Introduction to Jet Finding and Jetography (1)
Gavin Salam
CERN, Princeton University and LPTHE/Paris (CNRS)
2011 IPMU-YITP School and Workshop on Monte Carlo Tools for LHC Yukawa Institute for Theoretical Physics, Kyoto University, Japan September 2011 [Introduction] [Background knowledge] Jets
Jets are everywhere in QCD But not the same as partons: Our window on partons Partons ill-defined; jets well-definable
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 2 / 30 [Introduction] [Background knowledge] Why do we see jets? Parton fragmentation
Gluon emission: dE dθ α ≫ 1 quark Z s E θ
At low scales:
αs → 1
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 3 / 30 [Introduction] [Background knowledge] Why do we see jets? Parton fragmentation
Gluon emission: dE dθ α ≫ 1 quark Z s E θ θ At low scales: gluon αs → 1
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 3 / 30 [Introduction] [Background knowledge] Why do we see jets? Parton fragmentation
Gluon emission: dE dθ α ≫ 1 quark Z s E θ
At low scales:
αs → 1
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 3 / 30 [Introduction] [Background knowledge] Why do we see jets? Parton fragmentation
Gluon emission: dE dθ α ≫ 1 quark Z s E θ
At low scales:
αs → 1 hadronisation non−perturbative
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 3 / 30 [Introduction] [Background knowledge] Why do we see jets? Parton fragmentation
Gluon emission: π+ dE dθ α ≫ 1 quark Z s E θ KL π0 At low scales: K+ − αs → 1
hadronisation π non−perturbative
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 3 / 30 [Introduction] [Background knowledge] Why do we see jets? Parton fragmentation
Gluon emission: π+ dE dθ α ≫ 1 quark Z s E θ KL π0 At low scales: K+ − αs → 1
hadronisation π non−perturbative
High-energy partons unavoidably lead to collimated bunches of hadrons
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 3 / 30 [Introduction] [Background knowledge] Jets from scattering of partons Tevatron results Jets are unavoidable at hadron 1010 K D=0.7 colliders, e.g. from parton scat- T CDF data ( L = 1.0 fb-1 ) 7 tering 10 Systematic uncertainties NLO: JETRAD CTEQ6.1M
4 corrected to hadron level jet µ µ JET µ 10 R = F = max pT / 2 = 0 PDF uncertainties [nb/(GeV/c)] 10 JET T
JET 6
p dp -2 × 10 |y |<0.1 ( 10 ) JET
-5 JET 10 0.1<|y |<0.7 (× 103) / dy
σ JET 2 -8 0.7<|y |<1.1
p d 10
1.1<|yJET|<1.6 (× 10-3) 10-11
jet 1.6<|yJET|<2.1 (× 10-6) 10-14 0 100 200 300 400 500 600 700 JET pT [GeV/c] Jet cross section: data and theory agree over many orders of magnitude ⇔ probe of underlying interaction
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 4 / 30 [Introduction] [Background knowledge] Jets from scattering of partons CMS results Jets are unavoidable at hadron colliders, e.g. from parton scat- tering jet
p
p
jet
Jet cross section: data and theory agree over many orders of magnitude ⇔ probe of underlying interaction
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 4 / 30 [Introduction] [Background knowledge] Jets from scattering of partons ATLAS results Jets are unavoidable at hadron colliders, e.g. from parton scat- tering jet
p
p
jet
Jet cross section: data and theory agree over many orders of magnitude ⇔ probe of underlying interaction
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 4 / 30 [Introduction] [Background knowledge] Jets from heavy decays
Heavy objects: multi-jet final-states − ◮ 107 t¯t pairs for 1 fb 1 @ 14 TeV ◮ Vast # of QCD multijet events
− # jets # events for 1fb 1 3 2 1010 4 5 109 5 1 109 6 3 108 7 1 108 8 4 107
Tree level pt (jet) > 20 GeV, ∆Rij > 0.4, |yij | < 2.5 Gleisman & H¨oche ’08
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 5 / 30 [Introduction] [Background knowledge] Seeing v. defining jets
Jets are what we see. How many jets do you see? Clearly(?) 2 jets here Do you really want to ask yourself this question for 109 events?
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 6 / 30 [Introduction] [Background knowledge] Seeing v. defining jets
q
q
Jets are what we see. How many jets do you see? Clearly(?) 2 jets here Do you really want to ask yourself this question for 109 events?
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 6 / 30 [Introduction] [Background knowledge] Seeing v. defining jets
Jets are what we see. How many jets do you see? Clearly(?) 2 jets here Do you really want to ask yourself this question for 109 events?
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 6 / 30 [Introduction] [Background knowledge] Seeing v. defining jets
Jets are what we see. How many jets do you see? Clearly(?) 2 jets here Do you really want to ask yourself this question for 109 events?
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 6 / 30 [Introduction] [Background knowledge] Seeing v. defining jets
Jets are what we see. How many jets do you see? Clearly(?) 2 jets here Do you really want to ask yourself this question for 109 events?
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 6 / 30 [Introduction] [Background knowledge] Seeing v. defining jets
Jets are what we see. How many jets do you see? Clearly(?) 2 jets here Do you really want to ask yourself this question for 109 events?
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 6 / 30 [Introduction] [Background knowledge] Seeing v. defining jets
A jet definition is a fully specified set of rules for projecting information from an event’s partons or hadrons onto a handful of parton-like objects (jets):
π π p φ K
LO partons NLO partons parton shower hadron level
Jet Def n Jet Def n Jet Def n Jet Def n jet 1 jet 2 jet 1 jet 2 jet 1 jet 2 jet 1 jet 2
Projection to jets should be resilient to QCD effects Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 7 / 30 [Introduction] [Background knowledge] QCD jets flowchart
Jet (definitions) provide central link between expt., “theory” and theory And jets are an input to almost all analyses
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 8 / 30 [Introduction] [Background knowledge] QCD jets flowchart
Jet (definitions) provide central link between expt., “theory” and theory And jets are an input to almost all analyses
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 8 / 30 [Introduction] [Background knowledge] These lectures
Aims: to provide you with
◮ the “basics” needed to understand what goes into current jet-based measurements; ◮ some insight into the issues that are relevant when thinking about a jet measurement
Structure: ◮ General considerations
◮ Common jet definitions at LHC Today ◮ Physics with jets Tomorrow
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 9 / 30 Defining jets
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 10 / 30 [Introduction] [General considerations] There is no unique jet definition
The construction of a jet is unavoidably ambiguous. On at least two fronts: 1. which particles get put together into a common jet? Jet algorithm + parameters 2. how do you combine their momenta? Recombination scheme Most commonly used: direct 4-vector sums (E-scheme)
Taken together, these different elements specify a choice of jet definition
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 11 / 30 [Introduction] [General considerations] There is no unique jet definition
The construction of a jet is unavoidably ambiguous. On at least two fronts: 1. which particles get put together into a common jet? Jet algorithm + parameters 2. how do you combine their momenta? Recombination scheme Most commonly used: direct 4-vector sums (E-scheme)
Taken together, these different elements specify a choice of jet definition
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 11 / 30 [Introduction] [General considerations] Not all ambiguity is allowed
Jets should be invariant with respect to certain modifications of the event: ◮ collinear splitting ◮ infrared emission
Why? ◮ Because otherwise lose real-virtual cancellation in NLO/NNLO QCD calculations → divergent results ◮ Hadron-level ‘jets’ would become fundamentally non-perturbative ◮ Detectors can resolve neither full collinear nor full infrared event structure
Known as infrared and collinear safety
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 12 / 30 [Introduction] [General considerations] Not all ambiguity is allowed
Jets should be invariant with respect to certain modifications of the event: ◮ collinear splitting ◮ infrared emission
Why? ◮ Because otherwise lose real-virtual cancellation in NLO/NNLO QCD calculations → divergent results ◮ Hadron-level ‘jets’ would become fundamentally non-perturbative ◮ Detectors can resolve neither full collinear nor full infrared event structure
Known as infrared and collinear safety
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 12 / 30 [Introduction] [General considerations] Not all ambiguity is allowed
Jets should be invariant with respect to certain modifications of the event: ◮ collinear splitting ◮ infrared emission
Why? ◮ Because otherwise lose real-virtual cancellation in NLO/NNLO QCD calculations → divergent results ◮ Hadron-level ‘jets’ would become fundamentally non-perturbative ◮ Detectors can resolve neither full collinear nor full infrared event structure
Known as infrared and collinear safety
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 12 / 30
[Introduction] [General considerations] Two main classes of jet alg.
Sequential recombination (kt , etc.) ◮ bottom-up ◮ successively undoes QCD branching
Cone ◮ top-down ◮ centred around idea of an ‘invariant’, directed energy flow
Cones: most widely used at Tevatron Seq. rec.: most widely used at LHC and HERA
In this lecture we’ll concentrate on the sequential recombination algorithms
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 14 / 30 [Introduction] [General considerations] Two main classes of jet alg.
Sequential recombination (kt , etc.) ◮ bottom-up ◮ successively undoes QCD branching
Cone ◮ top-down ◮ centred around idea of an ‘invariant’, directed energy flow
Cones: most widely used at Tevatron Seq. rec.: most widely used at LHC and HERA
In this lecture we’ll concentrate on the sequential recombination algorithms
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 14 / 30 Sequential recombination jet algorithms
starting with a classic e+e− algorithm
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 15 / 30 [Sequential recombination] + − [kt in e e ] Motivating sequential recombination algorithms It’s a good approximation to think of the development of a jet as a consequence of the repeated 1 → 2 branching of quarks and gluons. E.g. this is how Pythia and Herwig have long modelled events
Sequential recombination algorithms try to work their way backwards through this branching, repeatedly combining pairs of particles into a single one.
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 16 / 30 [Sequential recombination] + − [kt in e e ] Motivating sequential recombination algorithms It’s a good approximation to think of the development of a jet as a consequence of the repeated 1 → 2 branching of quarks and gluons. E.g. this is how Pythia and Herwig have long modelled events
Sequential recombination algorithms try to work their way backwards through this branching, repeatedly combining pairs of particles into a single one.
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 16 / 30 [Sequential recombination] + − [kt in e e ] Motivating sequential recombination algorithms It’s a good approximation to think of the development of a jet as a consequence of the repeated 1 → 2 branching of quarks and gluons. E.g. this is how Pythia and Herwig have long modelled events
Sequential recombination algorithms try to work their way backwards through this branching, repeatedly combining pairs of particles into a single one.
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 16 / 30 [Sequential recombination] + − [kt in e e ] Motivating sequential recombination algorithms It’s a good approximation to think of the development of a jet as a consequence of the repeated 1 → 2 branching of quarks and gluons. E.g. this is how Pythia and Herwig have long modelled events
Sequential recombination algorithms try to work their way backwards through this branching, repeatedly combining pairs of particles into a single one.
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 16 / 30 [Sequential recombination] + − [kt in e e ] Motivating sequential recombination algorithms It’s a good approximation to think of the development of a jet as a consequence of the repeated 1 → 2 branching of quarks and gluons. E.g. this is how Pythia and Herwig have long modelled events
Sequential recombination algorithms try to work their way backwards through this branching, repeatedly combining pairs of particles into a single one.
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 16 / 30 [Sequential recombination] + − [kt in e e ] Motivating sequential recombination algorithms It’s a good approximation to think of the development of a jet as a consequence of the repeated 1 → 2 branching of quarks and gluons. E.g. this is how Pythia and Herwig have long modelled events
Sequential recombination algorithms try to work their way backwards through this branching, repeatedly combining pairs of particles into a single one.
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 16 / 30 [Sequential recombination] + − [kt in e e ] Motivating sequential recombination algorithms It’s a good approximation to think of the development of a jet as a consequence of the repeated 1 → 2 branching of quarks and gluons. E.g. this is how Pythia and Herwig have long modelled events
Sequential recombination algorithms try to work their way backwards through this branching, repeatedly combining pairs of particles into a single one. The main questions are: ◮ How do you choose which pair of particles to combine at any given stage?
◮ When do you stop combining them?
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 16 / 30 [Sequential recombination] + − [kt in e e ] kt/Durham algorithm
Majority of QCD branching is soft & collinear, with following divergences:
2 2αsCA dEj dθij [dkj ]|Mg→gi gj (kj )|≃ , (Ej ≪ Ei , θij ≪ 1) . π min(Ei , Ej ) θij
To invert branching process, take pair with strongest divergence between them — they’re the most likely to belong together.
+ − This is basis of kt/Durham algorithm (e e ): 1. Calculate (or update) distances between all particles i and j: 2 2 2 min(E , E )(1 − cos θij ) y = i j ij Q2
NB: relative kt between particles 2. Find smallest of yij ◮ If > ycut , stop clustering ◮ Otherwise recombine i and j, and repeat from step 1 Catani, Dokshitzer, Olsson, Turnock & Webber ’91
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 17 / 30 [Sequential recombination] + − [kt in e e ] kt/Durham algorithm
Majority of QCD branching is soft & collinear, with following divergences:
2 2αsCA dEj dθij [dkj ]|Mg→gi gj (kj )|≃ , (Ej ≪ Ei , θij ≪ 1) . π min(Ei , Ej ) θij
To invert branching process, take pair with strongest divergence between them — they’re the most likely to belong together.
+ − This is basis of kt/Durham algorithm (e e ): 1. Calculate (or update) distances between all particles i and j: 2 2 2 min(E , E )(1 − cos θij ) y = i j ij Q2
NB: relative kt between particles 2. Find smallest of yij ◮ If > ycut , stop clustering ◮ Otherwise recombine i and j, and repeat from step 1 Catani, Dokshitzer, Olsson, Turnock & Webber ’91
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 17 / 30 [Sequential recombination] + − [kt in e e ] kt/Durham algorithm
Majority of QCD branching is soft & collinear, with following divergences: 2α C dE dθ The2 algorithm hass oneA parameterj ij [dkj ]|Mg→gi gj (kj )|≃ , (Ej ≪ Ei , θij ≪ 1) . π min(Ei , Ej ) θij ◮ ycut: sets minimal relative transverse momentum between To invertany branching pair of process, jets take pair with strongest divergence between them — they’re the most likely to belong together.
+ − This is basis of kt/Durham algorithm (e e ): 1. Calculate (or update) distances between all particles i and j: 2 2 2 min(E , E )(1 − cos θij ) y = i j ij Q2
NB: relative kt between particles 2. Find smallest of yij ◮ If > ycut , stop clustering ◮ Otherwise recombine i and j, and repeat from step 1 Catani, Dokshitzer, Olsson, Turnock & Webber ’91
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 17 / 30 [Sequential recombination] + − [kt in e e ] kt/Durham algorithm features
◮ Gives hierarchy to event and jets Event can be charaterised
by y23, y34, y45.
◮ Resolution parameter related to minimal transverse momentum between jets
Most widely-used jet algorithm in e+e−
◮ Collinear safe: collinear particles recombined early on ◮ Infrared safe: soft particles have no impact on rest of clustering seq.
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 18 / 30 [Sequential recombination] + − [kt in e e ] kt/Durham algorithm features
◮ Gives hierarchy to event and jets Event can be charaterised
by y23, y34, y45.
◮ Resolution parameter related to minimal transverse momentum between jets
Most widely-used jet algorithm in e+e−
◮ Collinear safe: collinear particles recombined early on ◮ Infrared safe: soft particles have no impact on rest of clustering seq.
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 18 / 30 [Sequential recombination] [kt for hadron colliders] kt alg. at hadron colliders
1st attempt ◮ Lose absolute normalisation scale Q. So use unnormalised dij rather than yij : 2 2 dij = 2 min(Ei , Ej )(1 − cos θij )
◮ Now also have beam remnants (go down beam-pipe, not measured) Account for this with particle-beam distance
2 diB = 2Ei (1 − cos θiB ) squared transv. mom. wrt beam
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 19 / 30 [Sequential recombination] [kt for hadron colliders] kt alg. at hadron colliders
2nd attempt: make it longitudinally boost-invariant Catani, Dokshitzer, Seymour & Webber ’93
◮ Formulate in terms of rapidity (y), azimuth (φ), pt
2 2 2 2 2 2 dij = min(pti , ptj )∆Rij , ∆Rij = (yi − yj ) + (φi − φj )
NB: not ηi , Eti ◮ Beam distance becomes 2 diB = pti squared transv. mom. wrt beam Apart from measures, just like e+e− alg. Known as exclusive kt algorithm. Problem: at hadron collider, no single fixed scale (as in Q in e+e−). So how do you choose dcut ? See e.g. Seymour & Tevlin ’06
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 20 / 30 [Sequential recombination] [kt for hadron colliders] kt alg. at hadron colliders
3rd attempt: inclusive kt algorithm
◮ Introduce angular radius R (NB: dimensionless!)
∆R2 d = min(p2 , p2 ) ij , d = p2 ij ti tj R2 iB ti
◮ 1. Find smallest of dij , diB 2. if ij, recombine them 3. if iB, call i a jet and remove from list of particles 4. repeat from step 1 until no particles left. S.D. Ellis & Soper, ’93; the simplest to use
Jets all separated by at least R on y, φ cylinder.
NB: number of jets not IR safe (soft jets near beam); number of jets above pt cut is IR safe.
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 21 / 30 [Sequential recombination] [kt for hadron colliders] kt alg. at hadron colliders
3rd attempt: inclusive kt algorithm
◮ Introduce angular radius R (NB: dimensionless!)
∆R2 d = min(p2 , p2 ) ij , d = p2 ij ti tj R2 iB ti
Two parameters to remember ◮ 1. Find smallest of dij , diB 2. if ij◮, recombineR: sets y − themφ reach of the jet; minimal interjet separation 3. if iB, call i a jet and remove from list of particles ◮ 4. repeatpt fromcut stepon the 1 until jets no particles left. These parameters are commonS.D. to Ellis all & widelySoper, ’93; used the hadron- simplest to use Jets allcollider separated jet by algorithms. at least R on y, φ cylinder.
NB: number of jets not IR safe (soft jets near beam); number of jets above pt cut is IR safe.
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 21 / 30 [Sequential recombination] [kt for hadron colliders] kt in action
kt alg.: Find smallest of
∆R2 d = min(k2 , k2 ) ij , d = k2 ij ti tj R2 iB ti
◮ If dij recombine ◮ if diB , i is a jet
Example clustering with kt algo- rithm, R = 1.0 φ assumed 0 for all towers
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 22 / 30 [Sequential recombination] [kt for hadron colliders] kt in action
kt alg.: Find smallest of pt/GeV 60 ∆R2 d = min(k2 , k2 ) ij , d = k2 ij ti tj R2 iB ti 50 ◮ If dij recombine ◮ 40 if diB , i is a jet
Example clustering with kt algo- 30 rithm, R = 1.0 φ assumed 0 for all towers 20
10
0 0 1 2 3 4 y
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 22 / 30 [Sequential recombination] [kt for hadron colliders] kt in action
kt alg.: Find smallest of pt/GeV 60 ∆R2 d = min(k2 , k2 ) ij , d = k2 ij ti tj R2 iB ti 50 ◮ If dij recombine ◮ 40 if diB , i is a jet
Example clustering with kt algo- 30 rithm, R = 1.0 φ assumed 0 for all towers 20
10
0 0 1 2 3 4 y
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 22 / 30 [Sequential recombination] [kt for hadron colliders] kt in action
kt alg.: Find smallest of pt/GeV dmin is dij = 0.166597 60 ∆R2 d = min(k2 , k2 ) ij , d = k2 ij ti tj R2 iB ti 50 ◮ If dij recombine ◮ 40 if diB , i is a jet
Example clustering with kt algo- 30 rithm, R = 1.0 φ assumed 0 for all towers 20
10
0 0 1 2 3 4 y
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 22 / 30 [Sequential recombination] [kt for hadron colliders] kt in action
kt alg.: Find smallest of pt/GeV 60 ∆R2 d = min(k2 , k2 ) ij , d = k2 ij ti tj R2 iB ti 50 ◮ If dij recombine ◮ 40 if diB , i is a jet
Example clustering with kt algo- 30 rithm, R = 1.0 φ assumed 0 for all towers 20
10
0 0 1 2 3 4 y
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 22 / 30 [Sequential recombination] [kt for hadron colliders] kt in action
kt alg.: Find smallest of pt/GeV dmin is dij = 2.66556 60 ∆R2 d = min(k2 , k2 ) ij , d = k2 ij ti tj R2 iB ti 50 ◮ If dij recombine ◮ 40 if diB , i is a jet
Example clustering with kt algo- 30 rithm, R = 1.0 φ assumed 0 for all towers 20
10
0 0 1 2 3 4 y
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 22 / 30 [Sequential recombination] [kt for hadron colliders] kt in action
kt alg.: Find smallest of pt/GeV 60 ∆R2 d = min(k2 , k2 ) ij , d = k2 ij ti tj R2 iB ti 50 ◮ If dij recombine ◮ 40 if diB , i is a jet
Example clustering with kt algo- 30 rithm, R = 1.0 φ assumed 0 for all towers 20
10
0 0 1 2 3 4 y
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 22 / 30 [Sequential recombination] [kt for hadron colliders] kt in action
kt alg.: Find smallest of pt/GeV dmin is dij = 4.16493 60 ∆R2 d = min(k2 , k2 ) ij , d = k2 ij ti tj R2 iB ti 50 ◮ If dij recombine ◮ 40 if diB , i is a jet
Example clustering with kt algo- 30 rithm, R = 1.0 φ assumed 0 for all towers 20
10
0 0 1 2 3 4 y
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 22 / 30 [Sequential recombination] [kt for hadron colliders] kt in action
kt alg.: Find smallest of pt/GeV 60 ∆R2 d = min(k2 , k2 ) ij , d = k2 ij ti tj R2 iB ti 50 ◮ If dij recombine ◮ 40 if diB , i is a jet
Example clustering with kt algo- 30 rithm, R = 1.0 φ assumed 0 for all towers 20
10
0 0 1 2 3 4 y
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 22 / 30 [Sequential recombination] [kt for hadron colliders] kt in action
kt alg.: Find smallest of pt/GeV dmin is dij = 8.75775 60 ∆R2 d = min(k2 , k2 ) ij , d = k2 ij ti tj R2 iB ti 50 ◮ If dij recombine ◮ 40 if diB , i is a jet
Example clustering with kt algo- 30 rithm, R = 1.0 φ assumed 0 for all towers 20
10
0 0 1 2 3 4 y
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 22 / 30 [Sequential recombination] [kt for hadron colliders] kt in action
kt alg.: Find smallest of pt/GeV 60 ∆R2 d = min(k2 , k2 ) ij , d = k2 ij ti tj R2 iB ti 50 ◮ If dij recombine ◮ 40 if diB , i is a jet
Example clustering with kt algo- 30 rithm, R = 1.0 φ assumed 0 for all towers 20
10
0 0 1 2 3 4 y
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 22 / 30 [Sequential recombination] [kt for hadron colliders] kt in action
kt alg.: Find smallest of pt/GeV dmin is dij = 12.7551 60 ∆R2 d = min(k2 , k2 ) ij , d = k2 ij ti tj R2 iB ti 50 ◮ If dij recombine ◮ 40 if diB , i is a jet
Example clustering with kt algo- 30 rithm, R = 1.0 φ assumed 0 for all towers 20
10
0 0 1 2 3 4 y
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 22 / 30 [Sequential recombination] [kt for hadron colliders] kt in action
kt alg.: Find smallest of pt/GeV 60 ∆R2 d = min(k2 , k2 ) ij , d = k2 ij ti tj R2 iB ti 50 ◮ If dij recombine ◮ 40 if diB , i is a jet
Example clustering with kt algo- 30 rithm, R = 1.0 φ assumed 0 for all towers 20
10
0 0 1 2 3 4 y
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 22 / 30 [Sequential recombination] [kt for hadron colliders] kt in action
kt alg.: Find smallest of pt/GeV dmin is dij = 15.3298 60 ∆R2 d = min(k2 , k2 ) ij , d = k2 ij ti tj R2 iB ti 50 ◮ If dij recombine ◮ 40 if diB , i is a jet
Example clustering with kt algo- 30 rithm, R = 1.0 φ assumed 0 for all towers 20
10
0 0 1 2 3 4 y
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 22 / 30 [Sequential recombination] [kt for hadron colliders] kt in action
kt alg.: Find smallest of pt/GeV 60 ∆R2 d = min(k2 , k2 ) ij , d = k2 ij ti tj R2 iB ti 50 ◮ If dij recombine ◮ 40 if diB , i is a jet
Example clustering with kt algo- 30 rithm, R = 1.0 φ assumed 0 for all towers 20
10
0 0 1 2 3 4 y
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 22 / 30 [Sequential recombination] [kt for hadron colliders] kt in action
kt alg.: Find smallest of pt/GeV dmin is dij = 229.802 60 ∆R2 d = min(k2 , k2 ) ij , d = k2 ij ti tj R2 iB ti 50 ◮ If dij recombine ◮ 40 if diB , i is a jet
Example clustering with kt algo- 30 rithm, R = 1.0 φ assumed 0 for all towers 20
10
0 0 1 2 3 4 y
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 22 / 30 [Sequential recombination] [kt for hadron colliders] kt in action
kt alg.: Find smallest of pt/GeV 60 ∆R2 d = min(k2 , k2 ) ij , d = k2 ij ti tj R2 iB ti 50 ◮ If dij recombine ◮ 40 if diB , i is a jet
Example clustering with kt algo- 30 rithm, R = 1.0 φ assumed 0 for all towers 20
10
0 0 1 2 3 4 y
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 22 / 30 [Sequential recombination] [kt for hadron colliders] kt in action
kt alg.: Find smallest of pt/GeV dmin is dij = 285.007 60 ∆R2 d = min(k2 , k2 ) ij , d = k2 ij ti tj R2 iB ti 50 ◮ If dij recombine ◮ 40 if diB , i is a jet
Example clustering with kt algo- 30 rithm, R = 1.0 φ assumed 0 for all towers 20
10
0 0 1 2 3 4 y
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 22 / 30 [Sequential recombination] [kt for hadron colliders] kt in action
kt alg.: Find smallest of pt/GeV 60 ∆R2 d = min(k2 , k2 ) ij , d = k2 ij ti tj R2 iB ti 50 ◮ If dij recombine ◮ 40 if diB , i is a jet
Example clustering with kt algo- 30 rithm, R = 1.0 φ assumed 0 for all towers 20
10
0 0 1 2 3 4 y
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 22 / 30 [Sequential recombination] [kt for hadron colliders] kt in action
kt alg.: Find smallest of pt/GeV dmin is diB = 1776.02 60 ∆R2 d = min(k2 , k2 ) ij , d = k2 ij ti tj R2 iB ti 50 ◮ If dij recombine ◮ 40 if diB , i is a jet
Example clustering with kt algo- 30 rithm, R = 1.0 φ assumed 0 for all towers 20
10
0 0 1 2 3 4 y
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 22 / 30 [Sequential recombination] [kt for hadron colliders] kt in action
kt alg.: Find smallest of pt/GeV 60 ∆R2 d = min(k2 , k2 ) ij , d = k2 ij ti tj R2 iB ti 50 ◮ If dij recombine ◮ 40 if diB , i is a jet
Example clustering with kt algo- 30 rithm, R = 1.0 φ assumed 0 for all towers 20
10
0 0 1 2 3 4 y
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 22 / 30 [Sequential recombination] [kt for hadron colliders] kt in action
kt alg.: Find smallest of pt/GeV dmin is diB = 2155.61 60 ∆R2 d = min(k2 , k2 ) ij , d = k2 ij ti tj R2 iB ti 50 ◮ If dij recombine ◮ 40 if diB , i is a jet
Example clustering with kt algo- 30 rithm, R = 1.0 φ assumed 0 for all towers 20
10
0 0 1 2 3 4 y
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 22 / 30 [Sequential recombination] [kt for hadron colliders] kt in action
kt alg.: Find smallest of pt/GeV 60 ∆R2 d = min(k2 , k2 ) ij , d = k2 ij ti tj R2 iB ti 50 ◮ If dij recombine ◮ 40 if diB , i is a jet
Example clustering with kt algo- 30 rithm, R = 1.0 φ assumed 0 for all towers 20
10
0 0 1 2 3 4 y
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 22 / 30 The kt algorithms form one of several “families” of sequential recombination jet algorithm
Others differ in: 1. the choice distance measure between pairs of particles [i.e. the relative priority given to soft and collinear divergences, e.g. Cambridge/Aachen (C/A), which uses just angular distance]
2. using 3 → 2 clustering rather than 2 → 1 [ARCLUS; not used at hadron colliders, so won’t discuss it more]
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 23 / 30 The kt family of algorithms was widely used at LEP (e+e−) and HERA (ep and γp).
Tevatron instead used cone algorithms, as did the LHC experiments during the design and planning stages.
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 24 / 30 [Comparing algorithms] Essential characteristic of cones?
Cone (ICPR)
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 25 / 30 [Comparing algorithms] Essential characteristic of cones?
Cone (ICPR) (Some) cone algorithms give circular jets in y − φ plane Much appreciated by experi- ments e.g. for acceptance corrections
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 25 / 30 [Comparing algorithms] Essential characteristic of cones?
Cone (ICPR) (Some) cone algorithms give circular jets in y − φ plane Much appreciated by experi- ments e.g. for acceptance corrections
kt alg.
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 25 / 30 [Comparing algorithms] Essential characteristic of cones?
Cone (ICPR) (Some) cone algorithms give circular jets in y − φ plane Much appreciated by experi- ments e.g. for acceptance corrections
kt alg.
kt jets are irregular Because soft junk clusters to- gether first: 2 2 2 dij = min(kti , ktj )∆Rij
Regularly held against kt
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 25 / 30 [Comparing algorithms] Essential characteristic of cones?
Cone (ICPR) (Some) cone algorithms give circular jets in y − φ plane Much appreciated by experi- ments e.g. for acceptance corrections
Is there some other, non cone-based way of gettingkt alg. circular jets? kt jets are irregular Because soft junk clusters to- gether first: 2 2 2 dij = min(kti , ktj )∆Rij
Regularly held against kt
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 25 / 30 [Comparing algorithms] Adapting seq. rec. to give circular jets
Soft stuff clusters with nearest neighbour ∆R2 2 2 2 ij kt: dij = min(kti , ktj )∆Rij −→ anti-kt: dij = 2 2 max(kti , ktj )
Hard stuff clusters with nearest neighbour
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 26 / 30 [Comparing algorithms] Adapting seq. rec. to give circular jets
Soft stuff clusters with nearest neighbour ∆R2 2 2 2 ij kt: dij = min(kti , ktj )∆Rij −→ anti-kt: dij = 2 2 max(kti , ktj )
Hard stuff clusters with nearest neighbour
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 26 / 30 [Comparing algorithms] Adapting seq. rec. to give circular jets
Soft stuff clusters with nearest neighbour ∆R2 2 2 2 ij kt: dij = min(kti , ktj )∆Rij −→ anti-kt: dij = 2 2 max(kti , ktj )
Hard stuff clusters with nearest neighbour
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 26 / 30 [Comparing algorithms] Adapting seq. rec. to give circular jets
Soft stuff clusters with nearest neighbour ∆R2 2 2 2 ij kt: dij = min(kti , ktj )∆Rij −→ anti-kt: dij = 2 2 max(kti , ktj )
Hard stuff clusters with nearest neighbour
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 26 / 30 [Comparing algorithms] Adapting seq. rec. to give circular jets
Soft stuff clusters with nearest neighbour ∆R2 2 2 2 ij kt: dij = min(kti , ktj )∆Rij −→ anti-kt: dij = 2 2 max(kti , ktj )
Hard stuff clusters with nearest neighbour
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 26 / 30 [Comparing algorithms] Adapting seq. rec. to give circular jets
Soft stuff clusters with nearest neighbour ∆R2 2 2 2 ij kt: dij = min(kti , ktj )∆Rij −→ anti-kt: dij = 2 2 max(kti , ktj )
Hard stuff clusters with nearest neighbour
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 26 / 30 [Comparing algorithms] Adapting seq. rec. to give circular jets
Soft stuff clusters with nearest neighbour ∆R2 2 2 2 ij kt: dij = min(kti , ktj )∆Rij −→ anti-kt: dij = 2 2 max(kti , ktj )
Hard stuff clusters with nearest neighbour
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 26 / 30 [Comparing algorithms] Adapting seq. rec. to give circular jets
Soft stuff clusters with nearest neighbour ∆R2 2 2 2 ij kt: dij = min(kti , ktj )∆Rij −→ anti-kt: dij = 2 2 max(kti , ktj )
Hard stuff clusters with nearest neighbour
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 26 / 30 [Comparing algorithms] Adapting seq. rec. to give circular jets
Soft stuff clusters with nearest neighbour ∆R2 2 2 2 ij kt: dij = min(kti , ktj )∆Rij −→ anti-kt: dij = 2 2 max(kti , ktj )
Hard stuff clusters with nearest neighbour
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 26 / 30 [Comparing algorithms] Adapting seq. rec. to give circular jets
Soft stuff clusters with nearest neighbour ∆R2 2 2 2 ij kt: dij = min(kti , ktj )∆Rij −→ anti-kt: dij = 2 2 max(kti , ktj )
Hard stuff clusters with nearest neighbour
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 26 / 30 [Comparing algorithms] Adapting seq. rec. to give circular jets
Soft stuff clusters with nearest neighbour ∆R2 2 2 2 ij kt: dij = min(kti , ktj )∆Rij −→ anti-kt: dij = 2 2 max(kti , ktj )
Hard stuff clusters with nearest neighbour
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 26 / 30 [Comparing algorithms] Adapting seq. rec. to give circular jets
Soft stuff clusters with nearest neighbour ∆R2 2 2 2 ij kt: dij = min(kti , ktj )∆Rij −→ anti-kt: dij = 2 2 max(kti , ktj )
Hard stuff clusters with nearest neighbour
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 26 / 30 [Comparing algorithms] Adapting seq. rec. to give circular jets
Soft stuff clusters with nearest neighbour ∆R2 2 2 2 ij kt: dij = min(kti , ktj )∆Rij −→ anti-kt: dij = 2 2 max(kti , ktj )
Hard stuff clusters with nearest neighbour
anti-kt gives cone-like jets without using stable cones
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 26 / 30 [Comparing algorithms] Anti-kt experimental performance
As good as, or better than all previous experimentally- favoured algorithms.
Essentially because anti-kt has linear response to soft particles.
And it’s also infrared and collinear safe (needed for theory calcs.)
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 27 / 30 [Comparing algorithms] Linearity: kt v. anti-kt p /GeV t kt clustering, R=1 40
30 1
20
10 3 2 0 0 1 2 3 y [Comparing algorithms] Linearity: kt v. anti-kt p /GeV t kt clustering, R=1 40
30 1
20
10 3 2 0 0 1 2 3 y [Comparing algorithms] Linearity: kt v. anti-kt p /GeV t kt clustering, R=1 40
30 1
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10 3 2 0 0 1 2 3 y [Comparing algorithms] Linearity: kt v. anti-kt p /GeV t kt clustering, R=1 40
30 1
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10 3 2 0 0 1 2 3 y [Comparing algorithms] Linearity: kt v. anti-kt p /GeV t kt clustering, R=1 40
30 1
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10 3 2 0 0 1 2 3 y [Comparing algorithms] Linearity: kt v. anti-kt p /GeV t kt clustering, R=1 40
30 1
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10 3 2 0 0 1 2 3 y [Comparing algorithms] Linearity: kt v. anti-kt p /GeV t kt clustering, R=1 40
30 1
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10 3 2 0 0 1 2 3 y [Comparing algorithms] Linearity: kt v. anti-kt p /GeV t kt clustering, R=1 40
30 1
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10 3 2 0 0 1 2 3 y 50 jet pt v. pt,2 45 40 [GeV]
t,jet 35 p 30 kt alg. 0 5 10 15 pt,2 [GeV] [Comparing algorithms] Linearity: kt v. anti-kt p /GeV p /GeV t kt clustering, R=1 t anti−kt clustering, R=1 40 40
30 1 30 1
20 20
10 10 3 3 2 2 0 0 0 1 2 3 0 1 2 3 y y 50 jet pt v. pt,2 45 40 [GeV]
t,jet 35 p 30 kt alg. 0 5 10 15 pt,2 [GeV] [Comparing algorithms] Linearity: kt v. anti-kt p /GeV p /GeV t kt clustering, R=1 t anti−kt clustering, R=1 40 40
30 1 30 1
20 20
10 10 3 3 2 2 0 0 0 1 2 3 0 1 2 3 y y 50 jet pt v. pt,2 45 40 [GeV]
t,jet 35 p 30 kt alg. 0 5 10 15 pt,2 [GeV] [Comparing algorithms] Linearity: kt v. anti-kt p /GeV p /GeV t kt clustering, R=1 t anti−kt clustering, R=1 40 40
30 1 30 1
20 20
10 10 3 3 2 2 0 0 0 1 2 3 0 1 2 3 y y 50 jet pt v. pt,2 45 40 [GeV]
t,jet 35 p 30 kt alg. 0 5 10 15 pt,2 [GeV] [Comparing algorithms] Linearity: kt v. anti-kt p /GeV p /GeV t kt clustering, R=1 t anti−kt clustering, R=1 40 40
30 1 30 1
20 20
10 10 3 3 2 2 0 0 0 1 2 3 0 1 2 3 y y 50 jet pt v. pt,2 45 40 [GeV]
t,jet 35 p 30 kt alg. 0 5 10 15 pt,2 [GeV] [Comparing algorithms] Linearity: kt v. anti-kt p /GeV p /GeV t kt clustering, R=1 t anti−kt clustering, R=1 40 40
30 1 30 1
20 20
10 10 3 3 2 2 0 0 0 1 2 3 0 1 2 3 y y 50 jet pt v. pt,2 45 40 [GeV]
t,jet 35 p 30 kt alg. 0 5 10 15 pt,2 [GeV] [Comparing algorithms] Linearity: kt v. anti-kt p /GeV p /GeV t kt clustering, R=1 t anti−kt clustering, R=1 40 40
30 1 30 1
20 20
10 10 3 3 2 2 0 0 0 1 2 3 0 1 2 3 y y 50 jet pt v. pt,2 45 40 [GeV]
t,jet 35 p 30 kt alg. 0 5 10 15 pt,2 [GeV] [Comparing algorithms] Linearity: kt v. anti-kt p /GeV p /GeV t kt clustering, R=1 t anti−kt clustering, R=1 40 40
30 1 30 1
20 20
10 10 3 3 2 2 0 0 0 1 2 3 0 1 2 3 y y 50 jet pt v. pt,2 45 40 [GeV]
t,jet 35 p 30 kt alg. 0 5 10 15 pt,2 [GeV] [Comparing algorithms] Linearity: kt v. anti-kt p /GeV p /GeV t kt clustering, R=1 t anti−kt clustering, R=1 40 40
30 1 30 1
20 20
10 10 3 3 2 2 0 0 0 1 2 3 0 1 2 3 y y 50 50 jet pt v. pt,2 jet pt v. pt,2 45 45 40 40 [GeV] [GeV]
t,jet 35 t,jet 35 p p 30 30 kt alg. anti-kt alg. 0 5 10 15 0 5 10 15 pt,2 [GeV] pt,2 [GeV] [Comparing algorithms] Linearity: kt v. anti-kt p /GeV p /GeV t kt clustering, R=1 t anti−kt clustering, R=1 40 40
Anti-kt ’s linearity with respect to soft radiation and/or 30 1 30 1 detector fluctuations makes it simpler to use experimentally
20 20
10 10 3 3 2 2 0 0 0 1 2 3 0 1 2 3 y y 50 50 jet pt v. pt,2 jet pt v. pt,2 45 45 40 40 [GeV] [GeV]
t,jet 35 t,jet 35 p p 30 30 kt alg. anti-kt alg. 0 5 10 15 0 5 10 15 pt,2 [GeV] pt,2 [GeV] [Comparing algorithms] Nearly all algorithms available in FastJet
FastJet time to cluster N particles 102 R=0.7
1 t 10 anti-k kt
1 (SISCone) t Seedless IR Safe Cone Cam/Aachen 10-1 KtJet k t / s CDF MidPoint (seeds > 0 GeV)
10-2 FastJet CDF JetClu (very unsafe) 10-3 CDF MidPoint (seeds > 1 GeV)
LHC lo-lumi LHC hi-lumi LHC Pb-Pb 10-4 100 1000 10000 100000 N Used by all the LHC experiments Aavailable from http://fastjet.fr/
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 29 / 30 [Comparing algorithms] Summary
Today we’ve examined why we need jets and looked at some of the logic behind the way they’re defined.
Of the different algorithms we’ve discussed, the one that’s most widely used at LHC today is anti-kt . But the other algorithms we’ve seen will also play a role at the LHC.
Tomorrow’s subject will be making the best use of jets.
Jets lecture 1 (Gavin Salam) MC tools for LHC school September 2011 30 / 30