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*
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*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
mSUGRA LM1Zinv+ttZinv+tt+EWK+QCD
mSUGRA LM1Zinv+ttZinv+tt+EWK+QCD
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
mSUGRA LM1Zinv+ttZinv+tt+EWK+QCD
mSUGRA LM1Zinv+ttZinv+tt+EWK+QCD
mSUGRA LM1Zinv+ttZinv+tt+EWK+QCD
-1 + multijets, 1 fbmissTCMS E
(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
mSUGRA LM1Zinv+ttZinv+tt+EWK+QCD
mSUGRA LM1Zinv+ttZinv+tt+EWK+QCD
mSUGRA LM1Zinv+ttZinv+tt+EWK+QCD
-1 + multijets, 1 fbmissTCMS E
(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
mSUGRA LM1Zinv+ttZinv+tt+EWK+QCD
mSUGRA LM1Zinv+ttZinv+tt+EWK+QCD
mSUGRA LM1Zinv+ttZinv+tt+EWK+QCD
-1 + multijets, 1 fbmissTCMS E
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?
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
3
4
= 400 - 500 GeVt
p
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
3
4
= 600 - 700 GeVt
p
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
3
= 800 - 900 GeVt
p
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
[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?