Final State Reconstruction in Collider Experiments Part VII amp VIII Peter Loch University of Arizona Tucson Arizona USA Validity of Jet Algorithms Need to be valid to any order of perturbative ID: 1044692
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1. Introduction to Hadronic Final State Reconstruction in Collider Experiments(Part VII & VIII)Peter LochUniversity of ArizonaTucson, ArizonaUSA
2. Validity of Jet AlgorithmsNeed to be valid to any order of perturbative calculationsExperiment needs to keep sensitivity to perturbative infinities Jet algorithms must be infrared safe!Stable for multi-jet final statesClearly a problem for classic (seeded) cone algorithmsTevatron: modifications to algorithms and optimization of algorithm configurationsMid-point seeded cone: put seed between two particlesSplit & merge fraction: adjust between 0.5 – 0.75 for best “resolution”LHC: need more stable approachesMulti-jet context important for QCD measurementsExtractions of inclusive and exclusive cross-sections, PDFsSignal-to-background enhancements in searchesEvent selection/filtering based on topologyOther kinematic parameters relevant for discovery
3. Validity of Jet AlgorithmsNeed to be valid to any order of perturbative calculationsExperiment needs to keep sensitivity to perturbative infinities Jet algorithms must be infrared safe!Stable for multi-jet final statesClearly a problem for classic (seeded) cone algorithmsTevatron: modifications to algorithms and optimization of algorithm configurationsMid-point seeded cone: put seed between two particlesSplit & merge fraction: adjust between 0.5 – 0.75 for best “resolution”LHC: need more stable approachesMulti-jet context important for QCD measurementsExtractions of inclusive and exclusive cross-sections, PDFsSignal-to-background enhancements in searchesEvent selection/filtering based on topologyOther kinematic parameters relevant for discovery Starts to miss conesat next order!
4. Midpoint Seeded ConeAttempt to increase infrared safety for seeded coneMidpoint algorithm starts with seeded cone Seed threshold may be 0 to increase collinear safetyPlace new seeds between two close stable conesAlso center of three stable cones possibleRe-iterate using midpoint seedsIsolated stable cones are unchangedStill not completely safe!Apply split & mergeUsually split/merge fraction 0.75
5. Midpoint Seeded ConeAttempt to increase infrared safety for seeded coneMidpoint algorithm starts with seeded cone Seed threshold may be 0 to increase collinear safetyPlace new seeds between two close stable conesAlso center of three stable cones possibleRe-iterate using midpoint seedsIsolated stable cones are unchangedStill not completely safe!Apply split & mergeUsually split/merge fraction 0.75
6. Midpoint Seeded ConeAttempt to increase infrared safety for seeded coneMidpoint algorithm starts with seeded cone Seed threshold may be 0 to increase collinear safetyPlace new seeds between two close stable conesAlso center of three stable cones possibleRe-iterate using midpoint seedsIsolated stable cones are unchangedStill not completely safe!Apply split & mergeUsually split/merge fraction 0.75
7. Midpoint Seeded ConeAttempt to increase infrared safety for seeded coneMidpoint algorithm starts with seeded cone Seed threshold may be 0 to increase collinear safetyPlace new seeds between two close stable conesAlso center of three stable cones possibleRe-iterate using midpoint seedsIsolated stable cones are unchangedStill not completely safe!Apply split & mergeUsually split/merge fraction 0.75
8. Midpoint Seeded ConeAttempt to increase infrared safety for seeded coneMidpoint algorithm starts with seeded cone Seed threshold may be 0 to increase collinear safetyPlace new seeds between two close stable conesAlso center of three stable cones possibleRe-iterate using midpoint seedsIsolated stable cones are unchangedStill not completely safe!Apply split & mergeUsually split/merge fraction 0.75 (from G. Salam & G. Soyez, JHEP 0705:086,2007)
9. Seedless Fixed ConeImprovements to cone algorithms: no seedsAll stable cones are consideredAvoid collinear unsafety in seeded cone algorithmAvoid infrared safety issue Adding infinitively soft particle does not lead to new (hard) coneExact seedless cone finderProblematic for larger number of particlesApproximate implementationPre-clustering in coarse towersNot necessarily appropriate for particles and even some calorimeter signals
10. Seedless Fixed ConeImprovements to cone algorithms: no seedsAll stable cones are consideredAvoid collinear unsafety in seeded cone algorithmAvoid infrared safety issue Adding infinitively soft particle does not lead to new (hard) coneExact seedless cone finderProblematic for larger number of particlesApproximate implementationPre-clustering in coarse towersNot necessarily appropriate for particles and even some calorimeter signals
11. Seedless Fixed ConeImprovements to cone algorithms: no seedsAll stable cones are consideredAvoid collinear unsafety in seeded cone algorithmAvoid infrared safety issue Adding infinitively soft particle does not lead to new (hard) coneExact seedless cone finderProblematic for larger number of particlesApproximate implementationPre-clustering in coarse towersNot necessarily appropriate for particles and even some calorimeter signalsNote: 100 particles need ~1017 years to be clustered!
12. Seedless Fixed ConeImprovements to cone algorithms: no seedsAll stable cones are consideredAvoid collinear unsafety in seeded cone algorithmAvoid infrared safety issue Adding infinitively soft particle does not lead to new (hard) coneExact seedless cone finderProblematic for larger number of particlesApproximate implementationPre-clustering in coarse towersNot necessarily appropriate for particles and even some calorimeter signals
13. Seedless Infrared Safe ConeSISCone (Salam, Soyez 2007)Exact seedless cone with geometrical (distance) orderingSpeeds up algorithm considerably!Find all distinctive ways on how a segment can enclose a subset of the particlesInstead of finding all stable segments!Re-calculate the centroid of each segmentE.g., pT weighted re-calculation of direction“E-scheme” works as wellSegments (cones) are stable if particle content does not changeRetain only one solution for each segmentStill needs split & merge to remove overlapRecommended split/merge fraction is 0.75Typical timesN2lnN for particles in 2-dim plane 1-dim example:See following slides!(inspired by G. Salam & G. Soyez, JHEP 0705:086,2007)
14. SISCone Principle (1-dim!)
15. SISCone Principle (1-dim!)
16. SISCone Principle (1-dim!)
17. SISCone Principle (1-dim!)
18. SISConeSimilar ordering and combinations in 2-dimUse circles instead of linear segmentsStill need split & mergeOne additional parameter outside of jet/cone sizeNot very satisfactory!But at least a practical seedless cone algorithmVery comparable performance to e.g. Midpoint!(from G. Salam & G. Soyez, JHEP 0705:086,2007)
19. SISCone PerformanceInfrared safety failure ratesComputing performance(from G. Salam & G. Soyez, JHEP 0705:086,2007)
20. Recursive Recombination (kT)Computing performance an issueTime for traditional kT is ~N3Very slow for LHCFastJet implementations Use geometrical ordering to find out which pairs of particles have to be manipulated instead of recalculating them all!Very acceptable performance in this case!
21. Recursive Recombination (kT)Computing performance an issueTime for traditional kT is ~N3Very slow for LHCFastJet implementations Use geometrical ordering to find out which pairs of particles have to be manipulated instead of recalculating them all!Very acceptable performance in this case!kT (standard)ATLAS ConeFastJet kTkT (standard + 0.2 x 0.2 pre-clustering)
22. FastJet kTAddress the search approachNeed to find minimum in standard kT Order N3 operationsConsider geometrically nearest neighbours in FastJet kTReplace full search by search over (jet, jet neighbours)Need to find nearest neighbours for each proto-jet fastSeveral different approaches: ATLAS (Delsart 2006) uses simple geometrical model, Salam & Cacciari (2006) suggest Voronoi cellsBoth based on same fact relating dij and geometrical distance in ΔRBoth use geometrically ordered lists of proto-jets
23. Fast kT (ATLAS – Delsart)Possible implementation (P.A. Delsart, 2006)Nearest neighbour searchIdea is to only limit recalculation of distances to nearest neighbours Try to find all proto-jets having proto-jet k as nearest neighbourCenter pseudo-rapdity (or rapdity)/azimuth plane on kTake first proto-jet j closest to k in pseudo-rapidityCompute middle line Ljk between k and jAll proto-jets below Ljk are closer to j than k → k is not nearest neighbour of thoseTake next closest proto-jet i in pseudo-rapidityProceed as above with exclusion of all proto-jets above LikSearch stops when point below intersection of Ljk and Lik is reached, no more points have k as nearest neighbour
24. FastJet kT (Salam & Cacciari)Apply geometrical methods to nearest neighbour searchesVoronoi cell around proto-jet k defines area of nearest neighboursNo point inside area is closer to any other protojet Apply to protojets in pseudo-rapdity/azimuth planeUseful tool to limit nearest neighbour search Determines region of re-calculation of distances in kTAllows quick updates without manipulating too many long listsComplex algorithm!Read G. Salam & M. Cacciari, Phys.Lett.B641:57-61 (2006) (source http://en.wikipedia.org/wiki/Voronoi_diagram)
25. Jet Algorithm PerformanceVarious jet algorithms produce different jets from the same collision eventClearly driven by the different sensitivities of the individual algorithmsCannot expect completely identical picture of event from jetsDifferent topology/number of jetsDifferences in kinematics and shape for jets found at the same directionChoice of algorithm motivated by physics analysis goalE.g., IR safe algorithms for jet counting in W + n jets and othersNarrow jets for W mass spectroscopySmall area jets to suppress pile-up contributionMeasure of jet algorithm performance depends on final stateCone preferred for resonancesE.g., 2 – 3…n prong heavy particle decays like top, Z’, etc.Boosted resonances may require jet substructure analysis – need kT algorithm! Recursive recombination algorithms preferred for QCD cross-sectionsHigh level of IR safety makes jet counting more stablePile-up suppression easiest for regularly shaped jetsE.g., Anti-kT most cone-like, can calculate jet area analytically even after split and mergeMeasures of jet performanceParticle level measures prefer observables from final stateDi-jet mass spectra etc.Quality of spectrum importantDeviation from Gaussian etc.
26. Jet Shapes (1)(from P.A. Delsart)
27. Jet Shapes (2)(from P.A. Delsart)
28. Jet Shapes (3)(from G. Salam’s talk at the ATLAS Hadronic Calibration Workshop Tucson 2008)
29. Jet Reconstruction Performance (1)(from Salam ,Cacciari, Soyez, http://quality.fastjet.fr)Quality estimator for distributionsBest reconstruction: narrow GaussianWe understand the error on the mean!Observed distributions often deviate from GaussianNeed estimators on size of deviations!Should be least biased measuresBest performance gives closest to Gaussian distributionsList of variables describing shape of distribution on next slideFocus on unbiased estimatorsE.g., distribution quantile describes the narrowest range of values containing a requested fraction of all eventsKurtosis and skewness harder to understand, but clear message in case of Gaussian distribution!
30. Jet Reconstruction Performance Estimators
31. Jet Reconstruction PerformanceQuality of mass reconstruction for various jet finders and configurationsStandard model – top quark hadronic decayLeft plot – various jet finders and distance parametersBSM – Z’ (2 TeV) hadronic decay Right plot – various jet finders with best configuration
32. Jet Performance Examples (1)(from Cacciari, Rojo, Salam, Soyez, JHEP 0812:032,2008)
33. Jet Performance Examples (2)(from Cacciari, Rojo, Salam, Soyez, JHEP 0812:032,2008)
34. Jet Performance Examples (3)(from Cacciari, Rojo, Salam, Soyez, JHEP 0812:032,2008)
35. Jet Performance Examples (3)(from Cacciari, Rojo, Salam, Soyez, JHEP 0812:032,2008)Many more evaluations in the paper!
36. Interactive ToolWeb-based jet performance evaluation availablehttp://www.lpthe.jussieu.fr/~salam/jet-quality