Introduction to Hadronic Final State Reconstruction in Collider Experiments (Part VII & VIII)

Intr

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to

Had

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tate

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cons

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Introduction to Hadronic Final State Reconstruction in Collider Experiments

(Part VII & VIII)

Peter LochPeter LochUniversity of ArizonaUniversity of Arizona

Tucson, ArizonaTucson, ArizonaUSAUSA

2P. LochP. Loch

U of ArizonaU of ArizonaMarch 19, 2010March 19, 2010

Validity of Jet Algorithms

Need to be valid to any order of perturbative calculationsNeed to be valid to any order of perturbative calculations Experiment needs to keep sensitivity to perturbative infinities Experiment needs to keep sensitivity to perturbative infinities

Jet algorithms must be infrared safe!Jet algorithms must be infrared safe! Stable for multi-jet final statesStable for multi-jet final states

Clearly a problem for classic (seeded) cone algorithmsClearly a problem for classic (seeded) cone algorithms Tevatron: modifications to algorithms and optimization of algorithm configurationsTevatron: modifications to algorithms and optimization of algorithm configurations

Mid-point seeded cone: put seed between two particlesMid-point seeded cone: put seed between two particles Split & merge fraction: adjust between 0.5 – 0.75 for best “resolution”Split & merge fraction: adjust between 0.5 – 0.75 for best “resolution”

LHC: need more stable approachesLHC: need more stable approaches Multi-jet context important for QCD measurementsMulti-jet context important for QCD measurements

Extractions of inclusive and exclusive cross-sections, PDFsExtractions of inclusive and exclusive cross-sections, PDFs Signal-to-background enhancements in searchesSignal-to-background enhancements in searches

Event selection/filtering based on topologyEvent selection/filtering based on topology Other kinematic parameters relevant for discovery Other kinematic parameters relevant for discovery

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Validity of Jet Algorithms

Need to be valid to any order of perturbative calculationsNeed to be valid to any order of perturbative calculations Experiment needs to keep sensitivity to perturbative infinities Experiment needs to keep sensitivity to perturbative infinities

Jet algorithms must be infrared safe!Jet algorithms must be infrared safe! Stable for multi-jet final statesStable for multi-jet final states

Clearly a problem for classic (seeded) cone algorithmsClearly a problem for classic (seeded) cone algorithms Tevatron: modifications to algorithms and optimization of algorithm configurationsTevatron: modifications to algorithms and optimization of algorithm configurations

Mid-point seeded cone: put seed between two particlesMid-point seeded cone: put seed between two particles Split & merge fraction: adjust between 0.5 – 0.75 for best “resolution”Split & merge fraction: adjust between 0.5 – 0.75 for best “resolution”

LHC: need more stable approachesLHC: need more stable approaches Multi-jet context important for QCD measurementsMulti-jet context important for QCD measurements

Extractions of inclusive and exclusive cross-sections, PDFsExtractions of inclusive and exclusive cross-sections, PDFs Signal-to-background enhancements in searchesSignal-to-background enhancements in searches

Event selection/filtering based on topologyEvent selection/filtering based on topology Other kinematic parameters relevant for discovery Other kinematic parameters relevant for discovery

Starts to miss conesat next order!

4P. LochP. Loch


Midpoint Seeded Cone

Attempt to increase infrared Attempt to increase infrared safety for seeded conesafety for seeded cone Midpoint algorithm starts with Midpoint algorithm starts with

seeded cone seeded cone Seed threshold may be 0 to Seed threshold may be 0 to

increase collinear safetyincrease collinear safety Place new seeds between two Place new seeds between two

close stable conesclose stable cones Also center of three stable Also center of three stable

cones possiblecones possible Re-iterate using midpoint seedsRe-iterate using midpoint seeds

Isolated stable cones are Isolated stable cones are unchangedunchanged

Still not completely safe!Still not completely safe! Apply split & mergeApply split & merge

Usually split/merge fraction Usually split/merge fraction 0.75 0.75

2 2cone

Find midpoints for stable cones wi hi

2

t n

R y R

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2 2cone


2

t n

R y R

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2 2cone


2

t n

R y R

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2 2cone


2

t n

R y R

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(from G. Salam & G. Soyez, JHEP 0705:086,2007)

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Seedless Fixed Cone

Improvements to cone Improvements to cone algorithms: no seedsalgorithms: no seeds All stable cones are consideredAll stable cones are considered

Avoid collinear unsafety in Avoid collinear unsafety in seeded cone algorithmseeded cone algorithm

Avoid infrared safety issue Avoid infrared safety issue Adding infinitively soft Adding infinitively soft

particle does not lead to new particle does not lead to new (hard) cone(hard) cone

Exact seedless cone finderExact seedless cone finder Problematic for larger Problematic for larger

number of particlesnumber of particles Approximate implementationApproximate implementation

Pre-clustering in coarse Pre-clustering in coarse towerstowers

Not necessarily appropriate Not necessarily appropriate for particles and even some for particles and even some calorimeter signalscalorimeter signals

32

153

4 64 fixed order parton level10 10240 very low multiplicity fi

Exact seedless cone for particles:

# opera

( 2 ) operations

100 1.3 10 low multiplicity LHC fi

tio

nal state1,000 1.6 1

ns re

n

ma

al

rk

t

0

sta e

N

N

NO N

1

22

3

Approximate seedless cone ( 0.2 0.2):# operations rem

40 4.4 10

typical LHC final stateLHC high luminosity final state

surviving bins with two n70

10,00

8.3 10 surving bins witarrow jets

h two

a

0

rkN

wide jets

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Seedless Fixed Cone









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153



# opera

( 2 ) operations


tio


ns re

n

ma

al

rk

t

0

sta e

N

N

NO N

1

22

3


40 4.4 10



10,00


h two

a

0

rkN

wide jets

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Seedless Fixed Cone









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153



# opera

( 2 ) operations


tio


ns re

n

ma

al

rk

t

0

sta e

N

N

NO N

1

22

3

Approximate seedles cone ( 0.2 0.2):# operations rema

40


70 8.3 10 surving bins wit4.4 10 surviving bins with two narrow

h tw j

rk

oe

1

00

ts

0,0

N

wide jets

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Seedless Fixed Cone









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153



# opera

( 2 ) operations


tio


ns re

n

ma

al

rk

t

0

sta e

N

N

NO N

1

22

3


40 4.4 10



10,00


h two

a

0

rkN

wide jets

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Seedless Infrared Safe Cone

SISCone (Salam, Soyez 2007)SISCone (Salam, Soyez 2007) Exact seedless cone with geometrical (distance) orderingExact seedless cone with geometrical (distance) ordering

Speeds up algorithm considerably!Speeds up algorithm considerably! Find all distinctive ways on how a segment can enclose a subset of the Find all distinctive ways on how a segment can enclose a subset of the

particlesparticles Instead of finding all stable segments!Instead of finding all stable segments!

Re-calculate the centroid of each segmentRe-calculate the centroid of each segment E.g., pT weighted re-calculation of directionE.g., pT weighted re-calculation of direction ““E-scheme” works as wellE-scheme” works as well

Segments (cones) are stable if particle content does not changeSegments (cones) are stable if particle content does not change Retain only one solution for each segmentRetain only one solution for each segment

Still needs split & merge to remove overlapStill needs split & merge to remove overlap Recommended split/merge fraction is 0.75Recommended split/merge fraction is 0.75

Typical timesTypical times NN22lnlnNN for particles in 2-dim plane for particles in 2-dim plane

1-dim example:1-dim example: See following slides!See following slides!

(inspired by G. Salam & G. Soyez, JHEP 0705:086,2007)

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SISCone Principle (1-dim!)

coneFind all distinctive segments of size 2 ( ( ) operations in 1-dim)R O N

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Reposition segments to centroids (green - unchanged red - chan, ged)

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Retain only one stable solution for each segment

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Apply split & merge

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SISCone

Similar ordering and combinations in 2-dimSimilar ordering and combinations in 2-dim Use circles instead of linear segmentsUse circles instead of linear segments

Still need split & mergeStill need split & merge One additional parameter outside of jet/cone sizeOne additional parameter outside of jet/cone size

Not very satisfactory!Not very satisfactory! But at least a practical seedless cone algorithmBut at least a practical seedless cone algorithm

Very comparable performance to e.g. Midpoint!Very comparable performance to e.g. Midpoint!


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SISCone Performance

Infrared safety failure Infrared safety failure ratesrates

Computing performanceComputing performance


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Recursive Recombination (kT)

Computing performance an Computing performance an issueissue Time for traditional kT is ~Time for traditional kT is ~NN33

Very slow for LHCVery slow for LHC FastJet implementations FastJet implementations

Use geometrical ordering to Use geometrical ordering to find out which pairs of find out which pairs of particles have to be particles have to be manipulated instead of manipulated instead of recalculating them all!recalculating them all!

Very acceptable performance in Very acceptable performance in this case!this case!

3

6

9

12 3

14 5

LHC events (heavy ion

# operations time [s]10 10 0.05

100 10 0.501,000 10 5.00

# operations time [s]10,000 10 5 1050,000 1.

2

LHC even

5 10

ts

6.

( collisions

coll

25 10

on a m

is

odern compute

ions):

:

r (3 G

)

N

pp

N

Hz clock)

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Recursive Recombination (kT)

Computing performance an Computing performance an issueissue Time for traditional kT is ~Time for traditional kT is ~NN33

Very slow for LHCVery slow for LHC FastJet implementations FastJet implementations

Use geometrical ordering to Use geometrical ordering to find out which pairs of find out which pairs of particles have to be particles have to be manipulated instead of manipulated instead of recalculating them all!recalculating them all!

Very acceptable performance in Very acceptable performance in this case!this case!

6

6

3

6

3

3

6

# operations time [s]10 24 0.1 10

100 460 2 101,000 6,900 35 10

10,000 92,0

FastJ

00 0.5 1050,000 541,00

et impl

0 3 10

# operations time [s]10 32 0.2

kT & Cambridge/Aachen ln

Anti-kT

1

ementation

1

s:

0

N N

N

N

N

6

3

3

3

00 1,000 5 101,000 32,000 0.2 10

10,000 1,000,000 5 1050,000 11,200,000 56 10

kT (standard)

ATLAS Cone

FastJet kT

kT (standard + 0.2 x 0.2 pre-clustering)

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FastJet kT

Address the search approachAddress the search approach Need to find minimum in Need to find minimum in standard kT standard kT

Order Order NN33 operations operations Consider geometrically nearest Consider geometrically nearest neighbours in FastJet kTneighbours in FastJet kT

Replace full search by search Replace full search by search over (jet, jet neighbours)over (jet, jet neighbours)

Need to find nearest neighbours Need to find nearest neighbours for each proto-jet fastfor each proto-jet fast Several different approaches: Several different approaches:

ATLAS (Delsart 2006) uses ATLAS (Delsart 2006) uses simple geometrical model, simple geometrical model, Salam & Cacciari (2006) Salam & Cacciari (2006) suggest Voronoi cellssuggest Voronoi cells

Both based on same fact relating Both based on same fact relating ddijij and geometrical distance in and geometrical distance in ΔΔRR Both use geometrically Both use geometrically

ordered lists of proto-jetsordered lists of proto-jets

2T,

T, T,

2 3

Find minimum for particles in :

( ) searches,

standard kT

FastJet kTrepeated times ( )

uses nearest neighbours

min( , ) , , , 1,...,

min

search:

ij i j ij i i

ij i j

ij ik

d d d R R d p i j N

d p

N

p

R

O N O

R

N N

Assume an additional particle exists with geom

, i.e. , geometrical

nearest n

etrical distance to particle :

eighbours in , plPr

an

min( , )

oof

:e

mini k ik i ik

i

i

ij

ik

k

k j i j

y

d d d R R d Rd

k

Rd

R i

works only for ik

ij

ij

R

R

R

R

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Fast kT (ATLAS – Delsart)

Possible implementation Possible implementation (P.A. Delsart, 2006)(P.A. Delsart, 2006)

Nearest neighbour searchNearest neighbour search Idea is to only limit recalculation of Idea is to only limit recalculation of

distances to nearest neighbours distances to nearest neighbours Try to find all proto-jets having Try to find all proto-jets having

proto-jet proto-jet kk as nearest neighbour as nearest neighbour Center pseudo-rapdity (or Center pseudo-rapdity (or

rapdity)/azimuth plane on rapdity)/azimuth plane on kk Take first proto-jet Take first proto-jet jj closest to closest to kk in in

pseudo-rapiditypseudo-rapidity Compute middle line Compute middle line LLjkjk between between kk

and and jj All proto-jets below All proto-jets below LLjkjk are closer to are closer to

jj than than kk → → kk is not nearest is not nearest neighbour of thoseneighbour of those

Take next closest proto-jet Take next closest proto-jet ii in in pseudo-rapiditypseudo-rapidity Proceed as above with exclusion of Proceed as above with exclusion of

all proto-jets above all proto-jets above LLikik

Search stops when point below Search stops when point below intersection of intersection of LLjkjk and and LLikik is reached, is reached, no more points have no more points have kk as nearest as nearest neighbourneighbour

2

Assume proto-jets are uniformly distributed in , plane(rectangular with fintie size, area )Average number of proto-jets in circle with radius :

Complexity estimate:

If is mean distance be

NA

R

RN NA

R

tween two proto-jets:

1

Computation of proto-jet 's nearest neighbours is restricted to

, 2 operations for

total complexity (estimate)

k k

AN RN

kNR R N R N k

N NN

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FastJet kT (Salam & Cacciari)

Apply geometrical methods to Apply geometrical methods to nearest neighbour searchesnearest neighbour searches Voronoi cell around proto-jet Voronoi cell around proto-jet kk

defines area of nearest defines area of nearest neighboursneighbours No point inside area is closer No point inside area is closer

to any other protojet to any other protojet Apply to protojets in pseudo-Apply to protojets in pseudo-

rapdity/azimuth planerapdity/azimuth plane Useful tool to limit nearest Useful tool to limit nearest

neighbour search neighbour search Determines region of re-Determines region of re-

calculation of distances in kTcalculation of distances in kT Allows quick updates without Allows quick updates without

manipulating too many long manipulating too many long listslists

Complex algorithm!Complex algorithm! Read Read

G. Salam & M. Cacciari, Phys.Lett.B641:57-61 (2006)

(source http://en.wikipedia.org/wiki/Voronoi_diagram)

Complexity estimate (Monte Carlo eln tota

xperimel compl

nt)ty

:exiN N

http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=find+a+salam+and+t+kt

http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=find+a+salam+and+t+kt

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Jet Algorithm Performance

Various jet algorithms produce different jets from the same collision eventVarious jet algorithms produce different jets from the same collision event Clearly driven by the different sensitivities of the individual algorithmsClearly driven by the different sensitivities of the individual algorithms

Cannot expect completely identical picture of event from jetsCannot expect completely identical picture of event from jets Different topology/number of jetsDifferent topology/number of jets Differences in kinematics and shape for jets found at the same directionDifferences in kinematics and shape for jets found at the same direction

Choice of algorithm motivated by physics analysis goalChoice of algorithm motivated by physics analysis goal E.g., IR safe algorithms for jet counting in E.g., IR safe algorithms for jet counting in W W + + nn jets and others jets and others Narrow jets for Narrow jets for WW mass spectroscopy mass spectroscopy Small area jets to suppress pile-up contributionSmall area jets to suppress pile-up contribution

Measure of jet algorithm performance depends on final stateMeasure of jet algorithm performance depends on final state Cone preferred for resonancesCone preferred for resonances

E.g., 2 – 3…E.g., 2 – 3…nn prong heavy particle decays like top, prong heavy particle decays like top, Z’Z’, etc., etc. Boosted resonances may require jet substructure analysis – need kT algorithm! Boosted resonances may require jet substructure analysis – need kT algorithm!

Recursive recombination algorithms preferred for QCD cross-sectionsRecursive recombination algorithms preferred for QCD cross-sections High level of IR safety makes jet counting more stableHigh level of IR safety makes jet counting more stable

Pile-up suppression easiest for regularly shaped jetsPile-up suppression easiest for regularly shaped jets E.g., Anti-kT most cone-like, can calculate jet area analytically even after split and mergeE.g., Anti-kT most cone-like, can calculate jet area analytically even after split and merge

Measures of jet performanceMeasures of jet performance Particle level measures prefer observables from final stateParticle level measures prefer observables from final state

Di-jet mass spectra etc.Di-jet mass spectra etc. Quality of spectrum importantQuality of spectrum important

Deviation from Gaussian etc.Deviation from Gaussian etc.

26P. LochP. Loch


Jet Shapes (1)

(from P.A. Delsart)

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Jet Shapes (2)

(from P.A. Delsart)

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Jet Shapes (3)

(from G. Salam’s talk at the ATLAS Hadronic Calibration Workshop Tucson 2008)

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Jet Reconstruction Performance (1)

(from Salam ,Cacciari, Soyez, http://quality.fastjet.fr)

Quality estimator for distributionsQuality estimator for distributions Best reconstruction: narrow GaussianBest reconstruction: narrow Gaussian

We understand the error on the mean!We understand the error on the mean! Observed distributions often deviate from GaussianObserved distributions often deviate from Gaussian

Need estimators on size of deviations!Need estimators on size of deviations! Should be least biased measuresShould be least biased measures

Best performance gives closest to Gaussian distributionsBest performance gives closest to Gaussian distributions List of variables describing shape of distribution on next slideList of variables describing shape of distribution on next slide

Focus on unbiased estimatorsFocus on unbiased estimators E.g., distribution quantile describes the narrowest range of values E.g., distribution quantile describes the narrowest range of values containing a requested fraction of all eventscontaining a requested fraction of all events Kurtosis and skewness harder to understand, but Kurtosis and skewness harder to understand, but clear message in case of Gaussian distribution! clear message in case of Gaussian distribution!

http://quality.fastjet.fr/

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Jet Reconstruction Performance Estimators

median

mop

22

3

13 3

4

14

mop medianstatistical meanmedianmost probable value

standard deviation

skewness/left-right asymmet

Estimator Quantity Expectation for Gauss

ry

ian

0N

ii

Nii

R R R

R

RRR

RMS R R

R

MS

RN

R R

68%

4 3 kurtosis/"peakedness"

quantil 2e

0wf

wf

NQQ

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Jet Reconstruction Performance

Quality of mass reconstruction for various jet finders and Quality of mass reconstruction for various jet finders and configurationsconfigurations Standard model – top quark hadronic decayStandard model – top quark hadronic decay

Left plot – various jet finders and distance parametersLeft plot – various jet finders and distance parameters BSM – BSM – ZZ’ (2 TeV) hadronic decay ’ (2 TeV) hadronic decay

Right plot – various jet finders with best configurationRight plot – various jet finders with best configuration

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Jet Performance Examples (1)

(from Cacciari, Rojo, Salam, Soyez, JHEP 0812:032,2008)

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Interactive Tool

Web-based jet performance evaluation availableWeb-based jet performance evaluation available http://www.lpthe.jussieu.fr/~salam/jet-quality

http://www.lpthe.jussieu.fr/~salam/jet-quality

http://www.lpthe.jussieu.fr/~salam/jet-quality/

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Introduction to Hadronic Final State Reconstruction in Collider Experiments (Part VII & VIII)

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