Mass Resconstruction with HEP detectors

Mass ReconstructionMass Reconstruction Yuan CHAO (趙元 )

(National Taiwan University, Taipei, Taiwan)

Numerical Simulation in HEP2012/02/15

2

OutlinesOutlines

IntroductionIntroductionResonancesResonancesCoordination systemCoordination systemFour-vector conversionFour-vector conversionThe W & Z bosonsThe W & Z bosonsZ-boson (Ex. 1)Z-boson (Ex. 1)Invariant massInvariant massMissing ETMissing ETTransverse massTransverse massW-boson (Ex. 2)W-boson (Ex. 2)TracksTracksJetsJetsTop reconstruction (cascade)Top reconstruction (cascade) ......

3

The Origin of the UniverseThe Origin of the Universe

4

Goal of High Energy PhysicsGoal of High Energy Physics

LHC was built for the following LHC was built for the following purposes:purposes:

To find the origin of mass... To find the origin of mass... the the Higgs Higgs boson.boson.Looking for the unification.. Looking for the unification.. SupersymmetrySupersymmetry as well as as well as other candidates of other candidates of Dark Dark MaterMater & & Dark energyDark energyInvestigate the mystery of Investigate the mystery of anti-matteranti-matter disappearance disappearancePhysics at the early stage of Physics at the early stage of the universe: the universe: Heavy Ion Heavy Ion collisionscollisions and and QGPQGP

5

IntroductionIntroduction

Accelerators & detectorsAccelerators & detectorsLHC, CMS (hadron machine)LHC, CMS (hadron machine)

6

The Large Hadron ColliderThe Large Hadron Collider

Four major experiments at LHCFour major experiments at LHCAtlas, Alice, Atlas, Alice, CMSCMS, LHCb, LHCb

LHC first beam in Sep. 2008LHC first beam in Sep. 2008A technical trouble occurred A technical trouble occurred 10 days after the start10 days after the start

Physics restarted in Nov. 2009Physics restarted in Nov. 2009Energy starts at Energy starts at 0.9 TeV0.9 TeVPushed up to Pushed up to 2.36 TeV2.36 TeV in Dec. in Dec.

New energy record in 2010New energy record in 2010Collision at Collision at 7 TeV7 TeV on Mar. 30 on Mar. 30

Delivered data Delivered data ~36/pb ~36/pb in 2010in 2010Reached Reached ~5.7/fb~5.7/fb in 2011 in 2011To increase to To increase to 8 TeV8 TeV in 2012 in 2012

CERNCERN

LHCLHC

7







CERNCERN

LHCLHC

8

max L≈ 3.54x1033cm-2s-1

EPS dataset

LP11 dataset

13/12/11 dataset







9

Atlas DetectorAtlas Detector

A Toroidal LHC ApparatusA Toroidal LHC ApparatusA general purposed detectorA general purposed detector

10

CMS DetectorCMS Detector

Compact Muon SolenoidCompact Muon SolenoidA general purposed detectorA general purposed detector

3.8

11

CMS DetectorCMS Detector

Compact Muon SolenoidCompact Muon SolenoidA general purposed detectorA general purposed detector

3.8

12

IntroductionIntroduction

Accelerators & detectorsAccelerators & detectorsKEK-B, BELLE (lepton machine)KEK-B, BELLE (lepton machine)

3.5 GeV e3.5 GeV e++ on 8 GeV e on 8 GeV e--

WWCM CM

= M( = M( ΥΥ(4s) )(4s) )

3km circumference3km circumference~11mrad crossing angle~11mrad crossing angle

Lpeak

=2.1 x 1034 /cm2/s2

Tsukuba, Japan

EFC(online Lum.) µ / KL detection

14/15 lyr. RPC+Fe

Central Drift Chamber small cell +He/C2H6

CsI(Tl) 16X0

Aerogel Cherenkov counter n=1.015~1.030

Si vtx. det. 3/4 lyr. DSSD

TOF counter

SC solenoid 1.5T

8 GeV e−

3.5 GeV e+

BELLE Detector

13

Long Lived ParticlesLong Lived Particles

Most product of a collision decays before they reach Most product of a collision decays before they reach the detectorsthe detectors

Check the life-time on PDG handbook or web site:Check the life-time on PDG handbook or web site:http://pdglive.lbl.gov/http://pdglive.lbl.gov/Look for the value of cLook for the value of cττ

What we see in the detectors:What we see in the detectors:ee±±, , μμ±±, , γγ, , ππ±±,K,K±±, K, K

LL, n, p, n, p±±

http://pdglive.lbl.gov/

14

Long Lived ParticlesLong Lived Particles

Most product of a collision decays before they reach Most product of a collision decays before they reach the detectorsthe detectors

Check the life-time on PDG handbook or web site:Check the life-time on PDG handbook or web site:http://pdglive.lbl.gov/http://pdglive.lbl.gov/Look for the value of cLook for the value of cττ

What we see in the detectors:What we see in the detectors:ee±±, , μμ±±, , γγ, , ππ±±,K,K±±, K, K

LL, n, p, n, p±±

Others can be found through resonances searchOthers can be found through resonances searchResonance mass is like the finger print of particles: Resonance mass is like the finger print of particles: uniqueuniqueSimilar to line spectra analysis of lightsSimilar to line spectra analysis of lights

http://pdglive.lbl.gov/

15

ResonanceResonance

16

ResonanceResonance

Short life time particlesShort life time particlesTypical life-time of order 10Typical life-time of order 10-23-23

If flying at ~ speed of light → decay within 10If flying at ~ speed of light → decay within 10-15-15 m mRelationship between effective Relationship between effective cross-section cross-section σσ vs. the vs. the

energy Eenergy E, resonances often appear as , resonances often appear as bell-shapedbell-shaped

E = m cE = m c22

Natural unit:Natural unit: c = c = ħħ = 1 = 1

17

Resonance (cont.)Resonance (cont.)

Short life time particlesShort life time particlesTypical life-time of order 10Typical life-time of order 10-23-23

If flying at ~ speed of light → decay within 10If flying at ~ speed of light → decay within 10-15-15 m mRelationship between effective cross-section Relationship between effective cross-section σσ vs. the vs. the

energy energy EE, resonances often appear as , resonances often appear as bell-shapedbell-shapedUsually described as Usually described as Breit-WignerBreit-Wigner function function

Relativistic Breit-WignerRelativistic Breit-Wigner distribution: distribution:

Natural units:Natural units: c = c = ħħ = 1 = 1Experimentally often use Experimentally often use Gaussian Gaussian (for detector resolution)(for detector resolution)

¾(E) = ¾0(¡=2)2

(E0 ¡E)2 + (¡=2)2

¾(m;M;¡) = N ¢ 2¼¢ ¡2M2

(m2 ¡M2)2 +m4(¡2=M2)

18

Coordination SystemCoordination System

Most collider detectors built in Most collider detectors built in barrel shapebarrel shapeDetector build along the beam lineDetector build along the beam lineInteresting particles have higher Interesting particles have higher transverse momentatransverse momentaSymmetric shape to have uniform acceptanceSymmetric shape to have uniform acceptanceSpecial purpose detectors have different shapesSpecial purpose detectors have different shapes

LHCbLHCb

19

Coordination SystemCoordination System


Coordination convention:Coordination convention:Use cylindrical coordinate (r, Use cylindrical coordinate (r, θθ, , φφ))

Beam

directio

n

20

Coordination System (cont.)Coordination System (cont.)


Coordination convention:Coordination convention:Use cylindrical coordinate (r, Use cylindrical coordinate (r, θθ, , φφ))Adopt Adopt Lorentz invariantLorentz invariant variable: variable: rapidityrapidity

Pseudo-rapidityPseudo-rapidity (approximation for m (approximation for m ≈ ≈ 00))

y =1

2ln

µE + pLE ¡ pL

¶

´ =1

2ln

µ jpj+ pLjpj ¡ pL

¶= ¡ ln

·tan

µµ

2

¶¸

21

Four VectorsFour Vectors

The key variables: 4-vectorsThe key variables: 4-vectorsMotion of particles can be described withMotion of particles can be described with(px, py, pz, E)(px, py, pz, E) in Cartesian in CartesianMore common used:More common used:(p(p

TT, , η, Φ, mη, Φ, m

00) or (p) or (p

TT, η, Φ, E), η, Φ, E)

Conversions:Conversions:

Implemented in Implemented in ROOT, CLHEP, ...ROOT, CLHEP, ...Will use through out the exercisesWill use through out the exercises

One can use One can use TLorentzVectorTLorentzVector with helper functions with helper functions

px = pT cosÁpy = pT sinÁpz = pT = tan µ = pT sinh ´jpj = pT cosh´

pT =qp2x + p

2y

tanÁ = py=px

22

The W & Z bosonsThe W & Z bosons

The mediator of the weak interactionThe mediator of the weak interactionKnown as Known as weak bosonsweak bosons: W & Z: W & ZA major success of A major success of Standard ModelStandard ModelPredicted by Glashow, Weinberg, Salam in 1968Predicted by Glashow, Weinberg, Salam in 1968SU(2) gauge theorySU(2) gauge theory

DiscoveryDiscoveryNeutral current interaction observed in 1973Neutral current interaction observed in 1973Super Proton SynchrotronSuper Proton Synchrotron (SPS) at CERN (SPS) at CERNW found Jan. 1983 at UA1 & UA2W found Jan. 1983 at UA1 & UA2Z was found a few months laterZ was found a few months later

The four gauge bosons of electroweak: WThe four gauge bosons of electroweak: W++, W, W--, Z, Z00, , γγ

23

The Z bosonThe Z boson

PropertiesPropertiesCharge = 0. Spin J = 1Charge = 0. Spin J = 1Elementary particleElementary particleMass: 91.1876 Mass: 91.1876 ±± 0.0021 GeV 0.0021 GeVFull width Full width ΓΓ = 2.4952 = 2.4952 ±± 0.0023 GeV 0.0023 GeV

Decay modesDecay modesll++ll--: 3.3658 : 3.3658 ±± 0.0023 x 10 0.0023 x 10-2-2

Invisible: 20.00 Invisible: 20.00 ±± 0.06 x 10 0.06 x 10-2-2

Hadrons: 69.91 Hadrons: 69.91 ±± 0.06 x 10 0.06 x 10-2-2

We'll do exercise to find Z → eWe'll do exercise to find Z → e++ee-- or or μμ++μμ--

24

Ex. 1 reconstruct ZEx. 1 reconstruct Z

D/L the provided sampleD/L the provided sampleROOT: ROOT: http://dl.dropbox.com/u/5196749/example.tgzhttp://dl.dropbox.com/u/5196749/example.tgzPlain text: Plain text: http://dl.dropbox.com/u/5196749/dump_top_cz.txt.gzhttp://dl.dropbox.com/u/5196749/dump_top_cz.txt.gz

EvtInfo_RunNo,EvtInfo_RunNo,EvtInfo_EvtNo,EvtInfo_EvtNo,Leptons_Pt, Leptons_Eta, Leptons_PhiLeptons_Pt, Leptons_Eta, Leptons_PhiLeptons_Type (11: electron, 13: muon, and others)Leptons_Type (11: electron, 13: muon, and others)Leptons_ChargeLeptons_Charge

Identify an even:Identify an even:Check the Check the RUN#RUN#, , Event#Event#

The use of ROOTThe use of ROOTCheck ROOT website: Check ROOT website: http://root.cern.chhttp://root.cern.chTry Try TTree::MakeClassTTree::MakeClass to generate a framework to generate a frameworkYou can also use whatever you like with the plaint text ver.You can also use whatever you like with the plaint text ver.

Make use of the pre-defined Lorentz vector classMake use of the pre-defined Lorentz vector classAdd two vectors directlyAdd two vectors directlyGet pT, eta, phi...Get pT, eta, phi...Calculate Calculate ΔR, ΔΦ...ΔR, ΔΦ...

http://dl.dropbox.com/u/5196749/example.tgz

http://dl.dropbox.com/u/5196749/dump_top_cz.txt.gz

http://root.cern.ch/

25

Ex. 1 reconstruct ZEx. 1 reconstruct Z

Loop through all the leptonsLoop through all the leptonsFind two leptons with the same flavor, opposite chargeFind two leptons with the same flavor, opposite chargeSum up the four-vector and calculate the massSum up the four-vector and calculate the massDraw a plot of the Draw a plot of the mass, pT, eta, phi...mass, pT, eta, phi... distribution for all distribution for all

combinationscombinationsCheck the result plotCheck the result plot

Where is the peak position? (try a fit!)Where is the peak position? (try a fit!)How to improve the S/N? (re-fine the cuts)How to improve the S/N? (re-fine the cuts)What's the width?What's the width?Comparing with lifetime?Comparing with lifetime?Compare ee vs. mu mu Compare ee vs. mu mu

26

The W bosonThe W boson

PropertiesPropertiesCharge = Charge = ±±1 e. Spin J = 11 e. Spin J = 1Elementary particleElementary particleMass: 80.399 Mass: 80.399 ±± 0.023 GeV 0.023 GeVFull width Full width ΓΓ = 2.085 = 2.085 ±± 0.042 GeV 0.042 GeV

Decay modesDecay modesl+-nu: 10.80 l+-nu: 10.80 ±± 0.09 x 10 0.09 x 10-2-2

Hadrons: 67.60 Hadrons: 67.60 ±± 0.27 x 10 0.27 x 10-2-2

We'll do exercise to find W → eWe'll do exercise to find W → e±±νν or or μμ±±νν

27

How to find the invisibles?How to find the invisibles?

Neutrino detection at collidersNeutrino detection at collidersNo direct method due to its low interaction natureNo direct method due to its low interaction natureRelies on the knowledge of the whole eventRelies on the knowledge of the whole eventBasic idea: energy & momentum conservationBasic idea: energy & momentum conservation

To find the missing partTo find the missing partSum up all the particlesSum up all the particles→ → Transverse energy (calorimeter), momentum (tracks)Transverse energy (calorimeter), momentum (tracks)Calculate the "miss ET" as negative of the sumCalculate the "miss ET" as negative of the sumLongitudinal component not considered: loss & backgroundLongitudinal component not considered: loss & background

28

The Transverse MassThe Transverse Mass

DefinitionDefinitionFor the lack of longitudinal information of nuFor the lack of longitudinal information of nu

MissET is the key hereMissET is the key hereRelies on robust calorimeter detectorsRelies on robust calorimeter detectorsUsually poorer than direct measurementsUsually poorer than direct measurements

M2T = (ET;` + ET;º)

2 ¡ (~pT;` + ~pT;º)2= 2jpT;`jjpT;º j[1 ¡ cos(¢Á`;º)]

29

Ex. 2 reconstruct WEx. 2 reconstruct W

Use the same provided sampleUse the same provided sampleThere's a special entry for computed MissET (type: 0)There's a special entry for computed MissET (type: 0)Go through all the leptons and MissETGo through all the leptons and MissET

Find the best lepton to combine with MissETFind the best lepton to combine with MissETCalculate the transverse massCalculate the transverse massDraw a plot of the combinationsDraw a plot of the combinations

Check the result plotCheck the result plotWhere is the peak position? (try a fit!)Where is the peak position? (try a fit!)How to improve the S/N? (re-fine the cuts)How to improve the S/N? (re-fine the cuts)Do you see the cut-off?Do you see the cut-off?

30

TracksTracks

Charged particles can be detected as “tracks"Charged particles can be detected as “tracks"So called "tracking system"So called "tracking system"Silicon, wired chamber, gas tubes...Silicon, wired chamber, gas tubes...Magnetic filed for the momentumMagnetic filed for the momentumCurving direction for charge signCurving direction for charge sign

ParameterizationParameterizationHelix parametersHelix parameters

31

CalorimetersCalorimeters

Calorimeter for energy measurementCalorimeter for energy measurementElectroMagnetic CalorimeterElectroMagnetic CalorimeterHadron CalorimeterHadron Calorimeter

To fully absorb the particleTo fully absorb the particleHeavy materialHeavy materialShowers (see Chin-chen's)Showers (see Chin-chen's)Convert into counts or lightConvert into counts or lightGranularityGranularity

Used for electron & neutral particle detectionUsed for electron & neutral particle detectionBetter energy resolution at very high pTBetter energy resolution at very high pTUsually worse spatial resolutionUsually worse spatial resolution

32

CalorimetersCalorimeters

EM CalorimeterEM CalorimeterElectroMagnetic interactionsElectroMagnetic interactionsDetecting eDetecting e±±, , γγ

ShoweringShoweringBremsstrahlung (low E: compton) Bremsstrahlung (low E: compton) Pair productionPair productionPair annihilationPair annihilation

Shower sizeShower sizeMoliere radiusMoliere radius

Radiation lengthRadiation length

Shower lengthShower length

RM = 0:0265X0(Z + 1:2)

X = X0ln(E0=Ec)

ln 2

33

JetsJets

Jets are products of out-going partonsJets are products of out-going partonsIncluding quarks and gluonsIncluding quarks and gluonsHadronization as strong interactionHadronization as strong interactionParticles pulled out of vacuum for colorlessParticles pulled out of vacuum for colorless

Detecting JetsDetecting JetsBunches of particlesBunches of particlesIncluding kaons, pions, leptons...Including kaons, pions, leptons...Usually detected with "calorimeters"Usually detected with "calorimeters"

Various types and clustering algorithmsVarious types and clustering algorithms

34

Jets in Hadron MachinesJets in Hadron Machines

TrackJetTrackJetCharged TracksCharged Tracks are used for clustering are used for clusteringGood for Good for early data studyearly data study

CaloJetCaloJetUses ECal/HCal towers for clusteringUses ECal/HCal towers for clustering

JPT (Jet Plus Tracks)JPT (Jet Plus Tracks)Replace the avg. calo response with Replace the avg. calo response with individual charged hadrons measured individual charged hadrons measured in tracker systemin tracker system

Zero Supp. Zero Supp. offset correctionoffset correctionCorrection for Correction for in-calo-cone tracksin-calo-cone tracksAdding Adding out-of-calo-coneout-of-calo-cone tracks tracksCorrection for track eff. & muonsCorrection for track eff. & muons

PFJet (Particle Flow Jet)PFJet (Particle Flow Jet)New approach in CMSNew approach in CMS

JME-09-002JME-09-002

35

dij = min³k2pT i; k

2pTj

´ ¢ijD

Jets at LHCJets at LHC

Several jet Several jet clustering algorithmclustering algorithm available in CMS: available in CMS:Jet is the energy sum of a clusterJet is the energy sum of a clusterCone algorithm:Cone algorithm:

Iterative cone, midpoint cone, Iterative cone, midpoint cone, SISConeSISConeSequential recombination:Sequential recombination:

Pairing distance: Pairing distance: Kt: Kt: pp=1, CA: =1, CA: pp=0, =0, Anti-KtAnti-Kt: : pp=-1=-1

CMS uses CMS uses FastJetFastJet package package http://fastjet.frhttp://fastjet.frAlgorithm considerationAlgorithm consideration

Infrared & colinear safeInfrared & colinear safeGood performance (Energy, position ...)Good performance (Energy, position ...)Robust to Piled-ups & UERobust to Piled-ups & UECPU efficient: CPU efficient: OO( N( N22 ln(N) ) ln(N) ) : : OO( N ln(N) )( N ln(N) )

Priority needed on various jet algorithmsPriority needed on various jet algorithmsGood to have many for Good to have many for cross checkingcross checkingThe The default jet algorithmdefault jet algorithm is is Anti-KtAnti-Kt

G.

Sal

am,

“Jet

ogra

phy"

R =p¢´2 +¢Á2 ' 0:5

http://fastjet.fr/

36

Resonance from JetsResonance from Jets

37

The CDF AnomalyThe CDF Anomaly

38

Ways of ImprovementWays of Improvement

Constrained MassConstrained MassUsing constraints to refine the distributionUsing constraints to refine the distribution

39



Re-fit on vertexRe-fit on vertex, ex. , ex. Λ (cτ = 7.89 cm)Λ (cτ = 7.89 cm)¤! p¼

40



Re-fit on vertexRe-fit on vertexMass constraints Mass constraints in in cascaded decayscascaded decays, ex. , ex. ψψ(2s) → J/(2s) → J/ψψ

Ã(2s)! J=Ã + ¼+¼¡; J=Ã ! e+e¡

41



Re-fit on vertexRe-fit on vertexMass constraints in cascaded decaysMass constraints in cascaded decaysEnergy constraint fromEnergy constraint from accelerator info accelerator info

Mbc =qE2beam ¡ p2B

42



Re-fit on vertexRe-fit on vertexMass constraints in cascaded decaysMass constraints in cascaded decaysEnergy constraint from accelerator infoEnergy constraint from accelerator info

Be aware: could also Be aware: could also destroy the shapedestroy the shape......

43

Top ReconstructionTop Reconstruction

PropertiesPropertiesCharge = 2/3. Spin J = 1/2Charge = 2/3. Spin J = 1/2Elementary particleElementary particleMass: 172.9 Mass: 172.9 ±± 1.5 GeV 1.5 GeVFull width Full width ΓΓ = 2.0 = 2.0 ±± 0.7 GeV 0.7 GeV

Decay modesDecay modesWb 0.99 Wb 0.99 ± ± 0.090.09Lifetime so short (5 x 10Lifetime so short (5 x 10-25-25) that no hadron forms before it ) that no hadron forms before it

decays: decays: bare quarkbare quarkTheory: 1973 (K&M), Discovery 1995Theory: 1973 (K&M), Discovery 1995SearchSearch

Semi-leptonicSemi-leptonic

Di-leptonicDi-leptonic

Di-jetDi-jetpp! t¹t!W (`º)b;W (`0º0)¹b

pp! t¹t!W (q¹q)b;W (`0º0)¹b

pp! t¹t!W (q¹q)b;W (q¹q)¹b

44

Top ReconstructionTop Reconstruction

Semi-leptonic search:Semi-leptonic search:Higher branching fractionHigher branching fractionFully reconstruct by assigning W mass constraintFully reconstruct by assigning W mass constraint

Di-leptonic search:Di-leptonic search:Very clean mode as no extra jetsVery clean mode as no extra jetsSuffer from low branching fractionSuffer from low branching fractionCannot fully reconstructed due to two neutrinosCannot fully reconstructed due to two neutrinosAn upper mass bound on mass combinations:An upper mass bound on mass combinations:

pz =pz`(px`pxº + py`pyº +M

2W=2)§E`

p(px`pxº + py`pyº +M2

W=2)2 ¡E2Tº(E2` ¡ p2z`)

E2` ¡ p2z`

mT2(minvis) = minp(1)T ;p

(2)T

hmax[mT (minvis; p

(1)T ); mT (minvis; p

(2)T )]

i

mT (minvis; pinvisT ) =

qm2vis +m

2invis + 2(E

visT EinvisT ¡ pvisT ¢ pinvisT )

45

SummarySummary

Introduced the experimentsIntroduced the experimentsMotivation & goalsMotivation & goalsAccelerators & detectorsAccelerators & detectors

Basics on data analysisBasics on data analysisThe four-vectorThe four-vectorMass reconstructionMass reconstructionMissing ETMissing ET

Advance techniquesAdvance techniquesMore on detectorsMore on detectorsConstrained fitsConstrained fitsCascaded decaysCascaded decays

Summary & conclusionsSummary & conclusionsQ & AQ & A

以上Thank YOU!謝謝

Remercie de Votre Attention

47

Higgs Limits on Higgs Limits on σ/σσ/σSM SM

(CLs)(CLs)

95% CL: obs. 127-600, exp: 117-543 GeV95% CL: obs. 127-600, exp: 117-543 GeV

Education

Mass Resconstruction with HEP detectors