plehn

Spectrum

Production

Jets Signature

Masses

Spins

Boosted tops

GUT?




x-1 -0.5 0 0.5 1

x

-1

-0.5

0

0.5

1

0

1

2

3

4

= 600 - 700 GeVt

p

DM@LHC

Tilman Plehn

Spectrum

Production

Jets Signature

Masses

Spins

Boosted tops

GUT?




x-1 -0.5 0 0.5 1

x

-1

-0.5

0

0.5

1

0

1

2

3

= 800 - 900 GeVt

p

DM@LHC

Tilman Plehn

Spectrum

Production

Jets Signature

Masses

Spins

Boosted tops

GUT?




[GeV]T

p0 100 200 300 400 500

φ∆

π-

/2π-

0

/2π

π

/

DM@LHC

Tilman Plehn

Spectrum

Production

Jets Signature

Masses

Spins

Boosted tops

GUT?

Measuring unification

log(Q/GeV)4 6 8 10 12 14 16

M s

ferm

ion

s (G

eV)

0

100

200

300

400

500

600

selectron and smuon L

selectron and smuon R

light squarks L

light squarks R

log(Q/GeV)4 6 8 10 12 14 16

M g

aug

ino

(G

eV)

0

100

200

300

400

500

600

Gaugino masses

M1

M2

M3

tools for parameter extraction: SFitter/Suspect, Fittino/Spheno

DM@LHC

Tilman Plehn

Spectrum

Production

Jets Signature

Masses

Spins

Boosted tops

GUT?

LiteratureI basic: Ian Aitchison’s SUSY introduction (hep-ph/0505105)I more advanced: Steve Martin’s SUSY primer (hep-ph/9709356)I review with David Morrissey and Tim Tait

New Physics at the LHC (arXiv:0912.3259) [new version on my website]

I lecture notes on QCD and Higgs physicsAn LHC Lecture (arXiv:0910.4182) [new version on my website]

I many great TASI lectures...I you’d be surprized how much of this talk happened in the last five years!

DM@LHC

Tilman Plehn

Spectrum

Production

Jets Signature

Masses

Spins

Boosted tops

GUT?

Documents

Dark Matter at the LHC - mpi-hd.mpg.de · Dark Matter at the LHC Tilman Plehn ... 1 1.5 theoretical uncertainty ... dN/dM 10-1 1 10 102 103 mSUGRA LM1 Zinv+tt Zinv+tt+EWK