1 c. mills (edinburgh) 12 january 2015 higgs physics at atlas from the ww perspective corrinne mills...
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1c. mills (Edinburgh)12 January 2015
Higgs physics at ATLAS Higgs physics at ATLAS from the WW from the WW
perspectiveperspectivecorrinne mills
(University of Edinburgh)
Presentation at UPenn12 January 2015
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OverviewOverview• Study of the Higgs boson discovered at 125 GeV in 2012 has been a
fruitful enterprise So far, everything (interactions, quantum numbers) is in excellent agreement
with the Standard Model predictions
• H WW is a powerful channel for rate measurements Balance between large event yield and manageable S/B
• Final Run I results in WW channel are out! Substantial improvement since Moriond ‘13 (same dataset)
40% improvement in observed significance (4.3 6.1) and 65% in expected (3.5 5.8)
Reimagined almost every aspect of the analysis
Objects, background estimates, signal categorization Can’t cover an 80 page paper here, picking a few favorite things
Working on this measurement since mid-2011 and convener of the WW Higgs analysis group since March 2014
• Knowledge and tools gained apply to some of the most interesting measurements in the next LHC runs
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The MeasurementsThe Measurements
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The Standard Model The Standard Model Higgs BosonHiggs Boson
H
V
V
H
f
f
H
H
H
tree-level (LO) interactions:
Standard Model makes a very specific set of predictions for the Higgs bosonSpin-zero scalar particleResponsible for electroweak symmetry breaking (masses of W and Z bosons)Posited to give mass to all elementary particlesInteractions completely determined by the mass of the Higgs boson, the mass of the other particle, and the vacuum expecation value v
Standard Model makes a very specific set of predictions for the Higgs bosonSpin-zero scalar particleResponsible for electroweak symmetry breaking (masses of W and Z bosons)Posited to give mass to all elementary particlesInteractions completely determined by the mass of the Higgs boson, the mass of the other particle, and the vacuum expecation value v
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The Large Hadron The Large Hadron Collider, CERNCollider, CERN
The AlpsThe Alps
Lac LemanLac Leman
CERNCERN
GenèveGenève
airplanes go hereairplanes go here
world’s highest energy world’s highest energy particle colliderparticle colliderpp collisions at pp collisions at sqrt(s) = 8 TeVsqrt(s) = 8 TeV
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SM Higgs Boson SM Higgs Boson ProductionProduction
• LHC collisions are qq, gg, qg, qqbar (energetic protons gluons ⇒and sea quarks matter)
• H is colorless, gluon is massless no (direct) strong production⇒
• direct qqbar production suppressed by mq2/v
• LHC collisions are qq, gg, qg, qqbar (energetic protons gluons ⇒and sea quarks matter)
• H is colorless, gluon is massless no (direct) strong production⇒
• direct qqbar production suppressed by mq2/v
g
g
H
q’ q’’
q q’
W+
W–
H
ggFggF
VBFVBF
t, b, etc…
HW/Z(*)
W/Z
q
q
VHVH
ttHttH
g
gt
t
H
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SM Higgs Boson SM Higgs Boson ProductionProduction
g
g
H
q’ q’’
q q’
W+
W–
H
ggFggF
VBFVBF
t, b, etc…
HW/Z(*)
W/Z
q
q
VHVH
ttHttH
g
gt
t
H
process 8 TeV 13 TeV
ggF gluon-gluon fusion 19 pb 44 pb
VBF vector-boson fusion 1.6 pb 3.7 pb
VH associated production 1.1 pb 2.2 pb
ttH associated production 0.13 pb 0.51 pb
Cross sections for mH=125 GeV:
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H → diphoton (H → diphoton ()) • : good sensitivity at low mH, full mH
reconstruction from photon 4-vectors• Nothing else in the SM gives you a
resonant peak in the diphoton spectrum
• : good sensitivity at low mH, full mH reconstruction from photon 4-vectors
• Nothing else in the SM gives you a resonant peak in the diphoton spectrum
t, W, …H
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H → ZZ → 4lH → ZZ → 4lZZ: 4l channel (with Z → ee, Z → ) has excellent S/B, best resolution for mH reconstruction, but low branching ratio to 4l
ZZ: 4l channel (with Z → ee, Z → ) has excellent S/B, best resolution for mH reconstruction, but low branching ratio to 4l
Z
Z(*)H
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Detection: Fermionic Detection: Fermionic decaysdecaysbb and : large BRs at low mH, full mass reconstruction (but worse resolution than leptons or s), huge continuum background
bb and : large BRs at low mH, full mass reconstruction (but worse resolution than leptons or s), huge continuum background
f
f
H
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H → WW → lH → WW → lllW+
W–
’
125
~22%H
WW channel well-suited to exploring rare production modes and searching at high-mass
Large branching ratio and good S/B from clean dilepton signature
WW channel well-suited to exploring rare production modes and searching at high-mass
Large branching ratio and good S/B from clean dilepton signature
channel(pp→H)@ 8 TeV BR (H→VV) BR(VV→4l)
evt. yield in 20 fb-1
S/B (approx.)
H →
22.3 pb
0.0023 - 1000 0.03 – 0.5
H → ZZ → 4l 0.026 0.0011 130 2
H → WW → ll 0.22 0.047 4700 0.1 – 0.4
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The ATLAS DetectorThe ATLAS Detector
Inner Detector (tracking):Pixels (silicon)SCT (silicon strips)TRT (straw tubes / ionization)
Electromagnetic calorimeterLiquid Argon (LAr) with lead absorber
Hadronic calorimeter (jets, hadrons)Steel absorber + scintillatorLAr with copper/tungsten absorber
Solenoid
Toroids
Muon Detectors: large radii for precise momentum measurement Precision: Drift tubes (MDT) and Cathode Strip Chambers (CSC)Trigger: Resistive Plate Chamber (RPC) and Thin Gap Chamber (TGC)
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Hadron Collider Hadron Collider KinematicsKinematics
beam axisz
x
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Jets and b-taggingJets and b-tagging
Final state quarks and gluons fragment to produce additional quarks and gluons and hadronize into colorless particles (p, n, , , etc.)
Identified as a collimated “jet” of particles in tracker and calorimeter
Final state quarks and gluons fragment to produce additional quarks and gluons and hadronize into colorless particles (p, n, , , etc.)
Identified as a collimated “jet” of particles in tracker and calorimeter
Hadrons containing heavy quarks (b, c) travel some distance in the detector and can be identified by the resulting displaced tracks and decay vertices
“tagging” of b-jets: we use 85% efficient operating point
Hadrons containing heavy quarks (b, c) travel some distance in the detector and can be identified by the resulting displaced tracks and decay vertices
“tagging” of b-jets: we use 85% efficient operating point
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Electrons and MuonsElectrons and Muons• A pair of charged leptons is the foundation of the event selection
Guiding principle: reasonable efficiency and ruthless suppression of background from fake and non-prompt leptons
Why do we care? W+jets, that’s why:
(pp H WW ll) = 0.23 pb vs (pp W l) = 12,000 pb
• Muons: combined track from inner detector and muon spectrometer
• Electrons: cluster in EM calorimeter combined with inner detector track
• Isolation requirements check that there is not substantial activity in a small cone around the lepton direction (as from a jet)
Use both calorimeter and tracking information
• Impact parameter requirements reject leptons from heavy flavor decay
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Missing Transverse Missing Transverse EnergyEnergy
Detect neutrinos by summing up all of the other objects in the event•fully reconstructed objects (leptons, jets, photons) and “soft” stuff
invoke conservation of momentum in the plane transverse to the beam:
“Missing Transverse Energy”
corresponds to the transverse energy of the neutrinos in the event
Detect neutrinos by summing up all of the other objects in the event•fully reconstructed objects (leptons, jets, photons) and “soft” stuff
invoke conservation of momentum in the plane transverse to the beam:
“Missing Transverse Energy”
corresponds to the transverse energy of the neutrinos in the event
… but we have two neutral leptons – the neutrinos – to account for as well:
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TrackMETTrackMET• ETmiss from resolved objects (leptons, jets,
photons) and “soft term” of not-otherwise-identified objects, usually hadrons
• Soft term from tracks gives better resolution than hadron clusters for high pileup
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The WW analysisThe WW analysis
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The H The H WW signature WW signature
W
W*
Final-state signature: 2 charged leptons + 2 neutrinos
Off-shell W (mH < 2mW) means one lepton is soft
Final-state signature: 2 charged leptons + 2 neutrinos
Off-shell W (mH < 2mW) means one lepton is soft
(soft)
jets depend on production mode(VBF has two at LO)
jets depend on production mode(VBF has two at LO)
spin zero initial state influences final-state kinematics
spin zero initial state influences final-state kinematics
from 1201.3084v1
MT0 mH
Transverse mass MT: Like invariant mass, but drop missing pz information signal discriminant
Transverse mass MT: Like invariant mass, but drop missing pz information signal discriminant
g
g
H
t, b, …
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Begin from the beginning: two charged leptons (e or ) and missing transverse energy*:
Stacked plots show signal and background, compared to the data
[Yep, signal is so small as to be (almost) invisible here.]
e
ee/
Event selection vs. Event selection vs. backgroundsbackgrounds
* no missing ET cut applied in e VBF channel
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The backgroundsThe backgrounds
g
g
t
t
t W+
W–
b
b
W+
W–
q
q
Z/*
WW: quasi-irreducible
top: has jetsthe “easy” ones:
Z/* → → ll(not illustrated)
cake diagrams?
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The backgroundsThe backgrounds
q
q’
W±
g
W+jets: fake leptons
the tricky ones:
q
q
Z/*
Z/*: no neutrinos
W(*): soft/lost/merged leptons, q
W±
q *
split in two,show next to plots
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Event Selection & Higgs Event Selection & Higgs topologytopology
• Reject dominant BG like WW and Z and by using the spin correlations
Leptons tend to not be back-to-back, and one lepton is soft because of the off-shell W (mH < 2mW)
• Importance of pink (VV) and light blue (W+jets) grows
• Reject dominant BG like WW and Z and by using the spin correlations
Leptons tend to not be back-to-back, and one lepton is soft because of the off-shell W (mH < 2mW)
• Importance of pink (VV) and light blue (W+jets) grows
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Event selection vs. Event selection vs. backgroundsbackgrounds
• We start from the basics: two leptons and (usually) missing transverse energy, and then we split the data by the number of jets and by the flavor of the lepton pair
• Then we apply additional criteria to improve the signal-to-background ratio
• For most backgrounds, we can use one or two key event properties to reject them while keeping most signal
• The events that fail that requirement are typically enriched in the target background. We use these to normalize the background in question
reduces the uncertainties associated with theoretical cross sections with event requirements, particularly exclusive jet requirements
• Textbook example: irreducible background from continuum WW
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WW background and mWW background and mllllIn the zero-jet categories the dominant background is WW
Normalize to data in signal-depleted “control regions” (CR)
In the zero-jet categories the dominant background is WW
Normalize to data in signal-depleted “control regions” (CR)
55 110
extrapolate using MC simulation
Normalize to data subtract other
processes
validation region
signal region
control region
Dilepton invariant mass mll is a good signal discriminant because the spin-0 of the Higgs boson, combined with V-A structure of W decay correlates lepton directions
Dilepton invariant mass mll is a good signal discriminant because the spin-0 of the Higgs boson, combined with V-A structure of W decay correlates lepton directions
Estimated background
even
ts /
10 G
eV
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Better Living through Better Living through CategoriesCategories
• Back to ggF: categorize to separate signal(s) and backgrounds Njet – Dilepton invariant mass mll – pT of subleading lepton
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Better Living through Better Living through CategoriesCategories
• Categorize to separate signal(s) and backgrounds Njet – Dilepton invariant mass mll – pT of subleading lepton
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The Low pThe Low pTT Bin Binthe “low-pT” data (10 < pT
sublead < 15 GeV) add ~20% signal acceptance but challenging backgrounds
the “low-pT” data (10 < pTsublead < 15 GeV) add ~20% signal
acceptance but challenging backgrounds
(mH ~ 125 GeV) < 2 x (mW ~ 80 GeV) Signal produces one W off-shell, leptons produced by
one W are soft
Previous results did not have this bin (pTsublead > 15)
(mH ~ 125 GeV) < 2 x (mW ~ 80 GeV) Signal produces one W off-shell, leptons produced by
one W are soft
Previous results did not have this bin (pTsublead > 15)
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New Technology for New Technology for W+jetsW+jets
• W+jets normalized using isolated + non-isolated dilepton pair
• Extrapolate to SR using fake rate measured in jet-enriched sample
• Stringent lepton ID cuts these events are typically actually heavy-flavor meson decays
• Jet composition matters: tune sample in which we derive the fake rate pick Z+jets
• W+jets normalized using isolated + non-isolated dilepton pair
• Extrapolate to SR using fake rate measured in jet-enriched sample
• Stringent lepton ID cuts these events are typically actually heavy-flavor meson decays
• Jet composition matters: tune sample in which we derive the fake rate pick Z+jets
s
c
W±
g
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New Technology for New Technology for W+jetsW+jets
• W+jets normalized using isolated + non-isolated dilepton pair
• Extrapolate to SR using fake rate measured in jet-enriched sample
• Previously: large systematics (40%) from difference of extrapolation factors between multijet vs. W+jets
• Now: Use Z+jets data, a better analog (20% systematic, + stat uncertainty will improve!)
• W+jets normalized using isolated + non-isolated dilepton pair
• Extrapolate to SR using fake rate measured in jet-enriched sample
• Previously: large systematics (40%) from difference of extrapolation factors between multijet vs. W+jets
• Now: Use Z+jets data, a better analog (20% systematic, + stat uncertainty will improve!)
s
c
W±
g
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And a new control region And a new control region • “Other dibosons” = “Not WW”
• WZ, W*, W: Z, , *
• Produce lepton with same or opposite charge as W with equal probability
• Long-time pipe dream in dilepton WW: normalize “non-WW’’ using same-sign data
Need robust W+jets prediction
• And now we have one!!
• In this control region, extrapolate from same-sign to opposite-sign
• “Other dibosons” = “Not WW”
• WZ, W*, W: Z, , *
• Produce lepton with same or opposite charge as W with equal probability
• Long-time pipe dream in dilepton WW: normalize “non-WW’’ using same-sign data
Need robust W+jets prediction
• And now we have one!!
• In this control region, extrapolate from same-sign to opposite-sign
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ggF ≥2 jet categoryggF ≥2 jet category• Add acceptance by taking events from the complement of the
VBF category in events with ≥ 2 jets
• Closes the system of jet migrations between categories restores the total signal yield to being an inclusive measurement
• anticorrelations among signal yields in different categories results in improved total uncertainty
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VBF categoryVBF category• Numerous variables to distinguish the VBF channel from ggF
and backgrounds
Hig
gs
bo
son
kin
em
ati
cs
VB
F je
t k
ine
ma
tic
s
(ll)
mT
Y(jj)
m(jj)
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BDT VBFBDT VBF• Boosted Decision Tree (BDT)
event discriminant Automated cut sequence to optimize
expected signal-background separation
Repeat, giving higher weight to background events passing (and signal events failing)
Output a “forest” of decision trees
• Trained to select VBF signal events and reject background (including ggF H boson production)
-1 = background-like
1 = signal-like
• Rebin to manageable 4 bins 0th bin is “background-like”, not used
(ee/ is used as well, but is not shown)
e data, Njet ≥ 2 after preselection
S/B(B includes ggF)
0.110.01 2.10.6
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Top background and the Top background and the b-vetob-veto
g
g
t
t
t W+
W–
b
b
≥ 2-jet data after a veto on b-tagged jets: still top-dominated
But these jets are not the same:
1)Different kinematics (large opening angle, see left)
• Reflected in the BDT
2) t → Wb always, and we can tag b-jets using impact parameter + secondary vertex information
≥ 2-jet data after a veto on b-tagged jets: still top-dominated
But these jets are not the same:
1)Different kinematics (large opening angle, see left)
• Reflected in the BDT
2) t → Wb always, and we can tag b-jets using impact parameter + secondary vertex information
VBF signal
top
q’ q’’
q q’
W+
W–
HW+
W–
’
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Top quark BG in the VBF Top quark BG in the VBF channelchannel
• Simple extrapolation (from tagged to btag-vetoed) of a complex variable (the BDT discriminant)
• Check modeling of key variables (mjj shown) and the BDT discriminant itself
• Theory uncertainties from standardized program of QCD scale, generator and parton shower comparison, PDF dependence
• Simple extrapolation (from tagged to btag-vetoed) of a complex variable (the BDT discriminant)
• Check modeling of key variables (mjj shown) and the BDT discriminant itself
• Theory uncertainties from standardized program of QCD scale, generator and parton shower comparison, PDF dependence
(theory) uncertainty on yield in signal region
uncertainty on control region
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The ResultsThe Results
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Observation of HObservation of HWWWWProbability that the observed data are produced by the background alone:
(CMS: 4.3 observed (5.8 expected) from 1312.1129 [hep-ex])
z0 = 6.1 standard deviations(5.8 expected)
e data, Njet ≥ 2
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Signal strength: the Signal strength: the global pictureglobal picture
• Signal strength “” = (obs)/(pred(SM))
0 is bg-only, 1 is SM
• WW has best single-channel signal strength: 20% precision
CMS: 0.72 ± 0.12 (stat) ± 0.12 (expt.) +0.12-0.10 (theo.)
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VBF vs. ggF: testing the VBF vs. ggF: testing the SMSM
Different production mechanisms, can separate through different signal regions
Test for new physics in the loops
Different production mechanisms, can separate through different signal regions
Test for new physics in the loops
g
g
H
t,b,???
q’ q’
q q
W,Z
W,Z
H Best-fit values from WW → ll
ggF = 1.01± 0.19 (stat.) +0.22-0.18 (syst.)
VBF = 1.27 +0.44-0.40 (stat.) +0.29
-0.21 (syst.)
Best-fit values from WW → ll
ggF = 1.01± 0.19 (stat.) +0.22-0.18 (syst.)
VBF = 1.27 +0.44-0.40 (stat.) +0.29
-0.21 (syst.)
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• Use ggF signal regions as “control regions”, test for VBF signal
• Equivalently, test for a nonzero ratio VBF/ggF
likelihood curve: similar to a chi2
minimum is most probable value of tested quantity
significance from value at zero-crossing2.7 expected3.2 observedEvidence for VBF production
likelihood curve: similar to a chi2
minimum is most probable value of tested quantity
significance from value at zero-crossing2.7 expected3.2 observedEvidence for VBF production
VBF evidenceVBF evidence
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Vector and fermion Vector and fermion couplingscouplings
Simple scaling of production and decay modes involving vector boson (V) and fermions (f)
Simple scaling of production and decay modes involving vector boson (V) and fermions (f)
~75% ~25%
HW+
W–
g
g
H
quarks
q’ q’
q q
W,Z
W,Z
H
F2
V2
V2
Partial width scales with (V
2)Partial width scales with (V
2)
Branching ratio is the partial width divided by the total width, which appears in the denominator above
Branching ratio is the partial width divided by the total width, which appears in the denominator above
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Vector and fermion Vector and fermion couplingscouplings
Simple scaling of production and decay modes involving vector boson (V) and fermions (f)
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The road aheadThe road ahead
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The search path: high-The search path: high-mass Hmass H
• LHC Run II: centre-of-mass energy increase 8 13 TeV Correponding ability to produce higher-mass particles
• Newly-accessible particles will be quickly visible in the next run
from https://twiki.cern.ch/twiki/bin/view/LHCPhysics/HiggsEuropeanStrategy2012
ggF: x6 increase
VBF: x3 increase
for mH = 1 TeV:
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A second Higgs boson at A second Higgs boson at high mass?high mass?
• Q: Why would there be a high-mass copy of our friend at 125 GeV?
• A: Why not? Nature seems to like copies (leptons, quarks)
• A’: Predicted by numerous well-motivated models which also solve other problems
Supersymmetry “stabilizes” mH, gives a dark matter candidate
Two-higgs-doublet model Many variants; one is basically SUSY with decoupled superpartners
Type II Seesaw models Seesaw models give a “natural” mechanism for light neutrino masses
explains gap between neutrino and other fermion masses
Any of these can allow enough CP violation for a matter universe to arise from a matter-antimatter initial state
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High-mass H search with High-mass H search with WWWW
• WW possible or even favored decay mode at high mH
• ljj experimental signature Higher branching ratio than ll Single isolated high-pT lepton
(provides trigger)
Missing transverse energy
Two jets (sometimes merged for mH > 1 TeV)
• Bump hunting in m(ljj) Reconstruct m(WW) up to twofold
ambiguity in neutrino pZ
• Different background composition but similar challenges (top quark rejection, non-prompt leptons)
Apply tools from dilepton analysis
Starting with QCD
from 1206.6074 (7 TeV paper)
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Precision tests: ttHPrecision tests: ttH• Direct searches are not the only way
to look for BSM physics at the LHC
• There could well be new heavy particles hiding in the quantum loops of ggF production
Need to know the dominant ttH contribution
• ttH Yukawa coupling measurement Fundamental physics
Leading quantum correction to Higgs boson mass (“naturalness problem”)
Experimentally interesting (see right)
• These will steadily benefit from more data (complementary to searches)
Populate sidebands / control regions
Rare decay modes with good S/B become accessible
g
g t
t
H
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ttH multilepton ttH multilepton signaturessignatures
• At 13 TeV cross section increases by factor 5, faster than any other Higgs production mode multilepton decays become accessible
• Experimental and theoretical challenges Multi-object, complex final states with heavy flavor push limits of MC
generator technology
Bring experience from WW in data-driven fake lepton BGs
g
gt
t
H W+
W–
W+
W–
b
b
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ConclusionConclusion• Final Run I WW paper is a waypoint along a long but profitable
road Beyond cut and count: categorization of events improves precision by
separating signal and background
Improved background estimation and fit model result in the most powerful single channel on ATLAS for rate measurements
• Last details of Run I WW measurements being finalized for publication…
Spin/CP, high-mass search, VH production mode, differential cross section, off-shell couplings
• …and Run II is coming up fast
6.1 observation of H WW decay3.2 evidence for VBF production
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backupbackup
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W+jets systematicsW+jets systematics
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Control region yieldsControl region yields
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BDT VBFBDT VBF• Results (BDT discriminant and dilepton transverse mass mT)
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BDT schematicBDT schematic
http://tmva.sourceforge.net/docu/TMVAUsersGuide.pdf
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Drell Yan (Z/Drell Yan (Z/*)*)Measure missing transverse energy only with tracks: more robust against extra interactions (pileup)
Measure missing transverse energy only with tracks: more robust against extra interactions (pileup)
• Left: additional rejection after initial ET
miss requirement
First inclusion of ee+ channels in 2012 WW analysis
• Left: additional rejection after initial ET
miss requirement
First inclusion of ee+ channels in 2012 WW analysis
45
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The ATLAS DetectorThe ATLAS Detector
Inner Detector (tracking):Pixels (silicon)SCT (silicon strips)TRT (straw tubes / ionization)
Electromagnetic calorimeterLiquid Argon (LAr) with lead
absorber
Hadronic calorimeter (jets, hadrons)Steel absorber + scintillatorLAr with copper/tungsten absorber
Solenoid
Toroids
Muon Detectors: large radii for precise momentum measurement Precision: Drift tubes (MDT) and Cathode Strip Chambers (CSC)Trigger: Resistive Plate Chamber (RPC) and Thin Gap Chamber
(TGC)
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llll combined signal combined signal strengthstrength
Combined WW → ll signal strength = /SM (2011+2012, all Njet):
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Everybody loves the Everybody loves the banana plotbanana plot
• measured signal strength ((Nobs-B)/(BRSM x SM)) vs. mH
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One last pOne last p00 plot for old plot for old times’ saketimes’ sake• Probability that data can be produced by the background alone
• Slight mass sensitivity because mT binning evolves with mH
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Now it has friendsNow it has friends• “mango” (no BR in denom) and “papaya” (no in denom) plots
Residual sensitivity to mass through cross section (mango) and acceptance (papaya)
mango papaya
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Top background and the Top background and the b-vetob-veto
Therefore we reject events by selecting on the unique VBF topology Event discriminant: “boosted decision tree” (BDT) separates signal from background
(0 = background-like 3 = most signal-like)
And reject events in which a jet is b-tagged Use precision tracking to reconstruct b hadron decay vertex
And use the events with one b-tagged jet to normalize the top background
Therefore we reject events by selecting on the unique VBF topology Event discriminant: “boosted decision tree” (BDT) separates signal from background
(0 = background-like 3 = most signal-like)
And reject events in which a jet is b-tagged Use precision tracking to reconstruct b hadron decay vertex
And use the events with one b-tagged jet to normalize the top background
b-tagb-veto signal region
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The Englert-Brout-Higgs The Englert-Brout-Higgs MechanismMechanism
Gauge invariance does not allow fundamental particle masses: instead, generate masses through interaction with a scalar field
Electroweak Symmetry Breaking
Choice of ground state is arbitrary but sets the relationship between W and Z masses, renders photon massless
Interaction with nonzero field permeating space generates mass
Structure of the electroweak interactions appears to reflect this mechanism – what is its nature?
“vacuum expectation value”
Reduce four degrees of freedom to one:
1-d analog: choice of phase
64c. mills (Edinburgh)12 January 2015
The Higgs BosonThe Higgs BosonFor every field, a particle
Particles represent excitations of a quantum field
Photons for the electromagnetic field
Matter (think electrons) for corresponding fermionic fields
[Gravitons for gravitational fields]
Higgs boson for the Higgs field
This last prediction led to an almost 40-year search