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Jet Quenching and Jet FindingMarco van Leeuwen, UU
2
Fragmentation and parton showers
large Q2 Q ~ mH ~ QCDF
Analytical calculations: Fragmentation Function D(z, ) z=ph/EjetOnly longitudinal dynamics
High-energy
parton(from hard scattering)
Hadrons
MC event generatorsimplement ‘parton showers’
Longitudinal and transverse dynamics
3
Jet Quenching
1) How is does the medium modify parton fragmentation?• Energy-loss: reduced energy of leading hadron – enhancement of yield at
low pT?• Broadening of shower?• Path-length dependence• Quark-gluon differences• Final stage of fragmentation
outside medium?
2) What does this tell us about the medium ?• Density• Nature of scattering centers? (elastic vs radiative; mass of scatt. centers)• Time-evolution?
High-energy
parton(from hard scattering)
Hadrons
4
Medium-induced radition
If < f, multiple scatterings add coherently
2ˆ~ LqE Smed
22
Tf k
Zapp, QM09
Lc = f,max
propagating parton
radiatedgluon
Landau-Pomeranchuk-Migdal effectFormation time important
Radiation sees length ~f at once
Energy loss depends on density: 1
2
ˆq
q
and nature of scattering centers(scattering cross section)
Transport coefficient
5
Testing volume (Ncoll) scaling in Au+Au
PHENIX
Direct spectra
Scaled by Ncoll
PHENIX, PRL 94, 232301
ppTcoll
AuAuTAA dpdNN
dpdNR
/
/
Direct in A+A scales with Ncoll
Centrality
A+A initial state is incoherent superposition of p+p for hard probes
6
0 RAA – high-pT suppression
Hard partons lose energy in the hot matter
: no interactions
Hadrons: energy loss
RAA = 1
RAA < 1
0: RAA ≈ 0.2
: RAA = 1
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Two extreme scenarios
p+p
Au+Au
pT
1/N
bin d
2 N/d
2 pT
Scenario IP(E) = (E0)
‘Energy loss’
Shifts spectrum to left
Scenario IIP(E) = a (0) + b (E)
‘Absorption’
Downward shift
(or how P(E) says it all)
P(E) encodes the full energy loss process
RAA not sensitive to energy loss distribution, details of mechanism
8
Jet reconstructionSingle, di-hadrons: focus on a few fragments of the shower No information about initial parton energy in each event
Jet finding: sum up fragments in a ‘jet cone’Main idea: recover radiated energy – determine energy of initial partonFeasibility depends on background fluctuations, angular broadening of jets
Need: tracking or Hadron Calorimeter and EMCal (0)
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Generic expectations from energy loss
• Longitudinal modification:– out-of-cone energy lost, suppression of yield, di-jet energy
imbalance– in-cone softening of fragmentation
• Transverse modification– out-of-cone increase acoplanarity kT
– in-cone broadening of jet-profile
kT~Ejet
fragmentation after energy loss?
10
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
12
Collinear safety
Note also: detector effects, such as splitting clusters in calorimeter (0 decay)
Illustration by G. S
alam
13
Infrared safety
Infrared safety also implies robustness against soft background in heavy ion collisions
Illustration by G. S
alam
14
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(
RR
ppd ijjtitij
16
kT algorithm demo
17
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,
1,1minRR
ppd ij
jtitij
2
2
RR
d ijij Cambridge-Aachen:
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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
19
Cone algorithm demo
20
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 (,)
21
IR safety is subtle, but important
G. S
alam, arX
iv:0906.1833
22
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: Pt,shared large fraction of Pt1
Jet1 Jet2
Split: Pt,shared small fraction of Pt1
f = 0.5 … 0.75
23
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
24
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)
25
Speed matters
At LHC, multiplicities are largeA lot has been gained from improving implementations
G. S
alam, arX
iv:0906.1833
26
Jet algorithm examplesC
acciari, Salam
, Soyez, arX
iv:0802.1189simulated p+p event
27
Jet reco
p+p 200 GeV, pTrec ~ 21 GeV
p+p: no or little background
Cu+Cu: some background
STAR
PHENIX
28
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
29
Jet finding with background
By definition: all particles end up in a jetWith background: all - space filled with jets
Many of these jets are ‘background jets’
30
Background estimate from jets
M. Cacciari, arXiv:0706.2728
Single event: pT vs area = pT/area
Jet pT grows with area Jet energy density ~ independent of
Backgroundlevel
31
Example of pT distribution
Response over ~5 orders of magnitude
Response over range of ~40 GeV (sharply falling jet spectrum)
SIngle particle ‘jet’pT=20 GeVembedded in 8M real events
Gaussian fit to LHS:• LHS: good representation• RHS: non-Gaussian tail
• Centroid non-zero(~ ±1 GeV) contribution to jet energy scale uncertainty
32
Unfolding background fluctuations
unfolding
Pythia
Pythia smeared
Pythia unfolded
Simulation
PT distribution: ‘smearing’ of jet spectrumdue to background fluctuations
Large effect on yieldsNeed to unfold
Test unfolding with simulation – works
33
RAA at LHC
ALICE, H. Appelshauser, QM11
34
RAA at LHC
• pronounced pT dependence of RAA at LHC
sensitivity to details of the energy loss distribution
35
Jets at LHC
LHC: jet energies up to ~200 GeV in Pb+Pb from
1 ‘short’ run
Large energy asymmetry observed for central events
36
Jet RCP at LHC
Significant suppression of reconstructed jets in AAOut to large pT~250 GeV
No indication of rise vs pT like single hadrons
Significant out-of-cone radiation
ATLAS, B, Cole, QM11
37
Jet fragmentation
38
Di-jet (im)balance
CMS, arXiv:1102.1957
12
12
EEEEAJ
Jet-energy asymmetry Large asymmetry seen for central events
ATLA
S, arX
iv:1011.6182 (PR
L), QM
update
39
Di-jet (im)balance
CMS, arXiv:1102.1957
40
Di-Jet fragmentation
41
Summary
42
Extra slides
43
Four theory approaches
• Multiple-soft scattering (ASW-BDMPS)– Full interference (vacuum-medium + LPM)– Approximate scattering potential
• Opacity expansion (GLV/WHDG)– Interference terms order-by-order (first order default)– Dipole scattering potential 1/q4
• Higher Twist– Like GLV, but with fragmentation function evolution
• Hard Thermal Loop (AMY)– Most realistic medium– LPM interference fully treated– No finite-length effects (no L2 dependence)
44
Energy loss spectrum
BrickL = 2 fm, E/E = 0.2E = 10 GeV
Typical examples with fixed L
E/E> = 0.2 R8 ~ RAA = 0.2
Significant probability to lose no energy (P(0))
Broad distribution, large E-loss (several GeV, up to E/E = 1)
Theory expectation: mix of partial transmission+continuous energy loss– Can we see this in experiment?
45
Geometry
Density profile
Profile at ~ form known
Density along parton path
Longitudinal expansion dilutes medium Important effect
Space-time evolution is taken into account in modeling
46
Determining B
ass et al, PR
C79, 024901
q̂
ASW:HT:AMY:
/fmGeV2010ˆ 2q/fmGeV5.43.2ˆ 2q
/fmGeV4ˆ 2q
Large density:AMY: T ~ 400 MeVTransverse kick: qL ~ 10-20 GeV
All formalisms can match RAA, but large differences in medium density
At RHIC: E large compared to E, differential measurements difficult
After long discussions, it turns out that these differences are mostly due to uncontrolled approximations in the calculations Best guess: the truth is somewhere in-between
47