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
2
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?
3
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
4
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
5
-jet in Au+Au
Use shower shape in EMCal to form 0 sample and -rich sample
Combinatorial subtraction to obtain direct- sample
6
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
7
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
8
Collinear and infrared safetyIllustration by G
. Salam
Jets should not be sensitive to soft effects (hadronisation and E-loss)
- Collinear safe- Infrared safe
9
Collinear safety
Note also: detector effects, such as splitting clusters in calorimeter (0 decay)
Illustration by G. S
alam
10
Infrared safety
Infrared safety also implies robustness against soft background in heavy ion collisions
Illustration by G. S
alam
11
Clustering algorithms – kT algorithm
12
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
13
kT algorithm demo
14
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
15
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
16
Cone algorithm demo
17
IR safety is subtle, but important
G. S
alam, arX
iv:0906.1833
18
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 (,)
19
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
20
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
21
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)
22
Speed matters
At LHC, multiplicities are largeA lot has been gained from improving implementations
G. S
alam, arX
iv:0906.1833
23
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
24
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
25
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
26
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…
27
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?
28
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
29
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)
30
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
31
Modeling in-medium fragmentation
From C. Salgado
32
Sudakov prescription
From C. Salgado
33
Sudakov prescription
From C. Salgado
34
Sudakov MC implementation
Used by most MC event generators (PYTHIA, HERWIG)
From C. Salgado
35
Full MC event
From C. Salgado
36
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
37
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
38
Extra slides
39
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
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