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Lecture II: parton energy loss at high pT
Marco van LeeuwenUtrecht University
Jyväskylä Summer School 2008
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Hard probes of QCD matter
Use the strength of pQCD to explore QCD matter
Use ‘quasi-free’ partons from hard scatterings
to probe ‘quasi-thermal’ QCD matterInteractions between parton and medium:-Radiative energy loss-Collisional energy loss-Hadronisation: fragmentation and coalescence
Sensitive to medium density, transport properties
Calculable with pQCD
Quasi-thermal matter: dominated by soft (few 100 MeV) partons
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Energy loss in QCD matter
radiated gluon
propagating parton
2QCD bremsstrahlung(+ LPM coherence effects)
Density of scattering centers:
Nature of scattering centers, e.g. mass: radiative vs elastic loss
Or no scattering centers, but fields synchrotron radiation?
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2
ˆ q
2ˆ~ LqE Smed
Transport coefficient
Energy loss
Energy loss probes:
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STARSTAR
Relativistic Heavy Ion Collider
PHENIX STAR
Au+Au sNN= 200 GeV
RHIC: variety of beams: p+p, d+Au, Au+Au, Cu+CuTwo large experiments: STAR and PHENIX
Smaller experiments: PHOBOS, BRAHMS decomissioned
Recent years: Large data samples, reach to high pT
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STAR and PHENIX at RHIC
PHENIXSTARSTAR
(PHOBOS, BRAHMS more specialised)
PHENIX
2 coverage, -1 < < 1 for tracking + (coarse) EMCal
PID by TOF, dE/dx (STAR), RICH (PHENIX)
Partial coverage 2 x 0.5, -0.35 < < 0.35Finely segmented calorimeter
+ forward muon arm
Optimised for acceptance (correlations, jet-finding)
Optimised for high-pt 0, , e, J/(EMCal, high trigger rates)
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Hadron production in p+p and pQCD
NLO calculations: W. Vogelsang
Star, PRL 91, 172302Brahms, nucl-ex/0403005
0 and charged hadrons at RHIC in good agreement with NLO pQCD
PRL 91, 241803
Perturbative QCD ‘works’ at RHIC energies
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Nuclear geometry: Npart, Nbin, L,
b Npart: nA + nB (ex: 4 + 5 = 9 + …)Nbin: nA x nB (ex: 4 x 5 = 20 + …)
Two limits:- Complete shadowing, each nucleon only interacts once, Npart
- No shadowing, each nucleon interact with all nucleons it encounters, Nbin
Soft processes: long timescale, large tot Npart
Hard processes: short timescale, small , tot Nbin
Transverse view
Eccentricity
Path length L, mean <L>
Density profile : part or coll
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22
xy
xy
x
y
L
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Centrality examples
This is what you really measure... and this is what you see in a presentation
centralmid-centralperipheral
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Centrality dependence of hard processes
d/dNch
200 GeV Au+Au
Rule of thumb for A+A collisions (A>40) 40% of the hard cross section
is contained in the 10% most central collisions
Binary collisions weight towards small impact parameter
Total multiplicity: soft processes
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Direct photons: no interactions
PHENIX
Direct spectra
Scaled by Ncoll
PHENIX, PRL 94, 232301
ppTbin
AuAuTAA dpdNN
dpdNR
/
/
Direct in A+A scales with Ncoll
Centrality
A+A initial state is incoherent superposition of p+p for hard probes
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Testing Ncoll scaling II: Charm
PRL 94 (2005)
NLO prediction:m ≈ 1.3 GeV, reasonably hard scale at pT=0
Total charm cross section scales with Nbin in A+A
Scaling observed in PHENIX and STAR – scaling error in one experiment?
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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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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 details of mechanism
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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
Different theoretical approximation (ASW, WHDG) give different results – significant?
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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Parton energy loss and RAA modeling
Qualitatively:
)/()( , jethadrTjetshadrT
EpDEPdEdN
dpdN
`known’ from e+e-knownpQCDxPDF
extract
Parton spectrum Fragmentation (function)Energy loss distribution
This is what we are after
Need deconvolution to extract P(E)Parton spectrum and fragmentation function are steep non-trivial relation between RAA and P(E)
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Determining the medium densityPQM (Loizides, Dainese, Paic),Multiple soft-scattering approx (Armesto, Salgado, Wiedemann)Realistic geometry
GLV (Gyulassy, Levai, Vitev), Opacity expansion (L/), Average path length
WHDG (Wicks, Horowitz, Djordjevic, Gyulassy)GLV + realistic geometry
ZOWW (Zhang, Owens, Wang, Wang) Medium-enhanced power corrections (higher twist) Hard sphere geometry
AMY (Arnold, Moore, Yaffe) Finite temperature effective field theory (Hard Thermal Loops)
For each model:
1. Vary parameter and predict RAA
2. Minimize 2 wrt data
Models have different but ~equivalent parameters:
• Transport coeff. • Gluon density dNg/dy• Typical energy loss per L: 0
• Coupling constant S
q̂
PHENIX, arXiv:0801.1665,J. Nagle WWND08
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Medium density from RAA
PQM <q> = 13.2 GeV2/fm +2.1- 3.2
^
GLV dNg/dy = 1400 +270- 150
WHDG dNg/dy = 1400 +200- 375
ZOWW 0 = 1.9 GeV/fm +0.2- 0.5
AMY s = 0.280 +0.016- 0.012
Data constrain model parameters to 10-20%
Method extracts medium density given the model/calculation Theory uncertainties need to be further evaluated
e.g. comparing different formalisms, varying geometry
But models use different medium parameters– How to compare the results?
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Some pocket formula results
Large differences between models
GLV/WHDG: dNg/dy = 1400
2
1)(
Rdy
dN g
3
0 fm4.12)fm1( 32
202.116T
T(0) = 366 MeV
PQM: (parton average) /fmGeV2.13ˆ 2q
32202.172
ˆ Tq s
T = 1016 MeV
AMY: T fixed by hydro (~400 MeV), s = 0.297
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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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Naive picture for di-hadron measurements
PT,jet,1
PT,jet,2
Fragment distribution(fragmentation fuction)
Out-of-cone radiation:PT,jet2 < PT,jet1
jetT
hadrT
P
pz
,
,
dzdN
Ref: no ElossIn-cone radiation:PT,jet2 = pT,jet1
Softer fragmentation
Naive assumption for di-hadrons: pT,trig measures PT,jet
So, zT=pT,assoc/pT,trig measures z
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Di hadron yield suppression
No suppressionSuppression byfactor 4-5 in central Au+Au
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?
Note: per-trigger yields can be same with energy-loss
Near sideassociated
trigger
Away side associated
trigger
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d-Au
Au-Au
Medium density from di-hadron measurement
IAA constraintDAA constraintDAA + scale uncertainty
J. Nagle, WWND2008
associated
trigger
0=1.9 GeV/fm single hadrons
Medium density fromaway-side suppression
and single hadron suppression agree
Theory: ZOWW, PRL98, 212301
Data: STAR PRL 95, 152301
8 < pT,trig < 15 GeV
zT=pT,assoc/pT,trig
(Experiment and theory updates in the works)
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Conclusion so far
• Hard probes experimentally accessible at RHIC– Luminosity still increasing, so more to come?
• Ncoll scaling seen for , total charm xsec
• Large suppression of light hadrons parton energy loss
We have a dense, strongly interacting system in Heavy Ion collisions at RHIC
But how dense? All models say: T > 300 MeV, but large spread
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Path length dependence I
Centrality
Au+Au
Cu+Cu
In-plane
Out of plane
<L>, density increase with centralityVary L and density independently by changing Au+Au Cu+Cu
Change L in single system in-plane vs out of plane
Collision geometry
2ˆ~ LqE Smed
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Path length I: centrality dependence
Modified frag: nucl-th/0701045 - H.Zhang, J.F. Owens, E. Wang, X.N. Wang
6 < pT trig < 10 GeV
Away-side suppressionRAA: inclusive suppression
B. Sahlmüller, QM08
O. Catu, QM2008
Inclusive and di-hadron suppression seem to scale with Npart
Some models expect scaling, others (PQM) do not
Comparing Cu+Cu and Au+Au
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Npart scaling?
PQM - Loizides – private comunication
Geometry (thickness, area) of central Cu+Cu similar to peripheral Au+Au
PQM: no scaling of with Npartcollq ˆ q̂
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Path length II: RAA vs LPHENIX, PRC 76, 034904
In Plane
Out of Plane
3<pT<5 GeV/c
L
RAA as function of angle with reaction plane
Suppression depends on angle, path length
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RAA L Dependence
Au+Au collisions at 200GeV
Phenomenology: RAA scales best with L
Little/no energy loss for L< 2 fm ?
0-10%
50-60%
PH
EN
IX, P
RC
76
, 03
49
04
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Modelling azimuthal dependenceA. Majumder, PRC75, 021901
RAA
pT (GeV) pT (GeV)
RAA
RAA vs reaction plane sensitive to geometry model
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RAA vs reaction plane angle
Azimuthal modulation, path length dependence largest in ASW-BDMPS
Data prefer ASW-BDMPS
C. V
ale
, PH
EN
IX, Q
M0
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But why? – No clear answer yet
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Path length III: ‘surface bias’
Near side trigger, biases to small E-loss
Away-side large L
Away-side suppression IAA samples different path-length distribution than inclusives RAA
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L scaling: elastic vs radiativeT. 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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Summary of L-dependence
• Centrality, system size dependence as expected ( Npart)
• Angle-dependence under studymore subtle, needs work
• RAA vs IAA indicates L2 dependence radiative E-loss
2ˆ~ LqE Srad
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Heavy quark suppressionP
HE
NIX
nucl-ex/0611018, ST
AR
nucl-ex/0607012
Djordjevic, Phys. Lett. B632, 81
Armesto, Phys. Lett. B637, 362
Measured suppression of non-photonic electrons larger than
expected
Using non-photonic electrons
light
M.D
jordjevic PR
L 94
Wicks, H
orowitz et al, N
PA
784, 426
Expected energy loss
Expect: heavy quarks lose less energy due to dead-cone effect
Most pronounced for bottom
Radiative (+collisional) energy loss not dominant? E.g.: in-medium hadronisation/dissociation (van Hees, et al)
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Light flavour reference
Armesto, Cacciari, Salgado et al.
Note again: RAA and IAA fit same density
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Heavy Quark comparison
No minimum – Heavy Quark suppression too large for ‘normal’ medium density
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B
DX.Y. Lin, hep-ph/0602067
e h rBe hB (1 rB )e h
D
rB eB /(eD eB )
Charm/bottom separation
Idea: use e-h angular correlations to tag semi-leptonic D vs B decay
D → e + hadrons
B peak broader due to larger mass
Extract B contribution by fitting:
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RAA eB
AA eCAA
Nbin (eBpp eC
pp )
eBAA
NbineBpp
eBpp
(eBpp eC
pp )
eC
AA
NbineCpp
eCpp
(eBpp eC
pp )
rB RAAeb (1 rB )RAA
ec
rB eBpp /(eB
pp eCpp )
Charm/bottom separation
Combine rB and RAA to extract RAA for charm and bottom
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I: Djordjevic, Gyulassy, Vogt and Wicks, Phys. Lett. B 632 (2006) 81; dNg/dy = 1000II: Adil and Vitev, Phys. Lett. B 649 (2007) 139III: Hees, Mannarelli, Greco and Rapp, Phys. Rev. Lett. 100 (2008) 192301
pT > 5 GeV/c
RAA for c e and b eB
.Biritz Q
M09
Combined data show:electrons from bothB and D suppressed
Large suppression suggestsadditional energy loss mechanism
(resonant scattering, dissociative E-loss)
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• Use e-K invariant mass to separate charm and bottom
• Signal: unlike-sign near-side correlations
• Subtract like-sign pairs to remove background
• Use Pythia to extract D, B yields
arXiv:0903.4851 hep-ex
D/B from e-K correlations
B → e + D D → e + KD → e + K
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Charm-to-Bottom Ratio
PHENIX p+p measuments agree with pQCD (FONLL) calculation
arXiv:0903.4851 hep-ex
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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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Equilibration process: jet conversion
W. Liu, R.J. Fries, Phys. Rev. C77 (2008) 054902 hard
parton
path length L
Quark
gluon
Flavour of leading parton changesthrough interactions with medium
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RAA for , K and p
pT (GeV)
STAR preliminary
RAA(K) ~ 0.4 at high pT > 5.0 GeV
Consistent with jet conversion calculations
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Summary
• Large suppression of high-pT hadron production partons lose energy
• 4 different theoretical frameworks (radiative E-loss)– Can all describe single hadron suppression (and often di-
hadron suppression)– T = 300 - 1000 MeV
• Path length dependence– RAA vs reaction plane not fully understood?
– RAA, IAA simultaneous fit: Strong indication of L2 dependence radiative dominates
• Heavy quarks– Expected to lose less energy (dead cone effect)
Not observed
‘A lot of ins, a lot of outs’ – The Dude
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Extra slides
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Transport and medium properties
Broad agreement between different observables, and with theory
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2ˆ qpQCD:
2.8 ± 0.3 GeV2/fmq̂
(Baier)
23 ± 4 GeV/fm3
T 400 MeV
Transport coefficient
Total ETViscosity
10.008.0ˆ
25.13
q
T
s
(model dependent)
= 0.3-1fm/c
~ 5 - 15 GeV/fm3 T ~ 250 - 350 MeV
(Bjorken)
From v2
(see previous talk: Steinberg)dy
dE
RV
E T
02
1
GeV580
dy
dET1.0s
(Majumder, Muller, Wang)
Lattice QCD:/s < 0.1
A quantitative understanding of hot QCD matter is emerging
(Meyer)
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Kaons in p+p
Charged and neutral kaons are extended up to 15 GeV/c in p+p collisions.
Charged and neutral kaons are consistent.
Phys. Rev. C 75 (2007) 64901
STAR preliminary STAR preliminary
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Quark vs gluon energy loss
Energy Loss when jet pass the medium, which is characterized by
Color charge effect of parton energy loss in heavy ion collisions.
ddpdddpNd
NR
Tpp
TAB
binAB /
/12
2
QM08
arXiv: 0804.4760
STAR preliminary
Eg
Eq
~ 9/4In pQCD:
Suppression for proton >
hardparton
path length L
Quark
Quark
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