Jet Algorithms

Jet Algorithms
Pierre-Antoine Delsart
LPSC Grenoble
February 27, 2009
P.A. Delsart (LAPP)
Jet Algorithms
February 27, 2009
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Introduction
Jets are due to QCD interactions
Several level of jets
partons (QCD perturbative)
hadrons (QCD
non-perturbative)
experimental
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Jet Algorithms
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Jet Algorithms
List of particles :
- partons
- hadrons
- calorimeter clusters
- ...
Groups of particles :
Jet Algorithm
JETS
Theoretical constraints:
infrared & colinear safe (QCD issues, see later)
z-boost invariance
level Independence (parton,hadron, calorimeter)
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Jets families
Cones
simple geometric motivation
Find stable cones in eta,phi plan (stable : jet 4mom is along cone
axis)
Split/merge procedure for overlapping cones
sa
Clustering (Kt )
Pairwise successive aggregation of proto-jets
Dene a distance between constituents
Aggregate rst closest constituent
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Cones algorithms
Finding all stable cones : naive approach is extremely slow
=⇒Use
Seeded algorithms
Atlas Cone : a seeded algorithm
search stable cone only around highest Pt constituents
split/merge : if 2 jets overlap, compute fraction of Pt in overlap
region. Split if
P.A. Delsart (LAPP)
f
< 0.75
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Atlas Cone problems
Atlas cone not Infrared/collinear safe
Dark tower : signicant constituent can be excluded (in black below)
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Jets (p. 46)
Cone
xC-SM
IRC safety & real-life
Real life does not have infinities, but pert. infinity leaves a real-life trace
α2s + α3s + α4s × ∞ → α2s + α3s + α4s × ln pt /Λ → α2s + α3s + α3s
| {z }
BOTH WASTED
Among consequences of IR unsafety:
Inclusive jets
W /Z + 1 jet
3 jets
W /Z + 2 jets
mjet in 2j + X
Last meaningful order
JetClu, ATLAS MidPoint CMS it. cone
cone [IC-SM]
[ICmp -SM]
[IC-PR]
LO
NLO
NLO
LO
NLO
NLO
none
LO
LO
none
LO
LO
none
none
none
NB: $30 − 50M
Known at
NLO (→ NNLO)
NLO
NLO [nlojet++]
NLO [MCFM]
LO
investment in NLO
Multi-jet contexts much more sensitive: ubiquitous at LHC
And LHC will rely on QCD for background double-checks
extraction of cross sections, extraction of parameters
SISCone
Solution to previous problems : SISCone (Seedless Infrared Safe Cone
algorithm)
Developed by Salam, Soyez et al.
Seedless : no seeds. Absolutely
all
stable cones are considered
Smart split/merge procedure
=⇒No
more theoretical problems.
A smart implementation (using geometrical tricks) makes it relatively fast
(∼
O (N ²))
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Jet Algorithms
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Clustering algorithms
Algorithm description :
Dene a distance
∆Rij2
Dij = min(PTi , PTj ) R 2
Di = PTi2
Compute all {Dij , Di } and d = min({Dij , Di })
2
if
if
2
d = D : combine jet i with jet j
d = D dene jet i as a nal jet
ij
i
Exhaust all proto-jets
Variants : Anti-kt and Cambridge. In distance formula replace
PT2 −→ PT2p
p=1 : standard Kt
p=0 : cambridge
p=-1 : Antit-kt
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Algorithms in a picture
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Jet Algorithms
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Algorithms in a picture
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Algorithms performances
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Efficiency and Purity
Event samples: di­jet samples.
No Pile­up
ΔR Match= 0.2
Jet Size: R=0.4
Input: TopoClusters
AntiKt Topo|η|<0.4
AntiKt Topo|η|<0.4
Cone Topo |η|<0.4
Cone Topo |η|<0.4
ΔR Match= 0.2
P. Francavilla
Efficiency = NTruth
/ NTruth
Matched
Kt Topo |η|<0.4
Kt Topo |η|<0.4
SISCone Topo |η|<0.4
SISCone Topo |η|<0.4
P. Francavilla
Reco
Purity = NMatched
/ NReco
AntiKt Topo |η|<0.4
Cone Topo |η|<0.4
Kt Topo |η|<0.4
SISCone Topo |η|<0.4
Studies done on other samples:
W+Jets, Higgs: ATL­COM­PHYS­2008­021
Campanelli/Geerlings/Huston Top: Sanchez, De Cecco
Studies on different topologies and generators (i.e. AlpGen, Sherpa) are in preparation.
The clustering algorithms have a better efficiency and purity.
Paolo Francavilla Jet Algorithms
29
Calibration based on cell weighting derived for ATLAS Cone
Jet Size: R=0.4
Input: TopoClusters
AntiKt Topo η<0.4
Cone Topo η<0.4
SISCone Topo η<0.4
ΔR Match= 0.2
We will provide soon dedicated calibrations for the new jet algorithms (S. Eckweiler)
P. Francavilla
AntiKt Topo η<0.4
Cone Topo η<0.4
SISCone Topo η<0.4
Paolo Francavilla P. Francavilla
EReco/ETrue
Linearity and Resolution
The jet algorithms show
similar linearities and resolutions Similar results for the spatial resolution (Sanchez, De Cecco)
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Algorithms and Pileup
Compare same jets in same events with / without pile-up
Low luminosity
Central Calo jets
Study ratio mass ratio :
M(pileup) / M(no-pileup)
Anti-kt R=0.6
Kt R=0.6
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Conclusions
Choice of Jet Algorithm
matters
!
Theoretical aspects
Inuence of Pile-up
performances
(Largest eect still comes from size parameter)
Atlas will soon give up ATLAS Cone implementation in favor of SISCone or
Anti-Kt
More information in G. Salam lecture
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