MC4BSM Daejeon - May 2014

Jets and FastJet Matteo Cacciari LPTHE Paris

In collaboration with Gavin Salam and Gregory Soyez Outline

‣Introduction: jets ‣A little history: the genesis of FastJet ‣FastJet features and usage ‣Basic clustering ‣Jets as tools ‣Grooming and Tagging

Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 2 Clusters in HEP: jets

A jet is something that happens in high energy events:

a collimated bunch of hadrons flying roughly in the same direction

(though, in the following, we’ll extend this intuitive definition somewhat)

Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 3 Jet clustering algorithm A jet algorithm maps the momenta of the final state particles into the momenta of a certain number of jets:

jet algorithm {pi} {jk} particles, jets 4-momenta, calorimeter towers, ....

Most algorithms contain a resolution parameter, R, which controls the extension of the jet

Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 4 The pervasiveness of jets ‣ ATLAS and CMS have each published 300+ papers since 2010 ‣ More than a third 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?

Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 53 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

Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 6 Jets

Jets can serve two purposes

‣ They can be observables, that one can calculate and measure

‣ They can be tools, that one can employ to extract specific properties of the final state

What characteristics should they have?

21 Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 7 Snowmass

[Addition of a soft Infrared and particle or a collinear Speed splitting should not collinear safety change final hard jets] 6. Provide a physically meaningful clustering history

Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 10238 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, ….. Usually trivially made IRC safe, but their algorithmic complexity scales like N3

‣ 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…... Can be programmed to be fairly fast, at the price of being complex and IRC unsafe

Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 9 FastJet FastJet was born in 2005 to make the kt algorithm fast and therefore exploitable at hadron colliders MC and G. Salam, hepph/0512210 101 JetClu (almost IR unsafe)

0 MidPoint 10 OJF

10-1 KtJet FastJet -2

t (s) 10

10-3

-4 LHC (single LHC (c. 20 LHC 10 Tevatron interaction) interactions) Heavy Ion

10-5 102 103 104 105 N Algorithmic complexity reduced from N3 to NlnN

Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 10 The kt algorithm and its siblings

2 2 Δy + Δφ 2p d = min(k2p,k2p) d = k ij ti tj R2 iB 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

Y. Dokshitzer, G. Leder, S.Moretti and B. Webber, JHEP 08 (1997) 001 p = 0 Cambridge/Aachen algorithm M. Wobisch and T. Wengler, hep-ph/9907280

p = -1 anti-kt algorithm MC, G. Salam and G. Soyez, arXiv:0802.1189 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

Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 11 IRC safe algorithms SR 2 2 2 2 Catani et al ‘91 kt dij = min(kti ,ktj )ΔRij /R Ellis, Soper ‘93 NlnN hierarchical in rel p t SR Cambridge/ 2 2 Dokshitzer et al ‘97 dij = ΔRij /R Wengler, Wobish ‘98 NlnN Aachen hierarchical in angle SR -2 -2 2 2 MC, Salam, Soyez ’08 3/2 anti-kt dij = min(kti ,ktj )ΔRij /R (Delsart, Loch) N gives perfectly conical hard jets Seedless iterative cone SISCone with split-merge Salam, Soyez ‘07 N2lnN gives ‘economical’ jets ‘second-generation’ algorithms All are available in FastJet, http://fastjet.fr (As well as many IRC unsafe ones)

Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 12 FastJet speed test Time needed to cluster an event with N particles 102 t Intel i5 760 t k 10 FastJet 3.0.1 anti-k R=0.7 1

10-1 Cambridge/Aachen -2 SISCone PbPb 10 collisions -3

time (s) 10 -4 hadron 10 collisions with pileup anti-k 10-5 t kt -6 hadron 10 collisions C/A SISCone 10-7 1 10 102 103 104 105 106 107 N Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 13 kt Cam/Aa

SISCone anti-kt http://fastjet.fr

Authors: MC, Gavin Salam, Gregory Soyez

Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 15 Suppose you are a BSM person....

What can FastJet do for you?

FastJet is used as the main jet clustering code by all LHC experiments and by a number of packages (aMC@NLO, PYTHIA 8, Delphes, ....)

Chances are that, even if you didn’t realize it, you are already using it.

If you run one of these codes, and only need basic jet clustering, you are unlikely to need more.

Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 16 A word on how to include FastJet FastJet is a C++ library The basic, and recommended, usage mode is to install it and compile agains it ‣ All functionalities are available ‣ FJ updates are easily included Other options: ‣ A standalone fjcore.[cc|hh] small file is provided for direct inclusion into projects ‣ It contains most the main functionalities of FastJet ‣ It is designed so as not to interfere with linking with a full FJ version ‣ It is presently used by (at least) PYTHIA8 and aMC@NLO ‣ Copy the FJ files into your package [deprecated!!] ‣ This is the choice made by Delphes ‣ FJ cannot be easily updated ‣ Will likely interfere with a link to a different FJ version

PS. Whatever you do, if you are maintaining a public package that uses FastJet please print out the FJ banner where the users can see it

Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 17 ‘Jet substructure’ papers in INSPIRE Number of papers containing the words ‘jet substructure’

7

Papers containing "jet substructure" + pioneering papers by Mike Seymour in 1991 and 1994 6 (Source: INSPIRE)

5 More than 100 papers since 2008 (+ some background noise) 4

3 Pioneered by M. Seymour in the early papers / month ‘90s, rebooted by BDRS paper 2

Mike Seymour Butterworth, Cox, Forshaw 1

0 1990 1995 2000 2005 2010 2015 year

Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 1826 Why boosted objects

X X

Heavy particle X at rest Boosted heavy particle X

Easy to resolve jets and Cross section very much calculate invariant mass, reduced, but acceptance but signal very likely better and some swamped by background backgrounds smaller/ (eg H→bb v. tt →WbWb) reducible

Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 19 Why substructure

Scales: m ~ 100 GeV, pt ~ 500 GeV

‣ need small R (< 2m/pt ~ 0.4) to resolve two prongs ‣ need large R (>~ 3m/pt ~ 0.6) to cluster into a single jet

Possible strategies ‣ Use large R, get a single jet : background large ‣ Use small R, resolve the jets : what is the right scale? ‣ Let an algorithm find the ‘right’ substructure

Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 20 Jet substructure ‣The substructure of a jet (i.e. the ability to further resolve smaller components) can be exploited to ‣tag a particular structure inside the jet, i.e. a massive particle ‣ Examples: Higgs (2-prongs decay), top (3-prongs decay) ‣remove background contamination from the jet or its components, while keeping the bulk of the perturbative radiation ‣ Examples: filtering, trimming, pruning ‣ This operation if often generically denoted as grooming

In the following I’ll be mainly illustrating the BDRS tagger/filter as a pedagogical example, and also list other approaches

Matteo Cacciari - LPTHE MCnet-LPCC Summer School - July 2012 - CERN 21 pp →ZH → νν-bb- The BDRS tagger Butterworth, Davison, Rubin, Salam, 2008

It’s a two-prongs tagger for boosted Higgs, which

‣ Uses the Cambridge/Aachen algorithm ‣ Employs a Mass-Drop condition (as well as an asymmetry cut) to find the relevant splitting (i.e. ‘tag’ the heavy particle) ‣ Includes a post-processing step, using ‘filtering’ (introduced in the same paper) to clean as much as possible the resulting jets of UE contamination

Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 22 pp →ZH → νν-bb- Visualisation of BDRS Butterworth, Davison, Rubin, Salam, 2008

Undo the clustering into subjets, Re-cluster with smaller R, Cluster with a large R until a large mass drop and keep only 3 hardest is observed jets

Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 2331 BDRS in FastJet In FastJet #include “fastjet/tools/MassDropTagger.hh” #include “fastjet/tools/Filter.hh”

JetDefinition jet_def(cambridge_algorithm, 1.2); ClusterSequence cs(input_particles, jet_def);

// define the tagger and use it MassDropTagger md_tagger(0.667, 0.09); PseudoJet tagged = md_tagger(jets[0]);

// define the filter and use it Filter filter(0.3,SelectorNHardest(3)); Pseudojet higgs = filter(tagged); // this is the Higgs!!

The real analysis is slightly more refined (b-tagging, dynamical filter radius, etc) but the main features are already present here

Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 24 The strategy A generic substructure approach to tagging will

‣ Cluster initially with a large R, so as to collect all the decay products of a boosted heavy particle into a single jet ‣ Decluster this jet into subjets, using some conditions to decide when to stop the declustering (i.e. find the ‘relevant splitting’), possibly including kinematical cuts to reduce the QCD background. ‣ The stopping criterion automatically finds the ‘right size’ for the distance between the two prongs of the heavy particle decay ‣ Alternatively to declustering, one can employ one of the jet-shapes based tagging methods, i.e. N-subjettiness ratios ‣ Optionally add a final ‘cleaning’ procedure to remove as much as possible spurious soft/background radiation

Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 25 Generic tagging/grooming Fat-jet finding Often anti-kt, R ≈1

large pt, large mass fat-jet, signal or background

Tagging step

signal jet candidate, still background-contaminated Note that in some taggers (i.e. pruning) the tagging and grooming steps are grooming step not explicitly factorised Also, some tools may actually not follow rigidly this scheme

final candidate, potentially with little background contamination

Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 26 The jet substructure maze

Slide by G. Salam

Apologies for missing or misplaced items or links

Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 27 FastJet tools Due to historical reasons, some of these tools (typically the early ones) are available directly in FastJet, others from the separate FastJet Contrib project

Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 28 FastJet Contrib

Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 29 FastJet Contrib

Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 30 Certainly incomplete Jet substructure in BSM list of phenomenology papers

Discovering baryon-number violating neutralino decays at the LHC Jonathan M. Butterworth, John R. Ellis, Are R. Raklev, Gavin P. Salam, arXiv:0906.0728

Stop Reconstruction with Tagged Tops Tilman Plehn, Michael Spannowsky, Michihisa Takeuchi, Dirk Zerwas, arXiv:1006.2833

Boosted Semileptonic Tops in Stop Decays Tilman Plehn, Michael Spannowsky, Michihisa Takeuchi, arXiv:1102.0557

Scale-invariant resonance tagging in multijet events and new physics in Higgs pair production Maxime Gouzevitch, Alexandra Oliveira, Juan Rojo, Rogerio Rosenfeld, Gavin P. Salam, Veronica Sanz, arXiv:1303.6636

Pulling Out All the Stops: Searching for RPV SUSY with Stop-Jets Yang Bai, Andrey Katz, Brock Tweedie, arXiv:1309.6631

Measuring boosted tops in semi-leptonic ttbar events for the standard model and beyond Mihailo Backovic, Ofir Gabizon, Jose Juknevich, Gilad Perez, Yotam Soreq, arXiv:1311.2962

Reconstructing singly produced top partners in decays to Wb Nicolas Gutierrez Ortiz, James Ferrando, Deepak Kar, Michael Spannowsky, arXiv:1403.7490

Hadronic b′ search at the LHC with top and W taggers Shuo Yang, Ji Jiang, Qi-Shu Yan, Xiaoran Zhao, arXiv:1405.2514

Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 31 Jet substructure in BSM Slide by G. Salam Extensive experimental work Last 12 ATLAS & CMS preprints citing jet substructure work

Jet Cross-Section Measurements In CMS Searches for anomalous ttbar production in pp collisions at $ CMS Collaboration \sqrt{s}$=8 TeV Inspire. arXiv:1306.6604 (ps, pdf). Int.J.Mod.Phys. A28 (2013) CMS Collaboration 1330030. Inspire. arXiv:1309.2030 (ps, pdf). 6 cites [co]

Performance of jet substructure techniques for large-$R$ jets in Search for heavy resonances decaying to top -proton collisions at $\sqrt{s}$ = 7 TeV using the ATLAS for the CMS Collaboration detector Inspire. arXiv:1310.8183 (ps, pdf). ATLAS Collaboration Search for the standard model produced in association Inspire. arXiv:1306.4945 (ps, pdf). JHEP 1309 (2013) 076. 16 cites with a W or a Z boson and decaying to bottom quarks [co] CMS Collaboration Measurement of jet shapes in top pair events at $\sqrt{s}$ = 7 TeV Inspire. arXiv:1310.3687 (ps, pdf). 3 cites [co] using the ATLAS detector ATLAS Collaboration Search for the SM Higgs Boson Produced in Association with a Inspire. arXiv:1307.5749 (ps, pdf). Vector Boson and Decaying to Bottom Quarks for the CMS Collaboration Searches for New Physics in Multijet Final States Inspire. arXiv:1310.3551 (ps, pdf). for the CMS Collaboration Inspire. arXiv:1307.2518 (ps, pdf). Inclusive search for a vector-like T with charge 2/3 in pp collisions at $\sqrt{s}$=8 TeV Search for Single and Pair-Production of Dijet Resonances with the CMS Collaboration CMS Detector Inspire. arXiv:1311.7667 (ps, pdf). CMS Collaboration Inspire. arXiv:1307.1400 (ps, pdf). J.Phys.Conf.Ser. 455 (2013) Search for top-quark partners with charge 5/3 in the same-sign dilepton 012034. 1 cites [co] final state CMS Collaboration Search for dark matter in events with a hadronically decaying W Inspire. arXiv:1312.2391 (ps, pdf). or Z boson and missing transverse momentum in pp collisions at $ \sqrt{s}$=8 TeV with the ATLAS detector ATLAS Collaboration Inspire. arXiv:1309.4017 (ps, pdf). 5 cites [co]

Jet Substructure December 2013 24 Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 32 Summary ‣FastJet is a C++ library for performing jet clustering and a number of other jet-related tasks ‣ It includes tools for basic clustering, tagging, grooming, pileup subtraction, usually implemented with an eye to user-friendliness ‣ Used by all LHC experiments and a number of phenomenological projects, it is available under GPLv2 license at http://fastjet.fr

‣A sister project, FastJet Contrib, has been started in February 2013 ‣ It is hosted by HepForge at http://fastjet.hepforge.org/contrib ‣ It aims at collecting, under a common build framework, jet tools that make use of FastJet ‣ It is open to all third-party authors

Matteo Cacciari - LPTHE MC4BSM - Daejeon - May 2014 33