QCD lecture 4 (p. 1)
QCD (for LHC)Lecture 4
1. Merging parton showers and fixed order2. Jets
Gavin Salam
LPTHE, CNRS and UPMC (Univ. Paris 6)
At the 2009 European School of High-Energy PhysicsJune 2009, Bautzen, Germany
QCD lecture 4 (p. 2)
Combining PS + FO
Tree-level + PS
◮ Tree-level (LO) gives decent description of multi-jet structure
◮ NLO gives good normalisation
◮ Parton-shower gives good behaviour in soft-collinear regions andfully exclusive final state.
Can we combine the advantages of all three?
QCD lecture 4 (p. 3)
Combining PS + FO
Tree-level + PSDifficulties in merging Tree-level(s) + PS?
Suppose you ask for Z+jet as your initial hard process inPythia/Herwig.
◮ They contain the correct ME for Z+j.
◮ But you want Z+2j to be correct too.
Naive approach: you could also generate Z+2j events with Alpgen (orMadgraph, etc.) and run the shower from those configurations too.
QCD lecture 4 (p. 4)
Combining PS + FO
Tree-level + PSAdd Z+1jet, Z+2jet + shower
Z+parton
QCD lecture 4 (p. 4)
Combining PS + FO
Tree-level + PSAdd Z+1jet, Z+2jet + shower
shower Z+parton
QCD lecture 4 (p. 4)
Combining PS + FO
Tree-level + PSAdd Z+1jet, Z+2jet + shower
Z+2partons
+
shower Z+parton
QCD lecture 4 (p. 4)
Combining PS + FO
Tree-level + PSAdd Z+1jet, Z+2jet + shower
shower Z+2partons
+
shower Z+parton
QCD lecture 4 (p. 4)
Combining PS + FO
Tree-level + PSAdd Z+1jet, Z+2jet + shower
showergenerates hard gluon
of Z+parton
v.
shower Z+2partons
+
shower Z+parton
QCD lecture 4 (p. 4)
Combining PS + FO
Tree-level + PSAdd Z+1jet, Z+2jet + shower
showergenerates hard gluon
of Z+parton
v.
shower Z+2partons
+
shower Z+parton
QCD lecture 4 (p. 4)
Combining PS + FO
Tree-level + PSAdd Z+1jet, Z+2jet + shower
DOUBLECOUNTING
showergenerates hard gluon
of Z+parton
v.
shower Z+2partons
+
shower Z+parton
Double counting + associated issues with virtual corrections
are the main problems when merging PS + ME
QCD lecture 4 (p. 5)
Combining PS + FO
Tree-level + PSMerging procedures
ME + PS merging is an attempt to solve this. There are many variants.One common one is “MLM matching” — a summary of it is:
◮ Introduce a cutoff QME
◮ Use the matrix elements to generate tree-level events for Z+1parton,Z+2partons, . . . Z+Npartons, where all partons must have pt > QME ,and are separated from the others by some angle RME .
Numbers of events are in proportion to their cross sections with these cuts
◮ Take one of these tree level events, say with n-partons.
◮ Shower it with your favourite Parton Shower program.
◮ Identify all jets that have pt > Qmerge (chosen & QME )
◮ If each parton corresponds to one of the jets (≡ is nearby in angle) andthere are no extra jets above scale Qmerge , accept the event.
[Replace Qmerge → ptn if n = N ]◮ Otherwise reject it.
NB: MLM stands for Michelangelo L. Mangano
QCD lecture 4 (p. 6)
Combining PS + FO
Tree-level + PSMLM example
showergenerates hard gluon
of Z+parton
v.
shower Z+2partons
+
shower Z+parton
◮ Hard jets above scale Qmerge have distributions given by tree-level ME
◮ Rejection procedure eliminates “double-counted” jets from parton shower
◮ Rejection generates Sudakov form factors between individual jet scalesHow well? Depends on details of PS. One of the weaker points of MLM
QCD lecture 4 (p. 6)
Combining PS + FO
Tree-level + PSMLM example
p t cut
Qmerge
ACCEPT ACCEPT REJECT
showergenerates hard gluon
of Z+parton
v.
shower Z+2partons
+
shower Z+parton
◮ Hard jets above scale Qmerge have distributions given by tree-level ME
◮ Rejection procedure eliminates “double-counted” jets from parton shower
◮ Rejection generates Sudakov form factors between individual jet scalesHow well? Depends on details of PS. One of the weaker points of MLM
QCD lecture 4 (p. 6)
Combining PS + FO
Tree-level + PSMLM example
p t cut
Qmerge
ACCEPT ACCEPT REJECT
showergenerates hard gluon
of Z+parton
v.
shower Z+2partons
+
shower Z+parton
◮ Hard jets above scale Qmerge have distributions given by tree-level ME
◮ Rejection procedure eliminates “double-counted” jets from parton shower
◮ Rejection generates Sudakov form factors between individual jet scalesHow well? Depends on details of PS. One of the weaker points of MLM
QCD lecture 4 (p. 7)
Combining PS + FO
Tree-level + PSMerging – other schemes
MLM is the standard merging available from Alpgen
There are several other merging procedures on the market
◮ MLM a la MadGraph Mainly changes details of jet finding
◮ CKKW e.g. in Sherpa
◮ CKKW-L e.g. in Ariadne
◮ Pseudo Shower by Mrenna
They vary essentially in whether/how they match partons & jets, thedefinitions of the jets, and some include analytic Sudakov form factors (e.g.CKKW).
They all involve some implicit form of pt cutoff.Usually physics well above cutoff is independent of cutoff?
QCD lecture 4 (p. 8)
Combining PS + FO
Tree-level + PSZ + 1 jet
[1
/ G
eV]
je
t)
st
(1T
d p
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* γZ
/σ
d × | * γ
Z/
σ |1
-610
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t)
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d × | * γ
Z/
σ |1
-610
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-210Data at particle levelMCFM NLO
||
ee) + 1 jet + X→ (*γZ/
|| < 115 GeVee65 < M|
|
e / ye
TIncl. in p
||
| < 2.5jet
= 0.5, | yconejet
R
jet) [GeV] st (1T
p20 30 40 50 100 200 300
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io t
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M N
LO
jet) [GeV] st (1T
p20 30 40 50 100 200 300
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LO
DataMCFM NLOScale unc.
(b)
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Rat
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(c)
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QCD lecture 4 (p. 9)
Combining PS + FO
Tree-level + PSZ + 2 jets
[1
/ G
eV]
je
t)
nd
(2T
d p
|
* γZ
/σ
d × | * γ
Z/
σ |1
-610
-510
-410
-310
||
-1D0 Run II, L=1.04 fb
(a)
[1
/ G
eV]
je
t)
nd
(2T
d p
|
* γZ
/σ
d × | * γ
Z/
σ |1
-610
-510
-410
-310
Data at particle levelMCFM NLO
||
ee) + 2 jets + X→ (*γZ/
|| < 115 GeVee65 < M|
|
e / ye
TIncl. in p
||
| < 2.5jet
= 0.5, | yconejet
R
jet) [GeV] nd (2T
p20 30 40 50 60 100 200
Rat
io t
o M
CF
M N
LO
jet) [GeV] nd (2T
p20 30 40 50 60 100 200
Rat
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o M
CF
M N
LO
DataMCFM NLOScale unc.
(b)
MCFM LOScale unc.
0.5
1.0
1.5
2.02.5
Rat
io t
o M
CF
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LO
(c)
Rat
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CF
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LO
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0.5
1.0
1.5
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p20 30 40 50 60 100 200
Rat
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M N
LO
(d)
jet) [GeV] nd (2T
p20 30 40 50 60 100 200
Rat
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CF
M N
LO
DataALPGEN+PYTHIAScale unc.
SHERPAScale unc.
0.5
1.0
1.5
2.02.5
QCD lecture 4 (p. 9)
Combining PS + FO
Tree-level + PSZ + 2 jets
[1
/ G
eV]
je
t)
nd
(2T
d p
|
* γZ
/σ
d × | * γ
Z/
σ |1
-610
-510
-410
-310
||
-1D0 Run II, L=1.04 fb
(a)
[1
/ G
eV]
je
t)
nd
(2T
d p
|
* γZ
/σ
d × | * γ
Z/
σ |1
-610
-510
-410
-310
Data at particle levelMCFM NLO
||
ee) + 2 jets + X→ (*γZ/
|| < 115 GeVee65 < M|
|
e / ye
TIncl. in p
||
| < 2.5jet
= 0.5, | yconejet
R
jet) [GeV] nd (2T
p20 30 40 50 60 100 200
Rat
io t
o M
CF
M N
LO
jet) [GeV] nd (2T
p20 30 40 50 60 100 200
Rat
io t
o M
CF
M N
LO
DataMCFM NLOScale unc.
(b)
MCFM LOScale unc.
0.5
1.0
1.5
2.02.5
Rat
io t
o M
CF
M N
LO
(c)
Rat
io t
o M
CF
M N
LO
DataHERWIG+JIMMY
PYTHIA S0Scale unc.PYTHIA QWScale unc.
0.5
1.0
1.5
2.02.5
jet) [GeV] nd (2T
p20 30 40 50 60 100 200
Rat
io t
o M
CF
M N
LO
(d)
jet) [GeV] nd (2T
p20 30 40 50 60 100 200
Rat
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CF
M N
LO
DataALPGEN+PYTHIAScale unc.
SHERPAScale unc.
0.5
1.0
1.5
2.02.5
◮ ME + PS merging helps getcorrect pt dependence
◮ It works much better than plainparton showers
◮ Normalisation is still quiteuncertain
QCD lecture 4 (p. 10)
Combining PS + FO
Tree-level + PSZ + 3 jets
[1
/ G
eV]
je
t)
rd
(3T
d p
|
* γZ
/σ
d × | * γ
Z/
σ |1
-610
-510
-410
||
-1D0 Run II, L=1.04 fb
(a)
[1
/ G
eV]
je
t)
rd
(3T
d p
|
* γZ
/σ
d × | * γ
Z/
σ |1
-610
-510
-410
Data at particle levelMCFM LO
||
ee) + 3 jets + X→ (*γZ/
|| < 115 GeVee65 < M|
|
e / ye
TIncl. in p
||
| < 2.5jet
= 0.5, | yconejet
R
jet) [GeV] rd (3T
p20 30 40 50 60
Rat
io t
o M
CF
M L
O
jet) [GeV] rd (3T
p20 30 40 50 60
Rat
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CF
M L
O
DataMCFM LOScale unc.
(b)
0.5
1.0
1.52.0
3.0
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CF
M L
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(c)
Rat
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CF
M L
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DataHERWIG+JIMMY
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0.5
1.0
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3.0
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p20 30 40 50 60
Rat
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(d)
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DataALPGEN+PYTHIAScale unc.
SHERPAScale unc.
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1.0
1.52.0
3.0
QCD lecture 4 (p. 11)
Combining PS + FO
NLO + PS
Can we get parton-shower structure, with NLO accuracy
(e.g. control of normalisation, pattern of radiation of extraparton)?
QCD lecture 4 (p. 12)
Combining PS + FO
NLO + PS
MC@NLO ideas Frixione & Webber ’02
◮ Expand your Monte Carlo branching to first order in αs
Rather non-trivial – requires deep understanding of MC
◮ Calculate differences wrt true O (αs) both in real and virtual pieces
◮ If your Monte Carlo gives correct soft and/or collinear limits, thosedifferences are finite
◮ Generate extra partonic configurations with phase-space distributionsproportional to those differences and shower them
QCD lecture 4 (p. 13)
Combining PS + FO
NLO + PSMC@NLO cont.
Let’s imagine a problem with one phase-space dimension, e.g. E . ExpandMonte Carlo cross section for emission with energy E :
σMC ≡ 1 × δ(E ) + αsσMC1R (E ) + αsσ
MC1V δ(E ) + O
(α2
s
)
With true NLO real/virtual terms as αsσ1R(E ) and αsσ1V δ(E ), define
MC@NLO = MC ×(
1 + αs(σ1V − σMC1V ) + αs
∫
dE (σ1R(E ) − σMC1R (E ))
)
All weights finite, but can be ±1
Processes include Frixione, Laenen, Motylinski, Nason, Webber, White ’02–’08
Higgs boson, single vector boson, vector boson pair, heavy quark pair,single top (with and without associated W), lepton pair and associatedHiggs+W/Z
QCD lecture 4 (p. 14)
Combining PS + FO
NLO + PSPOWHEG
Aims to work around MC@NLO limitations Nason ’04
◮ the (small fraction of) negative weights
◮ the tight interconnection with a specific MC
Principle
◮ Write a simplified Monte Carlo that generates just one emission (thehardest one) which alone gives the correct NLO result.
Essentially uses special Sudakov
∆(kt) = exp(−∫
exact real-radition probability above kt)
◮ Lets your default parton-shower do branchings below that kt .
Processes include
pp → Heavy-quark pair, Higgs, single vector-bosonAlioli, Frixione, Nason, Oleari, Re ’07–08
pp → W ′, e+e− → tt Papaefstathiou, Latunde-Dada
QCD lecture 4 (p. 15)
Combining PS + FO
NLO + PSMC@NLO e.g.: tt pt distribution for LHC
figure from talk by Frixione ’04
◮ MC@NLO gets rightnormalisation
◮ correct behaviour at low pt
(∼ rescaled Herwig)
◮ correct behaviour at high pt
(∼ NLO)
QCD lecture 4 (p. 16)
Combining PS + FO
NLO + PSSummary of merging/matching
◮ You can merge many different tree-levels (Z+1, Z+2, Z+3, . . . ) withparton showering together into a consistent sample.
Shapes should be OK, normalisation is rather uncertain
Procedures are flexible and general — but not necessarily the final word
◮ You can merge NLO accuracy with parton showers for simple processes(at most one light jet — single top case)
Two main methods: MC@NLO / POWHEG
It is hard theory work — must be done on a case by case basis
◮ Incorporation of different multiplicities (Z+1, Z+2, Z+3, . . . )consistently at NLO for each multiplicity, together with parton showering,is a current research problem.
QCD lecture 4 (p. 17)
Jets
We’ve completed our tour of predictive methods in collider QCD
(LO, NLO, NNLO; parton showers; mergings and matchings)
The last topic of these lectures is jets
They’ve already arisen in various contexts; now look at them in detail
QCD lecture 4 (p. 18)
Jets Seeing v. defining jets
Jets are what we see.Clearly(?) 2 jets here
How many jets do you see?Do you really want to ask yourselfthis question for 109 events?
QCD lecture 4 (p. 18)
Jets Seeing v. defining jets
q
q
Jets are what we see.Clearly(?) 2 jets here
How many jets do you see?Do you really want to ask yourselfthis question for 109 events?
QCD lecture 4 (p. 18)
Jets Seeing v. defining jets
Jets are what we see.Clearly(?) 2 jets here
How many jets do you see?Do you really want to ask yourselfthis question for 109 events?
QCD lecture 4 (p. 18)
Jets Seeing v. defining jets
Jets are what we see.Clearly(?) 2 jets here
How many jets do you see?Do you really want to ask yourselfthis question for 109 events?
QCD lecture 4 (p. 18)
Jets Seeing v. defining jets
Jets are what we see.Clearly(?) 2 jets here
How many jets do you see?Do you really want to ask yourselfthis question for 109 events?
QCD lecture 4 (p. 18)
Jets Seeing v. defining jets
Jets are what we see.Clearly(?) 2 jets here
How many jets do you see?Do you really want to ask yourselfthis question for 109 events?
QCD lecture 4 (p. 19)
Jets Jets as projections
jet 1 jet 2
LO partons
Jet Def n
jet 1 jet 2
Jet Def n
NLO partons
jet 1 jet 2
Jet Def n
parton shower
jet 1 jet 2
Jet Def n
hadron level
π π
K
p φ
Projection to jets provides “universal” view of event
QCD lecture 4 (p. 20)
Jets QCD jets flowchart
Jet (definitions) provide central link between expt., “theory” and theory
And jets are an input to almost all analyses
QCD lecture 4 (p. 20)
Jets QCD jets flowchart
Jet (definitions) provide central link between expt., “theory” and theory
And jets are an input to almost all analyses
QCD lecture 4 (p. 21)
Jets 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, e.g. jet angular radius R
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 jetdefinition cf. Les Houches ’07 nomenclature accord
Ambiguity complicates life,but gives flexibility in one’s view of events
→ Jets non-trivial!
QCD lecture 4 (p. 21)
Jets 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, e.g. jet angular radius R
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 jetdefinition cf. Les Houches ’07 nomenclature accord
Ambiguity complicates life,but gives flexibility in one’s view of events
→ Jets non-trivial!
QCD lecture 4 (p. 21)
Jets 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, e.g. jet angular radius R
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 jetdefinition cf. Les Houches ’07 nomenclature accord
Ambiguity complicates life,but gives flexibility in one’s view of events
→ Jets non-trivial!
QCD lecture 4 (p. 22)
Jets 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
QCD lecture 4 (p. 23)
Jets
Sequential recomb.kt/Durham algorithm
Majority of QCD branching is soft & collinear, with following divergences:
[dkj ]|M2g→gigj
(kj )| ≃2αsCA
π
dEj
min(Ei ,Ej )
dθij
θij, (Ej ≪ Ei , θij ≪ 1) .
To invert branching process, take pair with strongest divergence betweenthem — 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 :
yij =2min(E 2
i ,E 2j )(1 − cos θij)
Q2
NB: relative kt between particles2. Find smallest of yij
◮ If > ycut , stop clustering◮ Otherwise recombine i and j , and repeat from step 1
Catani, Dokshitzer, Olsson, Turnock & Webber ’91
QCD lecture 4 (p. 24)
Jets
Sequential recomb.kt alg. at hadron colliders
inclusive kt algorithm
◮ Introduce angular radius R (NB: dimensionless!)
dij = min(p2ti , p
2tj )
∆R2ij
R2, diB = p2
ti [∆R2ij = (yi −yj)
2+(φi −φj)2]
◮ 1. Find smallest of dij , diB
2. if ij , recombine them3. if iB, call i a jet and remove from list of particles4. 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 abovept cut is IR safe.
QCD lecture 4 (p. 25)
Jets
Sequential recomb.Sequential recombination
kt alg.: Find smallest of
dij = min(k2ti , k
2tj )∆R2
ij/R2, diB = k2
ti
If dij recombine; if diB , i is a jetExample clustering with kt algo-rithm, R = 0.7
φ assumed 0 for all towers
QCD lecture 4 (p. 25)
Jets
Sequential recomb.Sequential recombination
p t/GeV
60
50
40
20
00 1 2 3 4 y
30
10
kt alg.: Find smallest of
dij = min(k2ti , k
2tj )∆R2
ij/R2, diB = k2
ti
If dij recombine; if diB , i is a jetExample clustering with kt algo-rithm, R = 0.7
φ assumed 0 for all towers
QCD lecture 4 (p. 25)
Jets
Sequential recomb.Sequential recombination
p t/GeV
60
50
40
20
00 1 2 3 4 y
30
10
kt alg.: Find smallest of
dij = min(k2ti , k
2tj )∆R2
ij/R2, diB = k2
ti
If dij recombine; if diB , i is a jetExample clustering with kt algo-rithm, R = 0.7
φ assumed 0 for all towers
QCD lecture 4 (p. 25)
Jets
Sequential recomb.Sequential recombination
p t/GeV
60
50
40
20
00 1 2 3 4 y
30
10
kt alg.: Find smallest of
dij = min(k2ti , k
2tj )∆R2
ij/R2, diB = k2
ti
If dij recombine; if diB , i is a jetExample clustering with kt algo-rithm, R = 0.7
φ assumed 0 for all towers
QCD lecture 4 (p. 25)
Jets
Sequential recomb.Sequential recombination
p t/GeV
60
50
40
20
00 1 2 3 4 y
30
10
dmin is dij = 2.0263kt alg.: Find smallest of
dij = min(k2ti , k
2tj )∆R2
ij/R2, diB = k2
ti
If dij recombine; if diB , i is a jetExample clustering with kt algo-rithm, R = 0.7
φ assumed 0 for all towers
QCD lecture 4 (p. 25)
Jets
Sequential recomb.Sequential recombination
p t/GeV
60
50
40
20
00 1 2 3 4 y
30
10
kt alg.: Find smallest of
dij = min(k2ti , k
2tj )∆R2
ij/R2, diB = k2
ti
If dij recombine; if diB , i is a jetExample clustering with kt algo-rithm, R = 0.7
φ assumed 0 for all towers
QCD lecture 4 (p. 25)
Jets
Sequential recomb.Sequential recombination
p t/GeV
60
50
40
20
00 1 2 3 4 y
30
10
dmin is dij = 4.06598kt alg.: Find smallest of
dij = min(k2ti , k
2tj )∆R2
ij/R2, diB = k2
ti
If dij recombine; if diB , i is a jetExample clustering with kt algo-rithm, R = 0.7
φ assumed 0 for all towers
QCD lecture 4 (p. 25)
Jets
Sequential recomb.Sequential recombination
p t/GeV
60
50
40
20
00 1 2 3 4 y
30
10
kt alg.: Find smallest of
dij = min(k2ti , k
2tj )∆R2
ij/R2, diB = k2
ti
If dij recombine; if diB , i is a jetExample clustering with kt algo-rithm, R = 0.7
φ assumed 0 for all towers
QCD lecture 4 (p. 25)
Jets
Sequential recomb.Sequential recombination
p t/GeV
60
50
40
20
00 1 2 3 4 y
30
10
dmin is dij = 4.8967kt alg.: Find smallest of
dij = min(k2ti , k
2tj )∆R2
ij/R2, diB = k2
ti
If dij recombine; if diB , i is a jetExample clustering with kt algo-rithm, R = 0.7
φ assumed 0 for all towers
QCD lecture 4 (p. 25)
Jets
Sequential recomb.Sequential recombination
p t/GeV
60
50
40
20
00 1 2 3 4 y
30
10
kt alg.: Find smallest of
dij = min(k2ti , k
2tj )∆R2
ij/R2, diB = k2
ti
If dij recombine; if diB , i is a jetExample clustering with kt algo-rithm, R = 0.7
φ assumed 0 for all towers
QCD lecture 4 (p. 25)
Jets
Sequential recomb.Sequential recombination
p t/GeV
60
50
40
20
00 1 2 3 4 y
30
10
dmin is dij = 20.0741kt alg.: Find smallest of
dij = min(k2ti , k
2tj )∆R2
ij/R2, diB = k2
ti
If dij recombine; if diB , i is a jetExample clustering with kt algo-rithm, R = 0.7
φ assumed 0 for all towers
QCD lecture 4 (p. 25)
Jets
Sequential recomb.Sequential recombination
p t/GeV
60
50
40
20
00 1 2 3 4 y
30
10
kt alg.: Find smallest of
dij = min(k2ti , k
2tj )∆R2
ij/R2, diB = k2
ti
If dij recombine; if diB , i is a jetExample clustering with kt algo-rithm, R = 0.7
φ assumed 0 for all towers
QCD lecture 4 (p. 25)
Jets
Sequential recomb.Sequential recombination
p t/GeV
60
50
40
20
00 1 2 3 4 y
30
10
dmin is dij = 27.1518kt alg.: Find smallest of
dij = min(k2ti , k
2tj )∆R2
ij/R2, diB = k2
ti
If dij recombine; if diB , i is a jetExample clustering with kt algo-rithm, R = 0.7
φ assumed 0 for all towers
QCD lecture 4 (p. 25)
Jets
Sequential recomb.Sequential recombination
p t/GeV
60
50
40
20
00 1 2 3 4 y
30
10
kt alg.: Find smallest of
dij = min(k2ti , k
2tj )∆R2
ij/R2, diB = k2
ti
If dij recombine; if diB , i is a jetExample clustering with kt algo-rithm, R = 0.7
φ assumed 0 for all towers
QCD lecture 4 (p. 25)
Jets
Sequential recomb.Sequential recombination
p t/GeV
60
50
40
20
00 1 2 3 4 y
30
10
dmin is dij = 35.524kt alg.: Find smallest of
dij = min(k2ti , k
2tj )∆R2
ij/R2, diB = k2
ti
If dij recombine; if diB , i is a jetExample clustering with kt algo-rithm, R = 0.7
φ assumed 0 for all towers
QCD lecture 4 (p. 25)
Jets
Sequential recomb.Sequential recombination
p t/GeV
60
50
40
20
00 1 2 3 4 y
30
10
kt alg.: Find smallest of
dij = min(k2ti , k
2tj )∆R2
ij/R2, diB = k2
ti
If dij recombine; if diB , i is a jetExample clustering with kt algo-rithm, R = 0.7
φ assumed 0 for all towers
QCD lecture 4 (p. 25)
Jets
Sequential recomb.Sequential recombination
p t/GeV
60
50
40
20
00 1 2 3 4 y
30
10
dmin is dij = 117.188kt alg.: Find smallest of
dij = min(k2ti , k
2tj )∆R2
ij/R2, diB = k2
ti
If dij recombine; if diB , i is a jetExample clustering with kt algo-rithm, R = 0.7
φ assumed 0 for all towers
QCD lecture 4 (p. 25)
Jets
Sequential recomb.Sequential recombination
p t/GeV
60
50
40
20
00 1 2 3 4 y
30
10
kt alg.: Find smallest of
dij = min(k2ti , k
2tj )∆R2
ij/R2, diB = k2
ti
If dij recombine; if diB , i is a jetExample clustering with kt algo-rithm, R = 0.7
φ assumed 0 for all towers
QCD lecture 4 (p. 25)
Jets
Sequential recomb.Sequential recombination
p t/GeV
60
50
40
20
00 1 2 3 4 y
30
10
dmin is diB = 154.864
kt alg.: Find smallest of
dij = min(k2ti , k
2tj )∆R2
ij/R2, diB = k2
ti
If dij recombine; if diB , i is a jetExample clustering with kt algo-rithm, R = 0.7
φ assumed 0 for all towers
QCD lecture 4 (p. 25)
Jets
Sequential recomb.Sequential recombination
p t/GeV
60
50
40
20
00 1 2 3 4 y
30
10
kt alg.: Find smallest of
dij = min(k2ti , k
2tj )∆R2
ij/R2, diB = k2
ti
If dij recombine; if diB , i is a jetExample clustering with kt algo-rithm, R = 0.7
φ assumed 0 for all towers
QCD lecture 4 (p. 25)
Jets
Sequential recomb.Sequential recombination
p t/GeV
60
50
40
20
00 1 2 3 4 y
30
10
dmin is diB = 1007
kt alg.: Find smallest of
dij = min(k2ti , k
2tj )∆R2
ij/R2, diB = k2
ti
If dij recombine; if diB , i is a jetExample clustering with kt algo-rithm, R = 0.7
φ assumed 0 for all towers
QCD lecture 4 (p. 25)
Jets
Sequential recomb.Sequential recombination
p t/GeV
60
50
40
20
00 1 2 3 4 y
30
10
kt alg.: Find smallest of
dij = min(k2ti , k
2tj )∆R2
ij/R2, diB = k2
ti
If dij recombine; if diB , i is a jetExample clustering with kt algo-rithm, R = 0.7
φ assumed 0 for all towers
QCD lecture 4 (p. 25)
Jets
Sequential recomb.Sequential recombination
p t/GeV
60
50
40
20
00 1 2 3 4 y
30
10
dmin is diB = 1619.62
kt alg.: Find smallest of
dij = min(k2ti , k
2tj )∆R2
ij/R2, diB = k2
ti
If dij recombine; if diB , i is a jetExample clustering with kt algo-rithm, R = 0.7
φ assumed 0 for all towers
QCD lecture 4 (p. 25)
Jets
Sequential recomb.Sequential recombination
p t/GeV
60
50
40
20
00 1 2 3 4 y
30
10
kt alg.: Find smallest of
dij = min(k2ti , k
2tj )∆R2
ij/R2, diB = k2
ti
If dij recombine; if diB , i is a jetExample clustering with kt algo-rithm, R = 0.7
φ assumed 0 for all towers
QCD lecture 4 (p. 25)
Jets
Sequential recomb.Sequential recombination
p t/GeV
60
50
40
20
00 1 2 3 4 y
30
10
dmin is diB = 2953.32
kt alg.: Find smallest of
dij = min(k2ti , k
2tj )∆R2
ij/R2, diB = k2
ti
If dij recombine; if diB , i is a jetExample clustering with kt algo-rithm, R = 0.7
φ assumed 0 for all towers
QCD lecture 4 (p. 25)
Jets
Sequential recomb.Sequential recombination
p t/GeV
60
50
40
20
00 1 2 3 4 y
30
10
kt alg.: Find smallest of
dij = min(k2ti , k
2tj )∆R2
ij/R2, diB = k2
ti
If dij recombine; if diB , i is a jetExample clustering with kt algo-rithm, R = 0.7
φ assumed 0 for all towers
QCD lecture 4 (p. 26)
Jets
ConesCone algorithms today
Unifying idea: momentum flow within a cone onlymarginally modified by QCD branching
But cones come in many variants
``
``
``
``
``
``
``
Finding conesProcessing Progressive
Split–Merge Split–DropRemoval
Seeded, Fixed (FC)GetJetCellJet
Seeded, Iterative (IC) CMS ConeJetClu (CDF)†
ATLAS cone
Seeded, It. + Midpoints CDF MidPointPxCone
(ICmp) D0 Run II cone
Seedless (SC) SISCone
†JetClu also has “ratcheting”
QCD lecture 4 (p. 26)
Jets
ConesCone algorithms today
Unifying idea: momentum flow within a cone onlymarginally modified by QCD branching
But cones come in many variants
``
``
``
``
``
``
``
Finding conesProcessing Progressive
Split–Merge Split–DropRemoval
Seeded, Fixed (FC)GetJetCellJet
Seeded, Iterative (IC) CMS ConeJetClu (CDF)†
ATLAS cone
Seeded, It. + Midpoints CDF MidPointPxCone
(ICmp) D0 Run II cone
Seedless (SC) SISCone
†JetClu also has “ratcheting”
QCD lecture 4 (p. 26)
Jets
ConesCone algorithms today
Unifying idea: momentum flow within a cone onlymarginally modified by QCD branching
But cones come in many variants
``
``
``
``
``
``
``
Finding conesProcessing Progressive
Split–Merge Split–DropRemoval
Seeded, Fixed (FC)GetJetCellJet
Seeded, Iterative (IC) CMS ConeJetClu (CDF)†
ATLAS cone
Seeded, It. + Midpoints CDF MidPointPxCone
(ICmp) D0 Run II cone
Seedless (SC) SISCone
†JetClu also has “ratcheting”
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeVOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV Seed = hardest_particleOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV Draw coneOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV sum of momenta != seedOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV Iterate seedOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV Draw coneOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV sum of momenta != seedOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV Iterate seedOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV Draw coneOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV sum of momenta == seedOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV Cone is stableOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV Convert into jetOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV Seed = hardest_particleOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV Draw coneOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV sum of momenta != seedOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV Iterate seedOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV Draw coneOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV sum of momenta == seedOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV Cone is stableOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV Convert into jetOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV Seed = hardest_particleOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV Draw coneOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV sum of momenta != seedOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV Iterate seedOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV Draw coneOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV sum of momenta == seedOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV Cone is stableOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV Convert into jetOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 27)
Jets
ConesIterative Cone, Prog Removal (IC-PR)
60
50
40
20
00 1 2 3 4 y
30
10
p t/GeV Convert into jetOne of the simpler cones
e.g. CMS iterative cone
◮ Take hardest particle as seed forcone axis
◮ Draw cone around seed
◮ Sum the momenta use as newseed direction, iterate until stable
◮ Convert contents into a “jet” andremove from event
Notes
◮ “Hardest particle” is collinearunsafe more right away...
QCD lecture 4 (p. 28)
Jets
ConesICPR iteration issue
100
200
300
400
500
pT (
GeV
/c)
rapidity
10−10
conecone axiscone iteration
Collinear splitting can modify the hard jets: ICPR algorithms arecollinear unsafe =⇒ perturbative calculations give ∞
QCD lecture 4 (p. 28)
Jets
ConesICPR iteration issue
100
200
300
400
500
pT (
GeV
/c)
rapidity
10−10
conecone axiscone iteration
Collinear splitting can modify the hard jets: ICPR algorithms arecollinear unsafe =⇒ perturbative calculations give ∞
QCD lecture 4 (p. 28)
Jets
ConesICPR iteration issue
100
200
300
400
500
pT (
GeV
/c)
rapidity
10−10
conecone axiscone iteration
Collinear splitting can modify the hard jets: ICPR algorithms arecollinear unsafe =⇒ perturbative calculations give ∞
QCD lecture 4 (p. 28)
Jets
ConesICPR iteration issue
100
200
300
400
500
pT (
GeV
/c)
rapidity
10−10
conecone axiscone iteration
Collinear splitting can modify the hard jets: ICPR algorithms arecollinear unsafe =⇒ perturbative calculations give ∞
QCD lecture 4 (p. 28)
Jets
ConesICPR iteration issue
100
200
300
400
500
pT (
GeV
/c)
rapidity
10−10
conecone axiscone iteration
Collinear splitting can modify the hard jets: ICPR algorithms arecollinear unsafe =⇒ perturbative calculations give ∞
QCD lecture 4 (p. 28)
Jets
ConesICPR iteration issue
jet 1
100
200
300
400
500
pT (
GeV
/c)
rapidity
10−10
conecone axiscone iteration
Collinear splitting can modify the hard jets: ICPR algorithms arecollinear unsafe =⇒ perturbative calculations give ∞
QCD lecture 4 (p. 28)
Jets
ConesICPR iteration issue
jet 1
100
200
300
400
500
pT (
GeV
/c)
rapidity
10−10
conecone axiscone iteration
Collinear splitting can modify the hard jets: ICPR algorithms arecollinear unsafe =⇒ perturbative calculations give ∞
QCD lecture 4 (p. 28)
Jets
ConesICPR iteration issue
100
200
300
400
500
pT (
GeV
/c)
rapidity
10−10
conecone axiscone iteration
Collinear splitting can modify the hard jets: ICPR algorithms arecollinear unsafe =⇒ perturbative calculations give ∞
QCD lecture 4 (p. 28)
Jets
ConesICPR iteration issue
100
200
300
400
500
pT (
GeV
/c)
rapidity
10−10
conecone axiscone iteration
Collinear splitting can modify the hard jets: ICPR algorithms arecollinear unsafe =⇒ perturbative calculations give ∞
QCD lecture 4 (p. 28)
Jets
ConesICPR iteration issue
100
200
300
400
500
pT (
GeV
/c)
rapidity
10−10
conecone axiscone iteration
Collinear splitting can modify the hard jets: ICPR algorithms arecollinear unsafe =⇒ perturbative calculations give ∞
QCD lecture 4 (p. 28)
Jets
ConesICPR iteration issue
100
200
300
400
500
pT (
GeV
/c)
rapidity
10−10
conecone axiscone iteration
Collinear splitting can modify the hard jets: ICPR algorithms arecollinear unsafe =⇒ perturbative calculations give ∞
QCD lecture 4 (p. 28)
Jets
ConesICPR iteration issue
100
200
300
400
500
pT (
GeV
/c)
rapidity
10−10
conecone axiscone iteration
Collinear splitting can modify the hard jets: ICPR algorithms arecollinear unsafe =⇒ perturbative calculations give ∞
QCD lecture 4 (p. 28)
Jets
ConesICPR iteration issue
jet 1
100
200
300
400
500
pT (
GeV
/c)
rapidity
10−10
conecone axiscone iteration
Collinear splitting can modify the hard jets: ICPR algorithms arecollinear unsafe =⇒ perturbative calculations give ∞
QCD lecture 4 (p. 28)
Jets
ConesICPR iteration issue
jet 1
100
200
300
400
500
pT (
GeV
/c)
rapidity
10−10
conecone axiscone iteration
Collinear splitting can modify the hard jets: ICPR algorithms arecollinear unsafe =⇒ perturbative calculations give ∞
QCD lecture 4 (p. 28)
Jets
ConesICPR iteration issue
jet 1
100
200
300
400
500
pT (
GeV
/c)
rapidity
10−10
conecone axiscone iteration
Collinear splitting can modify the hard jets: ICPR algorithms arecollinear unsafe =⇒ perturbative calculations give ∞
QCD lecture 4 (p. 28)
Jets
ConesICPR iteration issue
jet 1
100
200
300
400
500
pT (
GeV
/c)
rapidity
10−10
conecone axiscone iteration
Collinear splitting can modify the hard jets: ICPR algorithms arecollinear unsafe =⇒ perturbative calculations give ∞
QCD lecture 4 (p. 28)
Jets
ConesICPR iteration issue
jet 2
jet 1
100
200
300
400
500
pT (
GeV
/c)
rapidity
10−10
conecone axiscone iteration
Collinear splitting can modify the hard jets: ICPR algorithms arecollinear unsafe =⇒ perturbative calculations give ∞
QCD lecture 4 (p. 28)
Jets
ConesICPR iteration issue
jet 2
jet 1
100
200
300
400
500
pT (
GeV
/c)
rapidity
10−10
conecone axiscone iteration
Collinear splitting can modify the hard jets: ICPR algorithms arecollinear unsafe =⇒ perturbative calculations give ∞
QCD lecture 4 (p. 28)
Jets
ConesICPR iteration issue
jet 2
jet 1
100
200
300
400
500
pT (
GeV
/c)
rapidity
10−10
conecone axiscone iteration
Collinear splitting can modify the hard jets: ICPR algorithms arecollinear unsafe =⇒ perturbative calculations give ∞
QCD lecture 4 (p. 29)
Jets
ConesConsequences of collinear unsafety
jet 2jet 1jet 1jet 1 jet 1
αs x (+ )∞nαs x (− )∞n αs x (+ )∞nαs x (− )∞n
Collinear Safe Collinear Unsafe
Infinities cancel Infinities do not cancel
Invalidates perturbation theory
QCD lecture 4 (p. 29)
Jets
ConesConsequences of collinear unsafety
jet 2jet 1jet 1jet 1 jet 1
αs x (+ )∞nαs x (− )∞n αs x (+ )∞nαs x (− )∞n
Collinear Safe Collinear Unsafe
Infinities cancel Infinities do not cancel
Invalidates perturbation theory
QCD lecture 4 (p. 30)
Jets
ConesIRC safety & real-life
Real life does not have infinities, but pert. infinity leaves a real-life trace
α2s + α3
s + α4s ×∞ → α2
s + α3s + α4
s × ln pt/Λ → α2s + α3
s + α3s
︸ ︷︷ ︸
BOTH WASTED
Among consequences of IR unsafety:
Last meaningful order
JetClu, ATLAS MidPoint CMS it. cone Known atcone [IC-SM] [ICmp -SM] [IC-PR]
Inclusive jets LO NLO NLO NLO (→ NNLO)W /Z + 1 jet LO NLO NLO NLO3 jets none LO LO NLO [nlojet++]W /Z + 2 jets none LO LO NLO [MCFM]mjet in 2j + X none none none LO
NB: 50,000,000$/£/CHF/e investment in NLO
Multi-jet contexts much more sensitive: ubiquitous at LHCAnd LHC will rely on QCD for background double-checks
extraction of cross sections, extraction of parameters
QCD lecture 4 (p. 30)
Jets
ConesIRC safety & real-life
Real life does not have infinities, but pert. infinity leaves a real-life trace
α2s + α3
s + α4s ×∞ → α2
s + α3s + α4
s × ln pt/Λ → α2s + α3
s + α3s
︸ ︷︷ ︸
BOTH WASTED
Among consequences of IR unsafety:
Last meaningful order
JetClu, ATLAS MidPoint CMS it. cone Known atcone [IC-SM] [ICmp -SM] [IC-PR]
Inclusive jets LO NLO NLO NLO (→ NNLO)W /Z + 1 jet LO NLO NLO NLO3 jets none LO LO NLO [nlojet++]W /Z + 2 jets none LO LO NLO [MCFM]mjet in 2j + X none none none LO
NB: 50,000,000$/£/CHF/e investment in NLO
Multi-jet contexts much more sensitive: ubiquitous at LHCAnd LHC will rely on QCD for background double-checks
extraction of cross sections, extraction of parameters
QCD lecture 4 (p. 30)
Jets
ConesIRC safety & real-life
Real life does not have infinities, but pert. infinity leaves a real-life trace
α2s + α3
s + α4s ×∞ → α2
s + α3s + α4
s × ln pt/Λ → α2s + α3
s + α3s
︸ ︷︷ ︸
BOTH WASTED
Among consequences of IR unsafety:
Last meaningful order
JetClu, ATLAS MidPoint CMS it. cone Known atcone [IC-SM] [ICmp -SM] [IC-PR]
Inclusive jets LO NLO NLO NLO (→ NNLO)W /Z + 1 jet LO NLO NLO NLO3 jets none LO LO NLO [nlojet++]W /Z + 2 jets none LO LO NLO [MCFM]mjet in 2j + X none none none LO
NB: 50,000,000$/£/CHF/e investment in NLO
Multi-jet contexts much more sensitive: ubiquitous at LHCAnd LHC will rely on QCD for background double-checks
extraction of cross sections, extraction of parameters
QCD lecture 4 (p. 31)
Jets
ConesEssential characteristic of cones?
Cone (ICPR)
QCD lecture 4 (p. 31)
Jets
ConesEssential characteristic of cones?
Cone (ICPR) (Some) cone algorithms givecircular jets in y − φ plane
Much appreciated by experi-ments e.g. for acceptance
corrections
QCD lecture 4 (p. 31)
Jets
ConesEssential characteristic of cones?
Cone (ICPR)
kt alg.
(Some) cone algorithms givecircular jets in y − φ plane
Much appreciated by experi-ments e.g. for acceptance
corrections
QCD lecture 4 (p. 31)
Jets
ConesEssential characteristic of cones?
Cone (ICPR)
kt alg.
kt jets are irregular
Because soft junk clusters to-gether first:
dij = min(k2ti , k
2tj )∆R2
ij
Regularly held against kt
(Some) cone algorithms givecircular jets in y − φ plane
Much appreciated by experi-ments e.g. for acceptance
corrections
QCD lecture 4 (p. 31)
Jets
ConesEssential characteristic of cones?
Cone (ICPR)
kt alg.
kt jets are irregular
Because soft junk clusters to-gether first:
dij = min(k2ti , k
2tj )∆R2
ij
Regularly held against kt
(Some) cone algorithms givecircular jets in y − φ plane
Much appreciated by experi-ments e.g. for acceptance
corrections
Is there some other, noncone-based way of getting
circular jets?
QCD lecture 4 (p. 32)
Jets
ConesTwo directions
How do we solve
cone IR safety
problems?
Fix stable-cone finding
SISCone
Invent "cone-like" alg.
anti-kt
Cacciari, GPS & Soyez ’08
GPS & Soyez ’07
Same family as Tev. Run II alg
QCD lecture 4 (p. 33)
Jets
ConesAdapting seq. rec. to give circular jets
Soft stuff clusters with nearest neighbour
kt : dij = min(k2ti , k
2tj)∆R2
ij −→ anti-kt: dij =∆R2
ij
max(k2ti , k
2tj)
Hard stuff clusters with nearest neighbour
Privilege collinear divergence over soft divergence
Cacciari, GPS & Soyez ’08
QCD lecture 4 (p. 33)
Jets
ConesAdapting seq. rec. to give circular jets
Soft stuff clusters with nearest neighbour
kt : dij = min(k2ti , k
2tj)∆R2
ij −→ anti-kt: dij =∆R2
ij
max(k2ti , k
2tj)
Hard stuff clusters with nearest neighbour
Privilege collinear divergence over soft divergence
Cacciari, GPS & Soyez ’08
QCD lecture 4 (p. 33)
Jets
ConesAdapting seq. rec. to give circular jets
Soft stuff clusters with nearest neighbour
kt : dij = min(k2ti , k
2tj)∆R2
ij −→ anti-kt: dij =∆R2
ij
max(k2ti , k
2tj)
Hard stuff clusters with nearest neighbour
Privilege collinear divergence over soft divergence
Cacciari, GPS & Soyez ’08
QCD lecture 4 (p. 33)
Jets
ConesAdapting seq. rec. to give circular jets
Soft stuff clusters with nearest neighbour
kt : dij = min(k2ti , k
2tj)∆R2
ij −→ anti-kt: dij =∆R2
ij
max(k2ti , k
2tj)
Hard stuff clusters with nearest neighbour
Privilege collinear divergence over soft divergence
Cacciari, GPS & Soyez ’08
QCD lecture 4 (p. 33)
Jets
ConesAdapting seq. rec. to give circular jets
Soft stuff clusters with nearest neighbour
kt : dij = min(k2ti , k
2tj)∆R2
ij −→ anti-kt: dij =∆R2
ij
max(k2ti , k
2tj)
Hard stuff clusters with nearest neighbour
Privilege collinear divergence over soft divergence
Cacciari, GPS & Soyez ’08
QCD lecture 4 (p. 33)
Jets
ConesAdapting seq. rec. to give circular jets
Soft stuff clusters with nearest neighbour
kt : dij = min(k2ti , k
2tj)∆R2
ij −→ anti-kt: dij =∆R2
ij
max(k2ti , k
2tj)
Hard stuff clusters with nearest neighbour
Privilege collinear divergence over soft divergence
Cacciari, GPS & Soyez ’08
QCD lecture 4 (p. 33)
Jets
ConesAdapting seq. rec. to give circular jets
Soft stuff clusters with nearest neighbour
kt : dij = min(k2ti , k
2tj)∆R2
ij −→ anti-kt: dij =∆R2
ij
max(k2ti , k
2tj)
Hard stuff clusters with nearest neighbour
Privilege collinear divergence over soft divergence
Cacciari, GPS & Soyez ’08
QCD lecture 4 (p. 33)
Jets
ConesAdapting seq. rec. to give circular jets
Soft stuff clusters with nearest neighbour
kt : dij = min(k2ti , k
2tj)∆R2
ij −→ anti-kt: dij =∆R2
ij
max(k2ti , k
2tj)
Hard stuff clusters with nearest neighbour
Privilege collinear divergence over soft divergence
Cacciari, GPS & Soyez ’08
QCD lecture 4 (p. 33)
Jets
ConesAdapting seq. rec. to give circular jets
Soft stuff clusters with nearest neighbour
kt : dij = min(k2ti , k
2tj)∆R2
ij −→ anti-kt: dij =∆R2
ij
max(k2ti , k
2tj)
Hard stuff clusters with nearest neighbour
Privilege collinear divergence over soft divergence
Cacciari, GPS & Soyez ’08
QCD lecture 4 (p. 33)
Jets
ConesAdapting seq. rec. to give circular jets
Soft stuff clusters with nearest neighbour
kt : dij = min(k2ti , k
2tj)∆R2
ij −→ anti-kt: dij =∆R2
ij
max(k2ti , k
2tj)
Hard stuff clusters with nearest neighbour
Privilege collinear divergence over soft divergence
Cacciari, GPS & Soyez ’08
QCD lecture 4 (p. 33)
Jets
ConesAdapting seq. rec. to give circular jets
Soft stuff clusters with nearest neighbour
kt : dij = min(k2ti , k
2tj)∆R2
ij −→ anti-kt: dij =∆R2
ij
max(k2ti , k
2tj)
Hard stuff clusters with nearest neighbour
Privilege collinear divergence over soft divergence
Cacciari, GPS & Soyez ’08
QCD lecture 4 (p. 33)
Jets
ConesAdapting seq. rec. to give circular jets
Soft stuff clusters with nearest neighbour
kt : dij = min(k2ti , k
2tj)∆R2
ij −→ anti-kt: dij =∆R2
ij
max(k2ti , k
2tj)
Hard stuff clusters with nearest neighbour
Privilege collinear divergence over soft divergence
Cacciari, GPS & Soyez ’08
QCD lecture 4 (p. 33)
Jets
ConesAdapting seq. rec. to give circular jets
Soft stuff clusters with nearest neighbour
kt : dij = min(k2ti , k
2tj)∆R2
ij −→ anti-kt: dij =∆R2
ij
max(k2ti , k
2tj)
Hard stuff clusters with nearest neighbour
Privilege collinear divergence over soft divergence
Cacciari, GPS & Soyez ’08
anti-kt givescone-like jets
without using stablecones
QCD lecture 4 (p. 34)
Jets
Cones
There is plenty more choice for (IR safe) jet finding(4 good algs are Cam/Aachen, anti-kt, SISCone and kt)
Do all you can to avoid IR unsafe jet algorithms(ATLAS iterative cone, CMS iterative cone, etc.).
Think about the choice of parameters in your jet definition
(what radius for what problem?)
QCD lecture 4 (p. 35)
Jets
ConesAn example
Searching for high-pt (boosted) heavy particles, such as aHiggs boson.
Because LHC will have√
s ≫ mH , highly boosted Higgses,
ptH ≫ mH , are not so rare.
The boost factor collimates the Higgs decay into a singlejet. Can we still identify it?
QCD lecture 4 (p. 36)
Jets
Conespp → ZH → ννbb, @14TeV, mH =115GeV
Herwig 6.510 + Jimmy 4.31 + FastJet 2.3
Cluster event, C/A, R=1.2
SIGNAL
Zbb BACKGROUND
arbitrary norm.
QCD lecture 4 (p. 36)
Jets
Conespp → ZH → ννbb, @14TeV, mH =115GeV
Herwig 6.510 + Jimmy 4.31 + FastJet 2.3
Fill it in, → show jets more clearly
SIGNAL
Zbb BACKGROUND
arbitrary norm.
QCD lecture 4 (p. 36)
Jets
Conespp → ZH → ννbb, @14TeV, mH =115GeV
Herwig 6.510 + Jimmy 4.31 + FastJet 2.3
Consider hardest jet, m = 150 GeV
SIGNAL
0
0.05
0.1
0.15
80 100 120 140 160mH [GeV]
200 < ptZ < 250 GeV
Zbb BACKGROUND
0
0.002
0.004
0.006
0.008
80 100 120 140 160mH [GeV]
200 < ptZ < 250 GeV
arbitrary norm.
QCD lecture 4 (p. 36)
Jets
Conespp → ZH → ννbb, @14TeV, mH =115GeV
Herwig 6.510 + Jimmy 4.31 + FastJet 2.3
split: m = 150 GeV, max(m1,m2)m
= 0.92 → repeat
SIGNAL
0
0.05
0.1
0.15
80 100 120 140 160mH [GeV]
200 < ptZ < 250 GeV
Zbb BACKGROUND
0
0.002
0.004
0.006
0.008
80 100 120 140 160mH [GeV]
200 < ptZ < 250 GeV
arbitrary norm.
QCD lecture 4 (p. 36)
Jets
Conespp → ZH → ννbb, @14TeV, mH =115GeV
Herwig 6.510 + Jimmy 4.31 + FastJet 2.3
split: m = 139 GeV, max(m1,m2)m
= 0.37 → mass drop
SIGNAL
0
0.05
0.1
0.15
80 100 120 140 160mH [GeV]
200 < ptZ < 250 GeV
Zbb BACKGROUND
0
0.002
0.004
0.006
0.008
80 100 120 140 160mH [GeV]
200 < ptZ < 250 GeV
arbitrary norm.
QCD lecture 4 (p. 36)
Jets
Conespp → ZH → ννbb, @14TeV, mH =115GeV
Herwig 6.510 + Jimmy 4.31 + FastJet 2.3
check: y12 ≃ pt2
pt1≃ 0.7 → OK + 2 b-tags (anti-QCD)
SIGNAL
0
0.05
0.1
0.15
80 100 120 140 160mH [GeV]
200 < ptZ < 250 GeV
Zbb BACKGROUND
0
0.002
0.004
0.006
0.008
80 100 120 140 160mH [GeV]
200 < ptZ < 250 GeV
arbitrary norm.
QCD lecture 4 (p. 36)
Jets
Conespp → ZH → ννbb, @14TeV, mH =115GeV
Herwig 6.510 + Jimmy 4.31 + FastJet 2.3
Rfilt = 0.3
SIGNAL
0
0.05
0.1
0.15
80 100 120 140 160mH [GeV]
200 < ptZ < 250 GeV
Zbb BACKGROUND
0
0.002
0.004
0.006
0.008
80 100 120 140 160mH [GeV]
200 < ptZ < 250 GeV
arbitrary norm.
QCD lecture 4 (p. 36)
Jets
Conespp → ZH → ννbb, @14TeV, mH =115GeV
Herwig 6.510 + Jimmy 4.31 + FastJet 2.3
Rfilt = 0.3: take 3 hardest, m = 117 GeV
SIGNAL
0
0.05
0.1
0.15
80 100 120 140 160mH [GeV]
200 < ptZ < 250 GeV
Zbb BACKGROUND
0
0.002
0.004
0.006
0.008
80 100 120 140 160mH [GeV]
200 < ptZ < 250 GeV
arbitrary norm.
QCD lecture 4 (p. 37)
Closing
To conclude
QCD lecture 4 (p. 38)
Closing What kinds of searches?
mass peak
dσ
/ dm
[lo
g sc
ale]
mass
Signal
QCDprediction
New resonance (e.g. Z ′) where you see alldecay products and reconstruct an invari-ant mass
QCD may:
◮ swamp signal
◮ smear signal
leptonic case easy; hadronic case harder
QCD lecture 4 (p. 38)
Closing What kinds of searches?
mass edge
dσ
/ dm
[lo
g sc
ale]
mass
Signal
QCDprediction
New resonance (e.g. R-parity conservingSUSY), where undetected new stable par-ticle escapes detection.
Reconstruct only part of an invariant mass→ kinematic edge.
QCD may:
◮ swamp signal
◮ smear signal
QCD lecture 4 (p. 38)
Closing What kinds of searches?
high−mass excess
dσ
/ dm
[lo
g sc
ale]
mass
Signal
QCDprediction
Unreconstructed SUSY cascade. Study ef-
fective mass (sum of all transverse mo-menta).
Broad excess at high mass scales.
Knowledge of backgrounds is crucial isdeclaring discovery.
QCD is one way of getting handle on back-ground.
QCD lecture 4 (p. 38)
Closing What kinds of searches?d
σ / d
m [
log
scal
e]
mass
Signal ?
dσ
/ dm
[lo
g sc
ale]
mass
Signal ?
dσ
/ dm
[lo
g sc
ale]
mass
Signal ?
QCD lecture 4 (p. 39)
Closing If you want to find out more
Classic references
QCD and collider physicsEllis, Stirling & Webber,Cambridge University Press 1996
The Handbook of Perturbative QCD,the CTEQ Collaborationhttp://www.phys.psu.edu/~cteq/
Advanced topics
Monte Carlos, Matching, Heavy-quarks, Jets, PDFs, etc.E.g.: transparencies from CTEQ-MCNet 2008 QCD schoolhttp://tr.im/oUWG