Jets Lecture 1: jet algorithms Lecture 2: jet substructure

Transcription

1 MadGraph School Shanghai - November 2015 Jets Lecture 1: jet algorithms Lecture 2: jet substructure Matteo Cacciari LPTHE Paris

2 Why jets A jet is something that happens in high energy events: a collimated bunch of hadrons flying roughly in the same direction We could eyeball the collimated bunches, but it becomes impractical with millions of events The classification of particles into jets is best done using a clustering algorithm 2

3 The pervasiveness of jets ATLAS and CMS have each published 400+ papers since 2010 More than half of these papers make use of jets 60% of the searches papers makes use of jets Plot by G. Salam (Source: INSPIRE. Results may vary when employing different search keywords) Why are jets so important? 3

4 Taming reality Multileg + PS?? QCD predictions Real data Jets One purpose of a jet clustering algorithm is to reduce the complexity of the final state, simplifying many hadrons to simpler objects that one can hope to calculate 4

5 Jet clustering algorithm A jet algorithm maps the momenta of the final state particles into the momenta of a certain number of jets: {p } jet algorithm {j } i k particles, 4-momenta, calorimeter towers,... jets Most algorithms contain a resolution parameter, R, which controls the extension of the jet 5

6 A jet algorithm + its parameters (e.g. R) + a recombination scheme = a Jet Definition Jet Definition /// define a jet definition JetDefinition jet_def(jetalgorithm jet_algorithm, double R, RecombinationScheme rec_sch = E_scheme); 6

7 Two main classes of jet algorithms Sequential recombination algorithms Bottom-up approach: combine particles starting from closest ones How? Choose a distance measure, iterate recombination until few objects left, call them jets Works because of mapping closeness QCD divergence Examples: Jade, kt, Cambridge/Aachen, anti-kt,.. Cone algorithms Top-down approach: find coarse regions of energy flow. How? Find stable cones (i.e. their axis coincides with sum of momenta of particles in it) Works because QCD only modifies energy flow on small scales Examples: JetClu, MidPoint, ATLAS cone, CMS cone, SISCone... 7

8 A little history Cone-type jets were introduced first in QCD in the 1970s (Sterman-Weinberg 77) In the 1980s cone-type jets were adapted for use in hadron colliders (SppS, Tevatron...) iterative cone algorithms LEP was a golden era for jets: new algorithms and many relevant calculations during the 1990s Introduction of the theory-friendly kt algorithm sequential recombination type algorithm, IRC safe it allows for all order resummation of jet rates Several accurate calculations in perturbative QCD of jet properties: rates, jet mass, thrust,... 8

9 e + e - kt (Durham) algorithm [Catani, Dokshitzer, Olsson, Turnock, Webber 91] Distance: In the collinear limit, the numerator reduces to the relative transverse momentum (squared) of the two particles, hence the name of the algorithm Find the minimum ymin of all yij If ymin is below some jet resolution threshold ycut, recombine i and j into a single new particle ( pseudojet ), and repeat If no ymin < ycut are left, all remaining particles are jets 9

10 e + e - kt (Durham) algorithm in action 2-jet Characterise events in terms of number of jets (as a function of ycut) 4-jet 3-jet 5-jet Resummed calculations for distributions of ycut doable with the kt algorithm 10

11 e + e - kt (Durham) algorithm v. QCD kt is a sequential recombination type algorithm One key feature of the kt algorithm is its relation to the structure of QCD divergences: The yij distance is the inverse of the emission probability The kt algorithm roughly inverts the QCD branching sequence (the pair which is recombined first is the one with the largest probability to have branched) The history of successive clusterings has physical meaning 11

12 Jet challenges at the LHC The LHC environment differs from the LEP one (and even the Tevatron) under many respects Number of final state particles much larger (order 10 3 ) needs a fast algorithm Many higher order calculations (NLO, NNLO) available needs an IRC-safe algorithm Presence of background (underlying event and pileup) needs small/known susceptibility and/or ability to subtract background Jets often initiated by a large-momentum heavy particle needs capability to distinguish boosted objet jet from QCD jet 12

13 IRC safety An observable is infrared and collinear safe if, in the limit of a collinear splitting, or the emission of an infinitely soft particle, the observable remains unchanged: O(X; p 1,...,p n,p n+1 0) O(X; p 1,...,p n ) O(X; p 1,...,p n p n+1 ) O(X; p 1,...,p n + p n+1 ) This property ensures cancellation of real and virtual divergences in higher order calculations If we wish to be able to calculate a jet rate in perturbative QCD the jet algorithm that we use must be IRC safe: soft emissions and collinear splittings must not change the hard jets 13

14 From Wikipedia: In ancient Roman religion and myth, Janus (Latin: Ianus, pronounced [ˈiaː.nus]) is the god of beginnings and transitions, and thereby of gates, doors, passages, endings and time. He is usually depicted as having two faces, since he looks to the future and to the past. The Romans named the month of January (Ianuarius) in his honor. Janus Jets Like Janus, jets can serve two purposes: Observables Tools to be defined, calculated, measured to be used to extract specific properties of the final state Different clustering algorithms have different properties and characteristics that can make them more or less appropriate for each of these tasks 14

15 Jets as tools Background characterisation and subtraction Mass reconstruction Remove soft contamination from a hard jet Tag heavy objects originating the jet 15

16 (Boosted) jet studies at the LHC Lily Asquith, summary talk at BOOST 2015 Essentially none of these tools existed as lately as seven years ago 16

17 Glossary What i.e. When Ref. AKT Anti-kt algorithm CA Cambridge/Aachen algorithm BDRS mass-drop tagger, includes filtering trimmed Trimming, tagger/groomer pruned Pruning, tagger/groomer HTT HepTopTagger N-subjettiness jet shape function, used in tagging WTA Winner-Take-All (recombination scheme) one-pass choice of axis for N-subjettiness 2010 JVT Jet Vertex Tagger (used in pileup subtr.) 2014 ρ background density (used in pileup subtr.) D2 jet shape function, used in tagging PUPPI particle-by-particle pileup subtr Soft Drop tagger/groomer

18 Outline Algorithms, speed Infrared and collinear safety Lecture 1 Background (pileup) Substructure Lecture 2 18

19 Outline Algorithms, speed Infrared and collinear safety Background (pileup) Substructure 19

20 The common wisdom circa 2005 Cone algorithms are IRC unsafe Sequential recombination algorithms (i.e. kt) are slow and too susceptible to background contamination because, to make them reasonably fast, they were usually implemented via approximate methods using seeds because they scale like N 3 because they tend to collect soft particles up to large distances from centre because they were often run with R=1 and compared to cones with R=0.5! 20

21 Geometry The solution to the speed problem came from considering the clustering problem from a geometrical rather from a combinatorial point of view Sequential recombination algorithms could be implemented with O(N 2 ) or even O(NlnN) complexity rather than O(N 3 ) [MC, Salam, 2006] Cone algorithms could be implemented exactly (and therefore made IRC safe) with O(N 2 lnn) rather than O(N2 N ) complexity [Salam, Soyez 2007] 21

22 The kt algorithm and its siblings d ij = min(k 2p ti,k 2p tj )Δy2 + Δφ 2 R 2 d ib = k 2p ti p = 1 kt algorithm S. Catani, Y. Dokshitzer, M. Seymour and B. Webber, Nucl. Phys. B406 (1993) 187 S.D. Ellis and D.E. Soper, Phys. Rev. D48 (1993) 3160 p = 0 Cambridge/Aachen algorithm Y. Dokshitzer, G. Leder, S.Moretti and B. Webber, JHEP 08 (1997) 001 M. Wobisch and T. Wengler, hep-ph/ p = -1 anti-kt algorithm MC, G. Salam and G. Soyez, arxiv: NB: in anti-kt pairs with a hard particle will cluster first: if no other hard particles are close by, the algorithm will give perfect cones Quite ironically, a sequential recombination algorithm is the perfect cone algorithm 22

23 IRC safety of generalised-kt algorithms d ij = min(k 2p ti,k 2p tj )Δy2 + Δφ 2 R 2 d ib = k 2p ti p > 0 New soft particle (kt 0) means that d 0 clustered first, no effect on jets New collinear particle (Δy 2 +ΔΦ 2 0) means that d 0 clustered first, no effect on jets p = 0 New soft particle (kt 0) can be new jet of zero momentum no effect on hard jets New collinear particle (Δy 2 +ΔΦ 2 0) means that d 0 clustered first, no effect on jets p < 0 New soft particle (kt 0) means d clustered last or new zero-jet, no effect on hard jets New collinear particle (Δy 2 +ΔΦ 2 0) means that d 0 clustered first, no effect on jets 23

24 kt IRC safe algorithms SR dij = min(kti 2,ktj 2 )ΔRij 2 /R 2 Catani et al 91 Ellis, Soper 93 hierarchical in rel p t NlnN Cambridge/ Aachen SR dij = ΔRij 2 /R 2 hierarchical in angle Dokshitzer et al 97 Wengler, Wobish 98 NlnN anti-kt SR dij = min(kti -2,ktj -2 )ΔRij 2 /R 2 gives perfectly conical hard jets MC, Salam, Soyez 08 (Delsart, Loch) N 3/2 SISCone Seedless iterative cone with split-merge gives economical jets Salam, Soyez 07 N 2 lnn All are available in FastJet, second-generation algorithms (As well as many IRC unsafe ones) 24

25 Jet clustering in FastJet /// define a jet definition JetDefinition jet_def(jetalgorithm jet_algorithm, double R, RecombinationScheme rec_sch = E_scheme); jet_algorithm can be any one of the four IRC safe algorithms, or also most of the old IRC-unsafe ones, for legacy purposes /// create a ClusterSequence, extract the jets ClusterSequence cs(input_particles, jet_def); vector<pseudojet> jets = sorted_by_pt(cs.inclusive(jets));... // pt of hardest jet double pt_hardest = jets[0].pt();... // constituents of hardest jet vector<pseudojet> constits = jets[0].constituents(); 25

26 FastJet speed Time needed to cluster an event with N particles time (s) Intel i5 760 FastJet R=0.7 SISCone hadron collisions with pileup hadron collisions N anti-kt anti-k t k t C/A SISCone kt Cambridge/Aachen PbPb collisions 26

27 Outline Algorithms, speed Infrared and collinear safety Background (pileup) Substructure 27

28 Hard jets and background In a realistic set-up underlying event (UE) and pile-up (PU) from multiple collisions produce many soft particles which can contaminate the hard jet 28

29 Pileup 78-vertices event from CMS Pileup can deposit several tens of GeV (or even hundreds, in a heavy ion collision) into a medium-sized jet 29

30 Hard jets and background How are the hard jets modified by the background? Susceptibility (how much bkgd gets picked up) Jet areas Resiliency (how much the original jet changes) Backreaction 30

31 Jet areas A jet s area is defined as the extent of the region where infinitesimally soft particles get clustered into the jet More in details, a jet s active area is the extent of the region where a distribution of infinitesimally soft particles, that can also cluster among themselves, is clustered into the jet A jet s active area measures a jet s sensitivity to contamination from soft particles like underlying event and pileup Jets do not necessarily have cone-shaped profiles 31

32 kt Cam/Aa SISCone anti-kt

33 Resiliency: backreaction How (much) a jet changes when immersed in a background Without background With background Backreaction loss Backreaction gain 33

34 Resiliency: backreaction pt loss 1/N dn/dp t (GeV -1 ) R=1 SISCone (f=075) Cam/Aachen k t anti-k t Pythia 6.4 LHC (high lumi) 2 hardest jets p t,jet > 1 TeV y <2 pt gain (B) p t (GeV) Anti-kt jets are much more resilient to changes from background immersion (NB. Backreaction is a minimal issue in pp background and at large pt. Can be much more important in Heavy Ion collisions) 34

35 Anti-kt jets and background Anti-kt jets maximise resiliency, and their regular shapes makes them easier to correct for detector-related effects Default choice of all LHC collaborations 35

36 The IRC safe algorithms Speed Regularity UE/pileup contamination Backreaction Hierarchical substructure kt Cambridge /Aachen anti-kt / SISCone Array of tools with different characteristics. Pick the right one for the job 36

37 Hard jets and background Modifications of the hard jet p t = A ± ( A + A + A 2 A 2 )+ p BR t Background momentum density (per unit area) background back-reaction susceptibility resiliency 37

38 Background subtraction Two main approaches to background subtraction Jet-based Cluster the full event, determine the event-specific (ρ) and jetspecific (A) quantities, and subtract the relevant contamination from a given observable Pros: largely unbiased subtraction Cons: slow, potentially large(er) residual uncertainty Examples: `jet area/median in FastJet, GenericSubtractor for jet shapes, JetFFMoments for fragmentation functions,... Particle-based Produce a reduced event, by dropping some of the particles. Cluster this reduced event, and calculate from it the observables Pros: fast, often small(er) residual uncertainty Not natively unbiased, can depend on choice of parameters Examples: ConstituentSubtractor, SoftKiller, PUPPI,... 38

39 Background subtraction: jet-based Correction of a jet transverse momentum hard jet, corrected pt hard jet, raw = pt ρ Area hard jet MC, Salam, If ρ is measured on an event-by-event basis, and each jet subtracted individually, this procedure will remove many fluctuations and generally improve the resolution of, say, a mass peak p t = A ± ( A + A + A 2 A 2 )+ p BR t Irreducible fluctuations: uncertainty of the subtraction Needs two ingredients: ρ and Ajet 39

40 Definition of a specific jet area and its calculation for each jet in FastJEt Jet areas /// specify where to place the ghosts, their area, how many times /// to repeat the clustering double rapmax = 2.5; int nrepeat = 1; double ghost_area = 0.01; GhostedAreaSpec gas(rapmax, nrepeat, ghost_area); /// use this configuration to define the area /// A sensible default for gas is provided AreaDefinition area_def(active_area, gas); /// construct cluster sequence with areas ClusterSequenceArea(input_particles, jet_def, area_def);... jets[0].area() 40

41 Background estimation and subtraction // constructor for a background estimator JetMedianBackgroundEstimator bge(selector sel, JetDefinition jet_def, AreaDefinition area_def); // an alternative (faster) background estimator //GridMedianBackgroundEstimator bge(selector sel, grid_step); bge.set_particles(input_particles);... double rho = bge.rho(jet); // extract rho estimation // define a subtractor Subtractor sub(&bge); // apply it to a jet (or a vector of jets) PseudoJet subtracted_jet = sub(jet); 41

42 Numerical jet shape correction Soyez et al A generic jet shape (a function of the momenta of all constituents of a jet) is modified by the addition of pileup Correct it by calculating numerically the derivatives that enter its Taylor expansion and subtracting (this generalises the jet area/median subtraction for transverse mom.) Pileup momentum density Numerical derivative w.r.t. ghosts momenta 42

43 Shape subtraction Pilup subtraction from jet shapes using GenericSubtractor from fjcontrib #include ExampleShapes.hh #include GenericSubtractor.hh // define a specific jet shape contrib::angularity ang(1.0); // angularity with alpha=1.0 // define a generic subtractor... construct a background estimator bge_rho... contrib::genericsubtractor gen_sub(&bge_rho); // compute the subtracted shape double subtracted_ang = gen_sub(ang, jet); 43

44 Particle-level pilup removal Pilup removal using SoftKiller from fjcontrib (SoftKiller progressively removes soft particles until ρ of event is zero) #include SoftKiller.hh // define SoftKiller double grid_size = 0.4; contrib::softkiller soft_killer(rapmax, grid_size); // apply it to the full event double pt_thresh //returns threshold for killed particles vector<pseudojet> soft_killed_event; soft_killer.apply(full_event, soft_killed_event, pt_thresh); // proceed with clustering and calculating shapes with // the reduced soft_killed_event ClusterSequence(soft_killed_event,...) 44

45 Comparisons of pileup subtractions from the CERN pileup mitigation workshop, PRELIMINARY DISPERSION σ ΔO (GeV) areasub constitsub safeareasub soft killer puppi safenpcsub lin cl.(rsub=0.3) CHS event, jet m, pt=020 BIAS <ΔO> (GeV) BETTER anti-kt R=0.4 30, 60, 100, 140 PU WORSE BETTER 45

46 Recap of lecture 1 A number of different IRC-safe jet algorithms exist They all try to be good proxies for hard partons, but they have different characteristics, especially with respect to soft particles Jets from all algorithms inevitably suffer from pileup contamination Techniques exist to subtract it, either at jet-level, or at particle-level Both the jet algorithms and many pileup subtraction techniques are packaged aither in FastJet or in fjcontrib contributions Use of standard algorithms and packages (either directly or through interfaces) should be privileged, as it ensures reproducibility