Second MCTP Spring Symposium on Higgs Boson PhysicsAnn Arbor, April 16-20, 2012

Search for Higgs Bosons Beyond the StandardModel with ATLAS

Christoph AndersOn behalf of the ATLAS Collaboration

Universität Heidelberg

April 18th 2012

Overview 2/26

Fermiophobic Higgs bosonsH → γγMSSM neutral Higgs bosonsh/H/A→ ττCharged Higgs bosons:

H+ → τhadνH+ → τ`νH+ → cs̄

Doubly charged Higgs bosonsH++ → µ+µ+

NMSSM light neutral Higgs bosonsa1 → µµ

New preliminary resultswith 4.9fb−1

Preliminary results with 1.06fb−1

Submitted to JHEPlast week! (4.7fb−1)

Preliminary results with 0.035fb−1

Published in PRL(1.6fb−1)

Preliminary results with 0.037fb−1

Fermiophobic Higgs Bosons I 3/26Basics

2HDM and Higgs triplet models withreduced couplings to fermions.Simple benchmark scenario:

No fermion-Higgs couplingsSM boson-Higgs couplings

Production in VBF and associatedwith W /Z

Decay: γγ, WW , ZZ , Zγ

σ × BR larger than SM for light Higgsbosons

Higher pT (recoil)

σ × BR:

[GeV]HM100 150 200 250

BR

[pb]

× -310

-210

-110

1

10

210

LHC

HIG

GS

XS W

G 2

011

Fermiophobic = 7TeVs

(SM)

Z (SM)Z

WW

WW (SM)

ZZ

ZZ (SM)

LHC HIGGS XS WG 2011

Fermiophobic Higgs Bosons II 4/26Selection (Identical to SM H → γγ)

2 isolated photons,pT > 40 GeV, 25 GeV

100 < mγγ < 160 GeV

9 categories

Presence of photon conversionsPhoton calorimeter impact pointpTt, component of pT ,γγ ⊥ γγ-thrust axis

mγγ signal model:Crystal Ball + wide Gaussian(tail)

mγγ background model:Falling exponential

Fermiophobic Higgs Bosons III 5/26Exclusion Limits

Largest excess at mH = 125.5 GeVSignificance including look-elsewhere effect:1.6σ(Or 5% prob. for a background fluctuation)

Exclusion limitsat 95% confidence level using theprofile likelihood method with CLS

Expected mH exclusion:110.0− 123.5 GeVObserved mH exclusion:110.0− 118.0 GeV and119.5− 121.0 GeV

Neutral MSSM Higgs Bosons I 6/26Basics

2 Higgs-doublets → 5 Higgs bosonsΦ = H, h,A,H±

Free parameters at tree level: mA,tanβ = vu/vd

Enhanced couplings to b and τ in large partsof the parameter space (σbbA ≈ tan2 β)

Production:

Neutral MSSM Higgs Bosons II 7/26Hadronic Tau Decay Signature and Identification

Typical signature:

One or three charged tracks

Collimated calorimeter energy deposits

Large leading track momentumfraction

Secondary vertex reconstruction

Neutral MSSM Higgs Bosons III 8/26Selection

e + µ:

1 isolated e,pT > 22 GeV

1 isolated µ,pT > 20 GeV

Opposite charges

∆Φ(e, µ) > 2rad

PeT + PµT + E

missT

< 120 GeV

e/µ+ τhad:

1 isolated e/µ,pT > 25/20 GeV

1 τhad,pT > 20 GeV

Opposite charges

Di-lepton veto

EmissT > 20 GeV

mT < 30 GeV

τhad + τhad:

Di-τhadtrigger

2 τhad,pT > 45/30 GeV

Opposite charges

Light lepton veto

EmissT > 30 GeV

[GeV]µT,

+pT,e

+pT,missE

0 50 100 150 200 250 300 350 400

Events

/ 1

0 G

eV

0

100

200

300

400

500

600

700

800

900Data 2011

=20β, tanττ →A(120)/h/H ) embeddedττ→*(γZ/

Others

Diboson

QCD multi-jet

& single-tttsyst.

PreliminaryATLAS

-1Ldt = 1.06 fb∫ = 7 TeV, s

channelµe

[GeV]T,missE

0 10 20 30 40 50 60 70 80 90 100

Eve

nts

/ 2

Ge

V

0

100

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500

[GeV]T,missE

0 10 20 30 40 50 60 70 80 90 100

Eve

nts

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Ge

V

0

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200

300

400

500Data 2011

=20β, tanττ→A(120)/H/h) emb.(OS-SS)ττ→*(γZ/

Others(OS-SS)

W+jets (OS-SS)

Same Sign

stat.

channelshad

τµ + hadτe

-1 L = 1.06 fb∫ = 7TeV, s

ATLAS Preliminary

[GeV]missTE

0 20 40 60 80 100E

vents

/ 5

GeV

0

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120

140

[GeV]missTE

0 20 40 60 80 100E

vents

/ 5

GeV

0

20

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60

80

100

120

140 Data 2011=20β, tanττ →A(200)/H/h

Multi-Jet

)ττ→*(γZ/

) + jetsντ→W(

Others

stat.

-1Ldt = 1.06 fb∫ = 7 TeV, s

PreliminaryATLAS

channelhad

τhad

τ

Neutral MSSM Higgs Bosons IV 9/26Mass Reconstruction

Invariant mass mvis of visible decay products

Effective mass: meff =√

(pe + pµ + pmiss)2, withpmiss = (E

missT ,E

missx ,E

missy ,E

missz = 0).

New method called Missing Mass Calculator (MMC)(see arXiv:1012.4686)

MMC (lep-had case):7 unknowns: “Missing” 3-momenta and massof νν system

4 constraints: EmissT ,x , EmissT ,y , mτ1 , mτ2

→ scan ∆Φ1(ντ , h), ∆Φ2(ντν`, `), mννWeight solutions according to probability of 3Dangle in solution ↘

Maximum of weighted mττdistribution is the MMC mass mMMC

meff :

mMMC:

[rad]3Dθ∆0 0.05 0.1 0.15 0.2

Arb

itrar

y un

its

0

0.005

0.01

0.015 ATLAS Simulation

Simulationττ→Z

Probability function

decayτ1-prong 50 [GeV]≤τ45

Neutral MSSM Higgs Bosons V 10/26Background Estimation

Based on data control samples:

Z/γ∗ → ττ from “τ -embedded”Z/γ∗ → µµ data sampleQCD multijet backgrounds fromcontrol samples with same-signcharges and low EmissT orinverted lepton isolation

W+jets from high mT (`,EmissT )

control region

[GeV]ττMMC m

0 50 100 150 200 250 300

Eve

nts

/ 10

GeV

0

50

100

150

200

250

300

µ µ →* γEmbedded Z/

MCτ τ →* γZ/

channelshadτµ + hadτe

-1L dt = 1.06 fb∫ = 7 TeV, s

ATLAS Preliminary

Neutral MSSM Higgs Bosons IV 11/26Results

e + µ: e/µ+ τhad: τhad + τhad:

effective [GeV]ττm

0 50 100 150 200 250

Eve

nts

/ 10

GeV

0

100

200

300

400

500

600

700 Data 2011=20β, tanττ →A(120)/h/H

) embeddedττ→*(γZ/OthersDibosonQCD multi-jet

& single-tttsyst.

PreliminaryATLAS

-1Ldt = 1.06 fb∫ = 7 TeV, s

channelµe

[GeV]ττMMC m

0 50 100 150 200 250 300 350 400

Eve

nts

/ 10

GeV

0

50

100

150

200

250

300

350

400

[GeV]ττMMC m

0 50 100 150 200 250 300 350 400

Eve

nts

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GeV

0

50

100

150

200

250

300

350

400Data 2011

=20β, tanττ→A(120)/H/h) emb.(OS-SS)ττ→*(γZ/

Others(OS-SS)W+jets (OS-SS)Same Signstat.

channelshad

τµ + hadτe

-1 L = 1.06 fb∫ = 7TeV, sATLAS Preliminary

visible [GeV]ττm

0 100 200 300 400 500 600

Eve

nts

/ 15

GeV

0

10

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30

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60

70

visible [GeV]ττm

0 100 200 300 400 500 600

Eve

nts

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GeV

0

10

20

30

40

50

60

70Data 2011

=20β, tanττ →A(200)/H/h

Multi-Jet

)ττ→*(γZ/

) + jetsντ→W(

Others

stat.

-1Ldt = 1.06 fb∫ = 7 TeV, s PreliminaryATLAS

channelhadτhadτ

Final state Exp. Background Data

eµ (2.6± 0.2)× 103 2472`τhad (2.1± 0.4)× 103 1913τhadτhad 233

+44−28 245

Sum (4.9± 0.6)× 103 4630

Neutral MSSM Higgs Bosons VII 12/26Exclusion Limits (ATLAS-CONF-2011-132)

[GeV]φm

100 200 300 400 500 600

) [p

b]

ττ →φ

BR

(× φ

σ95%

CL u

pp

er

limit o

n

-110

1

10

210

310 CLsφ →Observed gg

φ →Expected gg

CLsφObserved bb

φExpected bb) theory ττ→

SM x BR(H

SMσ

-1 Ldt = 1.06 fb∫ = 7 TeV, s

All channels

ATLAS Preliminary

[GeV]Am

100 150 200 250 300 350 400 450β

tan

0

10

20

30

40

50

60All channels

-1 Ldt = 1.06 fb∫ = 7 TeV, s

>0µ, maxhm

ATLAS Preliminary

Observed CLs

Expected CLs

σ 1±σ 2±

LEP

observed-1

ATLAS 36 pb

expected-1

ATLAS 36 pb

σ × BR(Φ→ ττ)

Assume only one resonnance Φ

Pure gg → Φ or pure bbΦ production

mA, tan β plane

Need to assume specific (c)MSSM scenario

Here: mmaxh scenario

Neutral MSSM Higgs Bosons VIII 13/26Comparison of Search Channels

[GeV]Am

100 150 200 250 300 350 400 450

βta

n

0

10

20

30

40

50

60All channels

-1 Ldt = 1.06 fb∫ = 7 TeV, s

>0µ, maxhm

ATLAS Preliminary

Observed (hh only)

Observed (lh only)

Observed (emu only)

Observed CLs

Expected (hh only)

Expected (lh only)

Expected (emu only)

Expected CLs

LEP

Update to full 4.9fb−1 data set and with inclusion of b-tagging inprogress!

Charged Higgs Bosons I 14/26Basics

Predicted in Higgs doublet (e.g.MSSM) and triplet models

mH+ < mt : dominantly produced intop quark decays

mH+ > mt : gb → tH+ production

important (more data needed)

For tanβ > 3 preferred decay mode isH+ → τν (here: assume 100%, unless MSSM)

Channels:

Charged Higgs Bosons II 15/26Lepton+Jets Channel – Selection

1 isolated e/µ, pT > 25/20 GeV

≥ 4jets (2 b-tagged), pT > 20 GeVEmissT > 40 GeV if |Φ`,miss| ≥ π/6

EmissT × | sin Φ`,miss| > 20 GeV if |Φ`,miss| < π/6

Minimize χ2 =(mjjb−mtop)

2

σ2top+

(mjj−mW )2

σ2W

to get “hadronic side”

Discriminating variables: cos Θ∗` =2m2bl

m2top−m2W

− 1 ≈ 4pb·p`

m2top−m2W

− 1

(mHT )2 = (

√m2top + ( ~pT

` + ~pTb + ~pT

miss)2 − pbT)2 − ( ~pT` + ~pTmiss)2

Discriminatesbetween e/µfrom W andτ .

Lower boundon chargedboson(W /H+) mass

Signal region: cos Θ∗` < −0.6 and mEmissT ,`

T < 60 GeV

Charged Higgs Bosons III 16/26Lepton+Jets – Channel Results

Dominant background: tt̄, simulated withMC@NLO, normalized in −0.2 < cos Θ∗` < 1data control region

Misidentified-lepton background determinatedfrom control sample with loosened lepton ID

Charged Higgs Bosons IV 17/26τhad+Lepton Channel – Selection

1 τhad, pT > 20 GeV

1 e/µ, pT > 25/20 GeV, opposite charge

≥ 2 jets, pT > 20 GeV, including ≥ 1 b-tagged jet∑ptracksT > 100 GeV, for tracks asociated to

primary vertex

Discriminatingvariable: EmissT−→

Misidentified taus background:e: ≈ 1%, jets: ≈ 55%; jet→τhadmis-ID measured with W+jetsTrue tau background taken from simulation

Charged Higgs Bosons V 18/26τhad+Lepton Channel – Candidate Event

Charged Higgs Bosons VI 19/26τhad+jets Channel – Selection

τhad+ EmissT trigger

1 τhad, pT > 40 GeV

≥ 4 jets, pT > 20 GeV, at least one b-tagged

Veto: ≥ 2 τhad and light leptons

EmissT significance:EmissT

0.5√∑

pT> 13 GeV1/2

EmissT > 65 GeV

jjb combination (highest pT one)consistent with mtop

Discriminating variable:

mT =√

2pτhadT E

missT (1− cos∆φ)

True-tau background estimatedfrom τ embedded µ+jets events(with tt̄ like event topology)

Charged Higgs Bosons VII 20/26Results – τhad+jets Channel

Estimate multijet background byfitting EmissT shapes to data incontrol sample with inverted τ and bID.

Charged Higgs Bosons VIII 21/26Exclusion Limits (arXiv:1204.2760)

Combination: Tevatron Limits:BR < 15− 20%

Charged Higgs Bosons IX 22/26Exclusion Limits – MSSM (arXiv:1204.2760)

Combination:

Charged Higgs Bosons XI 23/26H+ → cs̄ (ATLAS-CONF-2011-094)

H+ → cs̄ is sizable fortanβ < 1

Suppress multijetbackground by requiringlarge EmissT and mT

Kinematic fit with W andtop mass contraints to findbest H+ candidate

AssumeBR(H+ → cs̄) = 100%, toset limits on BR(t → H+b)

Doubly Charged Higgs 24/26(ATLAS-CONF-2011-127)

Predicted in left-rightsymmetric, Higgs triplet andlittle Higgs models

Select same sign di-muons,pT > 20 GeV

Look for resonance in di-muonmass spectrum

95% confidence limits, exclude:Right-handed Higgs mass < 251 GeVLeft -handed Higgs mass < 355 GeVWith BR(H++ → µµ) = 100%

NMSSM a1 → µµ 25/26(ATLAS-CONF-2011-020)

NMSSM: additional complexsinglet scalar field to solve µproblem→ 3 CP-even scalars (h1, h2, h3)and 2 CP-odd scalars (a1, a2)

a1 can be very light, i.e.ma1 < 2mb!

Selection:

Opposite sign di-muons,pµT > 4 GeV

Likelihood ratio selectionbased on µ+µ− vertex χ2

and µ isolation

Limit setting by fit to massspectrum

Υ region excluded

Conclusions 26/26

Many interesting beyond SM Higgs scenarios are beingprobed!

New: Fermiphobic H → γγ, charged Higgs H+ → τνMSSM neutral h/H/A→ ττ , charged H+ → cs̄,H++ → µ+µ+, NMSSM a1 → µ+µ−

No indication of a signal yet...but: lots of limits on cross sections and branching ratios!

The searches are being continued with improved methods andnew data.→ There’s still lots of parameter space to cover within thisyear and after!

Backup 27/26

BackupBackup

Backup

Fermiophobic Higgs Boson 28/26

Systematic uncertainties: Signal Model vs. MC:

Fermiophobic and SM(arXiv:1202.1414) Limit:

Neutral MSSM Higgs Bosons – MSSM Higgs Sector 29/26

2 Higgs-doublets → 5 Higgs bosonsΦ = H(CP = 1), h(CP = 1),A(CP = −1),H±

Free parameters at tree level: mA, tanβ = vu/vd

Fixed mass relations at tree level:m2H,h =

12

(m2A + m

2Z ±

√(m2A + m

2Z )

2 − 4m2Zm2A cos2 2β)

m2h ≤ m2Z cos2 2β ≤ m2ZUpper mass bound modified byradiative corrections (depending onSUSY parameters)

Benchmark scenarios (everythingfixed but mA, tanβ:

Neutral MSSM Higgs Bosons – MSSM Higgs Sector II 30/26

Enhanced coupling to 3rd generation:

Dominant production processes: Branching ratios:

Neutral MSSM Higgs Bosons – Final States andBackgrounds 31/26

Final states considered:

1 “lepton-hadron”: ττ → `τhad (3ν) with ` = e/µ

2 “lepton-lepton”: ττ → eµ(4ν)

3 “hadron-hadron”: ττ → τhadτhad (2ν)

Signal and background samples:

Signal process (mA = 120GeV , tanβ = 20) σ × BR [pb] Generatorbb̄A/H/h(→ ττ) ↘ mh = 118GeV 7.62/0.69/7.3 Sherpagg → A/H/h(→ ττ) mH = 130GeV 4.93/2.21/4.1 POWHegBackground process σ [pb] GeneratorW → `ν (` = e, µ, τ) 10.5× 103 AlpgenZ/γ∗ → `+`− (m`` > 10GeV ) 4.96× 103 Alpgen/Pythiatt̄ 165 MC@NLOSingle-top (t-, s- and Wt-channels) 58.7, 3.9, 13.1 MC@NLO/AcerDi-boson (WW , WZ and ZZ) 46.2, 18.0, 5.6 Herwig/MC@NLOQCD multijet ??? –

Neutral MSSM Higgs Bosons – MMC 32/26

[rad]3Dθ∆0 0.05 0.1 0.15 0.2

Arb

itrar

y un

its

0

0.005

0.01

0.015 ATLAS Simulation

Simulationττ→Z

Probability function

decayτ1-prong 50 [GeV]≤τ45

Neutral MSSM Higgs Bosons – Z → ττ Background 33/26

Reliable model of mass distribution shape is essential (lowmass Higgs)

Real Z → ττ data would be ideal, but it cannot be selectedsignal free

Instead: use high purity Z → µµ sample (≈signal free, due tosmall Higgs muon coupling)

Neutral MSSM Higgs Bosons – Z → ττ Embedding 34/26

Select Z → µµ dataevents

Remove muon tracks andnearby calorimeter cells

Simulate standaloneZ → ττ decays, so that τfour-momenta match theoriginal muon ones

Merge into singleMC-data hybrid event

Re-reconstruct objectsand EmissT

Neutral MSSM Higgs Bosons – Embedding II 35/26

lep-had: lep-lep:

[GeV]ττMMC m

0 50 100 150 200 250 300

Eve

nts

/ 10

GeV

0

50

100

150

200

250

300

µ µ →* γEmbedded Z/

MCτ τ →* γZ/

channelshadτµ + hadτe

-1L dt = 1.06 fb∫ = 7 TeV, s

ATLAS Preliminary

effective [GeV]ττm

0 50 100 150 200 250 300

Ent

ries

/ 10

GeV

0

100

200

300

400

500

600

µµ →* γEmbedded Z/

MCττ →* γZ/

PreliminaryATLAS

-1Ldt = 1.06 fb∫ = 7 TeV, s

channelµe

Replaces Z → ττ MC shapes in the following.

Neutral MSSM Higgs Bosons – Embedding III 36/26

had-had:Z → ττ W → τν

visible [GeV]ττm

0 50 100 150 200

Fra

ctio

n of

Eve

nts

/ 10

GeV

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

µµ→*γEmbedded Z/

MCττ→*γZ/

-1Ldt = 1.06 fb∫ = 7 TeV, s

PreliminaryATLAS channelhadτhadτ

visible [GeV]ττm

0 50 100 150 200

Fra

ctio

n of

Eve

nts

/ 20

GeV

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

νµ→Embedded W

MCντ→W

-1Ldt = 1.06 fb∫ = 7 TeV, s

PreliminaryATLAS channelhadτhadτ

Used as cross check.

Neutral MSSM Higgs Bosons – Background Estimation –QCD 37/26

Separate QCD estimates for all final states using an“ABCD”-method. 4 regions based on:

lepton-hadron:

Charge product and lepton isolation, shape: region C

lepton-lepton:

Charge product and lepton isolation, shape: region B

hadron-hadron:Charge product and Tau ID, shape: region B

Subtract non QCD backgrounds in CRs B,C,D (for lep-had W+ jetsnormalization is fixed in high mT region)

For lep-had, QCD in signal region A:

nQCDA = rB/D × n(data−non QCD MC)C (similar for lep-lep & had-had)

Neutral MSSM Higgs Bosons – Estimation of QCD &W+jets in Lepton-Hadron 38/26Basic idea and assumptions

Charge correlation: qlep × qτ =−1→ “Opposite Sign′′(OS) Signal+1→ “Same Sign′′(SS)

=⇒ nBkgOS = nBkgSS + n

QCDOS−SS + n

W +JetsOS−SS + n

ZOS−SS + n

otherOS−SS

≈ 0

Data with qlep × qτ = +1

W+jets: n(OS) > n(SS)

⇒ W+jets Add-On

Normalization from mT > 50 GeVcontrol sampleMMC mass shape from MC

Shape and normalization for Z → ττ andother BGs from Embedding/MC

Neutral MSSM Higgs Bosons – Background Estimationhad-had 39/26

QCD multijet background from ABCD

Other backgrounds taken from simulation

Corrections for trigger and tau “fake rate” appliedW /Z MC cross-checked with embedding

Tau trigger and ID efficiencies are measured in Z → τhadτµFake tau trigger efficiency and tau fake rate measured inW → µν + jets

Neutral MSSM Higgs Bosons – Cross-check of 2Background Estimates – lep-had 40/26

Same-Sign method: ABCD method:

[GeV]ττMMC m

0 50 100 150 200 250 300 350 400

Eve

nts

/ 10

GeV

0

50

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250

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[GeV]ττMMC m

0 50 100 150 200 250 300 350 400

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GeV

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250

300

350

400Data 2011

=20β, tanττ→A(120)/H/h) emb.(OS-SS)ττ→*(γZ/

Others(OS-SS)W+jets (OS-SS)Same Signstat.

channelshad

τµ + hadτe

-1 L = 1.06 fb∫ = 7TeV, sATLAS Preliminary

[GeV]ττMMC m

0 50 100 150 200 250 300 350 400

Events

/ 1

0 G

eV

0

50

100

150

200

250

300

350Data 2011

=20β, tan τ τ →A(120)/H/h

) emb.ττ→(*

γZ/

Others

W+jets

QCD multi-jet

stat.

ATLAS Preliminary

-1Ldt = 1.06 fb∫ = 7 TeV, s

channelshad

τµ + hadτe

Good agreement.

Neutral MSSM Higgs Bosons – Systematics 41/26

ll/lh/hh W+jets Di-boson tt̄+ Z/γ∗ → Z/γ∗ → Signal,tanβ = 20single-top ee, µµ τ+τ− 120/120/200GeV

σinclusive -/-/5 7 10 5/5/- 5 14/14/16

Acceptance -/-/20 4/2/7 3/2/9 2/14/- 5/14/14 5/7/9

e efficiency -/-/0.8 4/3.1/0.5 4/3.6/0.3 4/3.1/- 4/3.0/0.5 4/3.6/0.1

µ efficiency -/-/0.3 2/1.2/0.4 2/1.1/0.0 2/1.3/- 2/1.8/0.4 2/1.0/0.1

τ efficiency/fake rate -/-/21 -/9.1/15 -/9.1/13 -/48/- -/9.1/15 -/9.1/15

Energy scales/resolution -/-/+34−21 2/+19−9 /

+26−12 6/

+5−4/12 1/

+39−25/- 1/11/

+63−23 1/

+30−23/

+9−8

Luminosity -/-/3.7 3.7 3.7 3.7/3.7/- 3.7 3.7

Total uncertainty -/-/+45−36 10/+23−16/

+32−22 13/15/23 8/

+64−56/- 9/21/

+67−31 16/

+35−30/

+26−25

Background estimation:

Same Sign stat. 17%

OS/SS ratio 19%

W normalization 11%

Z embedding

Charged Higgs Misidentified Lepton BackgroundEstimation 42/26

Control samples, with only lepton ID changed:Tight sample, containing mostly true leptonsLoose sample, containing mostly fake leptons (looser ID&Isolation)Number of mis-IDed and real leptons: NLm, N

Tm , N

Lr , N

Tr

NL = NLm + NLr

NT = NTm + NTr

Number of mis-IDed events passing the selection is then defined as:NTm =

pmpr−pm (prN

L − NT )

with pr =NTrNLr

(from Z → `` events)

and pm =NTmNLm

(from multijet events)

Charged Higgs Systematic Uncertainties I 43/26

Charged Higgs Systematic Uncertainties II 44/26

Doubly Charged Higgs – Yields and More Plots 45/26

NMSSM a1 → µµ Systematic Uncertainties 46/26