Power Week pQCD+Energy LossIntroduction
Marco van Leeuwen,Utrecht University
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Hard probes of QCD matter
Use the strength of pQCD to explore QCD matter
Hard-scatterings produce ‘quasi-free’ partons Initial-state production known from pQCD Probe medium through energy loss
Heavy-ion collisions produce‘quasi-thermal’ QCD matter
Dominated by soft partons p ~ T ~ 100-300 MeV
Sensitive to medium density, transport properties
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Plan of the next few days
• Perturbative QCD tools:– PDFs, matrix elements, Fragmentation
• DGLAP evolution and Monte-Carlo showers• Geometry
– Woods-Saxon geometry, tools
• Energy loss models– Using Quenching weights; multiple gluon radiation
Goals: • Provide hands-on experience with all ingredients of a simple energy loss model• Increase understanding of the models, the assumptions and uncertainties• Provide a basic knowledge and experience that allows you to answer your own questions
Plus introduction to MC techniques
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Hard processes in QCD
• Hard process: scale Q >> QCD
• Hard scattering High-pT parton(photon) Q~pT
• Heavy flavour production m >> QCD
Cross section calculation can be split into • Hard part: perturbative matrix element• Soft part: parton density (PDF), fragmentation (FF)
Soft parts, PDF, FF are universal: independent of hard process
QM interference between hard and soft suppressed (by Q2/2 ‘Higher Twist’)
Factorization
c
chbbaa
abcdba
T
hpp
z
Dcdab
td
dQxfQxfdxdxK
pdyd
d
0
/222
)(ˆ
),(),( parton density matrix element FF
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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
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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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A simple model
)/()( , jethadrTjetshadrT
EpDEPdEdN
dpdN
`known’ from e+e-knownpQCDxPDF
extract
Parton spectrum Fragmentation (function)Energy loss distribution
This is where the information about the medium isP(E) combines geometry with the intrinsic process
– Unavoidable for many observables
Notes:• This formula is the simplest ansatz – Independent fragmentation
after E-loss assumed• Jet, -jet measurements ‘fix’ E, removing one of the convolutions
We will explore this model during the week; was ‘state of the art’ 3-5 years ago
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Two extreme scenarios
p+p
Au+Au
pT
1/N
bin
d2 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
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Energy loss distribution
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?
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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
(Glauber geometry)
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Some existing calculationsB
ass e
t al, P
RC
79
, 02
49
01
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
This week: looking behind the scenes for such calculations
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RAA at LHC
RAA at LHC: increase with pT first sign of sensitivity to P(E)
Nuclear modificationfactor ppTcoll
PbPbTAA dpdNN
dpdNR
/
/
By the way: RAA is also pT-dependent at RHIC?
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Comparing to theory
Many theory calculations available
Ingredients:- pQCD production- Medium density profile
tuned to RHIC data, scaled- Energy loss model
Large spread of predictions:• Will be narrowed down
by discussion/thought• Need to understand
models/calculations to sort it out
All calculations show increase with pT
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Path length dependence: RAA vs LPHENIX, PRC 76, 034904
In Plane
Out of Plane
3<pT<5 GeV/c
RAA as function of angle with reaction plane
Suppression depends on angle, path length
Relation between RAA() and v2:
)(2cos21 2 vRR AAAA
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Path length dependence and v2
PH
EN
IX P
RL
10
5, 1
42
30
1
v2 at high pT due to energy loss
Most calculations give too small effectPath length dependence stronger than expected?
Depends strongly on geometry – stay tuned
3ˆ LqE 2ˆ LqE
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Di hadron correlations
associated
trigger
8 < pTtrig < 15 GeV
pTassoc > 3 GeV
Use di-hadron correlations to probe the jet-structure in p+p, d+Au
Near side Away side
and Au+Au
Combinatorialbackground
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pT
assoc > 3 G
eVp
Tassoc >
6 GeV
d+Au Au+Au 20-40% Au+Au 0-5%
Suppression of away-side yield in Au+Au collisions: energy loss
High-pT hadron production in Au+Au dominated by (di-)jet fragmentation
Di-hadrons at high-pT: recoil suppression
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Di hadron yield suppression
Away-side: Suppressed by factor 4-5 large energy loss
Near side Away side
STAR PRL 95, 152301
8 < pT,trig < 15 GeV
Yield of additional particles in the jet
Yield in balancing jet, after energy loss
Near side: No modification Fragmentation outside medium?
Near sideassociated
trigger
Away side associated
trigger
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Path length II: ‘surface bias’
Near side trigger, biases to small E-loss
Away-side large L
Away-side suppression IAA samples longer path-lengths than inclusives RAA
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L scaling: elastic vs radiative
T. Renk, PRC76, 064905
RAA: input to fix density Radiative scenario fits data; elastic scenarios underestimate suppression
Indirect measure of path-length dependence: single hadrons and di-hadrons probe different path length distributions
Confirms L2 dependence radiative loss dominates
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Factorisation in perturbative QCD
c
chbbaa
abcdba
T
hpp
z
Dcdab
td
dQxfQxfdxdxK
pdyd
d
0
/222
)(ˆ
),(),(
Parton density functionNon-perturbative: distribution of partons in protonExtracted from fits to DIS (ep) data
Matrix elementPerturbative component
Fragmentation functionNon-perturbativeMeasured/extracted from e+e-
Factorisation: non-perturbative parts (long-distance physics) can be factored out in universal distributions (PDF, FF)
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PYTHIA (by Adam Kocoloski)
gg
gq
Subprocesses and quark vs gluon
p+pbar dominantly from gluon fragmentation?
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PRL 97, 152301 (2006)STAR Preliminary, QM08
Curves: X-N. Wang et al PRC70(2004) 031901
Baryon & meson NMF
STAR Preliminary
Comparing quark and gluon suppression
Protons less suppressed than pions, not more
No sign of large gluon energy loss
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Quark vs gluon suppression
+ renk plot
WHDG
Renk and Eskola, PRC76,027901
GLV formalism BDMPS formalism
Quark/gluon difference larger in GLV than BDMPS(because of cut-off effects E < Ejet?)
~10% baryons from quarks, so baryon/meson effect smaller than gluon/quarkAre baryon fragmentation functions under control?
Conclusion for now: some homework to do... Day 1, 3 of this week
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Equalibration of rare probes
• Rare probes: not chemically equilibrated in the jet spectrum.• Example 1: flavor not contained in the medium, but can be produced
off the medium (e.g. photons)
– Need enough yield to outshine other sources of Nrare.
• Example 2: flavor chemically equilibrated in the medium
– E.g. strangeness at RHIC– Coupling of jets (flavor not equilibrated) to the equilibrated medium should
drive jets towards chemical equilibrium.
L
N
NN
dt
dN
jet
excess rare,jet
rare
1
gssg e.g. %50
for RHIC GeV 10 @ %5
mediumce
jetjet
du
sw
du
sw
dug ,,
dug ,, s
R. Fries, QM09
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Determining the initial energy
)/()( , jethadrTjetshadrT
EpDEPdEdN
dpdN
`known’ from e+e-knownpQCDxPDF
extract
Parton spectrum Fragmentation (function)Energy loss distribution
This is where the information about the medium isP(E) combines geometry with the intrinsic process
Jet, -jet measurements ‘fix’ E, removing one of the convolutions
Allows to study energy loss as function of E(at least in principle)
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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?
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Fragmentation functions
Qualitatively: )()()( zDEPzD vacmed
Fragmentation functions sensitive to P(E)Distinguish GLV from BDMPS?
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Modified fragmentation functionsSmall-z enhancement from gluon fragments (only included in HT, not important for RAA)
Differences between formalisms large, both magnitude of supresion and z-dependence
Can we measure this directly? Jet reconstruction
A. M
ajum
der, M
vL, arXiv:100
2.2206
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Jet shapes
Energy distribution in sub-jets
Energy loss changes radial distribution of energy
Several ‘new’ observables considered Discussion: sensitivity viability … ongoing
q-P
ythia
, Eu
r Ph
ys J C 6
3, 6
79
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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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IAA(zT) =DAA (zT)
Dpp (zT)
Direct- recoil suppression
Large suppression for away-side: factor 3-5
Reasonable agreement with model predictions
8 < ET, < 16 GeV
ST
AR
, arXiv:0912
.1871
NB: gamma pT = jet pT still not very large
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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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Jets at LHC
LHC: jet energies up to ~200 GeV in Pb+Pb from
1 ‘short’ run
Large energy asymmetry observed for central events
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Jets at LHCCentrality
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12
EEEE
AJ
AT
LA
S, a
rXiv:1
01
1.6
18
2 (P
RL
)
Jet-energy asymmetry Large asymmetry seen for central events
N.B. only measures reconstructed di-jetsDoes not show ‘lost’ jets
Large effect on recoil: qualitatively consistent with RHIC jet IAA
Energy losses: tens of GeV, ~ expected from BDMPS, GLV etcbeyond kinematic reach at RHIC
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Jets at LHC
CM
S, arX
iv:1102.19
57
CMS sees similar asymmetries
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Jet RCP
R=0.2 R=0.4
RCP < 1: jet production suppressed, even at high pT
Out-of-cone radiation with R=0.4 significantNB: Jet-measurements are difficult: important experimental questions about
(trigger) bias and background fluctuations
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Jet imbalance calculationsQin, Muller, arXiv:1012.5280
Radiation plus evolution
Parton transport (brick)
Coleman-Smith, Qin, Bass, Muller, arXiv:1108.5662
MARTINI: AMY+MC
Young, S
chenke, Jeon, Gale, arX
iv:1103.5769
Several calculations describemeasured imbalance
Need to keep track of all fragments:Various approximations made
Most natural approach: parton showers(qPYTHIA, qHERWIG, JEWEL ?)
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Fragmentation and parton showers
large Q2 Q ~ mH ~ QCDF
Analytical calculations: Fragmentation Function D(z, ) z=ph/Ejet
Only longitudinal dynamics
High-energy
parton(from hard scattering)
Ha
dro
ns
MC event generatorsimplement ‘parton showers’
Longitudinal and transverse dynamics
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Getting ready
Software set-up:• ROOT• LHAPDF• Fragmentation function libraries• AliFastGlauber• AliQuenchingWeights
Day 1
See also http://www.staf.science.uu.nl/~leeuw179/powerweek/software
Day 2Day 3
Make sure that you have the code and that the test macros work
Questions/problems See me or Andreas
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Extra slides
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Seeing quarks and gluons
In high-energy collisions, observe traces of quarks, gluons (‘jets’)