lecture iv: jet finding techniques and results marco van leeuwen utrecht university jyväskylä...
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Lecture IV: Jet finding techniques and results
Marco van LeeuwenUtrecht University
Jyväskylä Summer School 2008
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Parton energy from -jet and jet reconstruction
Qualitatively:
)/()( , jethadrTjetshadrT
EpDEPdEdN
dpdN
`known’ from e+e-knownpQCDxPDF
extract
Full deconvolution large uncertainties (+ not transparent)
Fix/measure Ejet to take one factor out
Two approaches: -jet- Jet reconstruction
Second-generation measurements at RHIC – first generation at LHC?
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Perturbative QCD processes
• Hadron production• Heavy flavours• Jet production
– e+e- → jets – p(bar)+p → jets
• Direct photon production
Measurem
ent difficulty
The
ory
diff
icul
ty
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Fixing the parton energy with -jet eventsT. Renk, PRC74, 034906
-jet: know jet energy sensitive to P(E)
RAA insensitive to P(E)
Nuclear modification factor
Away-side spectra in -jet
E = 15 GeV
Away-side spectra for -jet are sensitive to P(E)
Input energy loss distribution
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-jet in Au+Au
Use shower shape in EMCal to form 0 sample and -rich sample
Combinatorial subtraction to obtain direct- sample
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STAR Preliminary
IAA(zT) =DAA (zT)
Dpp (zT)
Direct- recoil suppression
Large suppression for away-side: factor 3-5
Results agree with model predictions
Uncertainties still sizable Some improvements expected for final resultsFuture improvements with increased RHIC luminosity
J. Frantz, H
ard Probes 2008
A. H
amed, H
ard Probes 2008
8 < ET, < 16 GeV
ET,
2 < pTassoc < 10 GeV
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Jet reconstruction algorithms
Two categories of jet algorithms:
• Sequential recombination kT, anti-kT, Durham
– Define distance measure, e.g. dij = min(pTi,pTj)*Rij
– Cluster closest
• Cone– Draw Cone radius R around starting point
– Iterate until stable ,jet = <,>particles
For a complete discussion, see: http://www.lpthe.jussieu.fr/~salam/teaching/PhD-courses.html
Sum particles inside jet Different prescriptions exist, most natural: E-scheme, sum 4-vectors
Jet is an object defined by jet algorithmIf parameters are right, may approximate parton
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Collinear and infrared safetyIllustration by G
. Salam
Jets should not be sensitive to soft effects (hadronisation and E-loss)
- Collinear safe- Infrared safe
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Collinear safety
Note also: detector effects, such as splitting clusters in calorimeter (0 decay)
Illustration by G. S
alam
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Infrared safety
Infrared safety also implies robustness against soft background in heavy ion collisions
Illustration by G. S
alam
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Clustering algorithms – kT algorithm
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kT algorithm
• Calculate – For every particle i: distance to beam
– For every pair i,j : distance
• Find minimal d
– If diB, i is a jet
– If dij, combine i and j
• Repeat until only jets
Various distance measures have been used, e.g. Jade, Durham, Cambridge/Aachen
Current standard choice:
2,itiB pd
2
22,
2, ),min(
R
Rppd ij
jtitij
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kT algorithm demo
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kT algorithm properties
• Everything ends up in jets• kT-jets irregular shape
– Measure area with ‘ghost particles’
• kT-algo starts with soft stuff– ‘background’ clusters first, affects jet
• Infrared and collinear safe• Naïve implementation slow (N3). Not necessary
Fastjet
Alternative: anti-kT
2,
1
itiB pd
2
2
2,
2,
1,
1min
R
R
ppd ij
jtitij
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Cone algorithm
• Jets defined as cone• Iterate until stable:
(,)Cone = <,>particles in cone
• Starting points for cones, seeds, e.g. highest pT particles
• Split-merge prescription for overlapping cones
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Cone algorithm demo
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IR safety is subtle, but important
G. S
alam, arX
iv:0906.1833
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Seedless cone
Limiting cases occur when two particles are on the edge of the cone
1D: slide cone over particles and search for stable coneKey observation: content of cone only changes when the cone boundary touches a particle
Extension to 2D (,)
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Split-merge procedure
• Overlapping cones unavoidable• Solution: split-merge procedure
Evaluate Pt1, Pt,shared
– If Pt,shared/Pt1> f merge jets
– Else split jets (e.g. assign Pt,shared to closest jet or split Pt,shared according to Pt1/Pt2)
Jet1 Jet2
Merge: Ptshared large fraction of Pt1
Jet1 Jet2
Split: Ptshared small fraction of Pt1
f = 0.5 … 0.75
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Note on recombination schemes
ET-weighted averaging:Simple
Not boost-invariant for massive particles
Most unambiguous scheme: E-scheme, add 4-vectors
Boost-invariantNeeds particle masses (e.g. assign pion mass)Generates massive jets
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Current best jet algorithms
• Only three good choices:– kT algorithm (sequential recombination, non-
circular jets)– Anti-kT algoritm (sequential recombination, circular
jets)– SISCone algorithm (Infrared Safe Cone)
+ some minor variations: Durham algo, differentcombination schemes
These are all available in the FastJet package:http://www.lpthe.jussieu.fr/~salam/fastjet/
Really no excuse to use anything else (and potentially run into trouble)
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Speed matters
At LHC, multiplicities are largeA lot has been gained from improving implementations
G. S
alam, arX
iv:0906.1833
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Relating jets and single hadrons
High-pT hadrons from jet fragmentation
Qualitatively: )/( ,, jetThadrT
jetsThadrT
ppDdpdN
dpdN
Single hadrons are suppressed:
- Suppression of jet yield (out-of-cone radiation) RAAjets < 1
- Modification of fragment distribution (in-cone radiation) softening of fragmentation function and/or broadening of jet structure
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Jet finding in heavy ion events
η
p t p
er g
rid c
ell [
GeV
]
STAR preliminary~ 21 GeV
FastJet:Cacciari, Salam and Soyez; arXiv: 0802.1188http://rhig.physics.yale.edu/~putschke/Ahijf/A_Heavy_Ion_Jet-Finder.html
Jets clearly visible in heavy ion events at RHIC
Use different algorithms to estimate systematic uncertainties:• Cone-type algorithms
simple cone, iterative cone, infrared safe SISCone
• Sequential recombination algorithmskT, Cambridge, inverse kT
Combinatorial backgroundNeeds to be subtracted
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p+p Au+Au central
STAR Preliminary
Jet spectra
STAR Preliminary
Note kinematic reach out to 50 GeV
• Jet energy depends on R, affects spectra• kT, anti-kT give similar results
Take ratios to compare p+p, Au+Au
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Jet RAA at RHIC
Jet RAA >> 0.2 (hadron RAA)
Jet finding recovers most of the energy loss measure of initial parton energy
M. P
loskon, ST
AR
, QM
09
Some dependence on jet-algorithm? Under study…
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Radius dependence
RAA depends on jet radius:Small R jet is single hadron
M. P
loskon, ST
AR
, QM
09
Jet broadening due to E-loss?
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Fragmentation functions
STAR Preliminary
pt,rec(AuAu)>25 GeV20<pt,rec(AuAu)<25 GeV
Use recoil jet to avoid biases
Suppression of fragmentation also small (>> 0.2)
E. B
runa, ST
AR
, QM
09
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Di-jet spectra
29
Ele
na B
run
a fo
r the S
TA
R C
olla
bora
tion
- Q
M0
9STAR PreliminarySTAR Preliminary
E. B
runa, ST
AR
, QM
09
Jet IAA
Away-side jet yield suppressed partons absorbed
... due to large path lentgh(trigger bias)
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Emerging picture from jet results
• Jet RAA ~ 1 for sufficiently large R – unbiased parton selection
• Away side jet fragmentation ummodified – away-side jet emerges without E-loss
• Jet IAA ~ 0.2 – Many jets are absorded (large E-loss)
Study vs R, E to quantify P(E) and broadening
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Modeling in-medium fragmentation
From C. Salgado
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Sudakov prescription
From C. Salgado
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Sudakov prescription
From C. Salgado
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Sudakov MC implementation
Used by most MC event generators (PYTHIA, HERWIG)
From C. Salgado
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Full MC event
From C. Salgado
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MC resultsQ-PYTHIA
N. A
rme
sto e
t al, a
rXiv:0
90
7.1
01
4
Softening of fragmentation(pT-spectra)
Broadening
Caveat: all plot are parton-level. Effect of hadronisation may be large
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Summary
• Jet-finding, -jet to fix parton energy Sensitivity to P(E), jet broadening
• -hadron results agree with predictionNeed more statistics for P(E)
• Jet-algorithm requirements: Infrared and Collinear safe
• Jet results from RHIC:– Can recover full parton energy (R=0.4)– Indicate large broadening
– Away-side jet IAA ~ 0.2, jet absorption?
• Full event MC genartors are being developed important reference/benchmark for jet-analyses
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Extra slides
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Direct- recoil yields
A. H
amed, H
ard Probes 2008
Run 4 p+p/Au+Au @ 200 GeV
M. N
guyen, Quark M
atter 2006
Direct-–jet measurements being pursued by STAR and PHENIXRequires large data samples
Suppression of away-side yield visible
Similar to di-hadrons, but now with selected parton energy