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Marco van Leeuwen,Marta Verweij,
Utrecht University
Energy loss in a realistic geometry
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Soft QCD matter and hard probes
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 talk
• Energy loss in a brick: reminder of main differences between formalisms
• How do these carry over to full geometry
• Surface bias?
• Can we exploit full geometry, different observables to constrain/test formalisms?
• Case study: RAA vs IAA
• Some results for LHC
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The Brick ProblemGluon(s)
Compare energy-loss in a well-defined model system:Fixed-length L (2, 5 fm)Density T, qQuark, E = 10, 20 GeV
kT
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Energy loss models Multiple soft scattering approximation ASW-MS
Opacity expansions (OE)
ASW-SH
(D)GLV
Phys.Rev.D68 014008
Nucl.Phys.A784 426
AMY, HT only in brick part(discussed at JET symposium)
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Some (overly) simple arguments
This is a cartoon!Hadronic, not partonic energy lossNo quark-gluon differenceEnergy loss not probabilistic P(E)
Ball-park numbers: E/E ≈ 0.2, or E ≈ 2 GeV for central collisions at RHIC
0 spectra Nuclear modification factor
PH
EN
IX, P
RD
76, 051106, arXiv:0801.4020
Note: slope of ‘input’ spectrum changes with pT: use experimental reach to exploit this
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Energy loss distributionsTECHQM ‘brick problem’L = 2 fm, E/E = 0.2E = 10 GeV
‘Typical for RHIC’
Not a narrow distribution: Significant probability for E ~ E Conceptually/theoretically difficult
Significant probability to lose no energy P(0) = 0.5 – 0.6
AS
W: A
rmesto, S
algado, Wiedem
annW
HD
G: W
icks, Horow
itz, Dordjevic, G
yulassy
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8Large impact of P(0); broad distribution
Spread in E reduces suppression (RAA~0.6 instead of 0.2)
〈 E/E 〉 not very relevant for RAA at RHIC
Quarks only
RAA with E/E= 0.2
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Rn to summarize E-loss
1
0)()1( xPxdxR n
n
n: power law indexn ~ 8 at RHIC R8 ~ RAA
Use Rn to characterise P(E)
(Brick report uses R7,
numerical differences small)
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Suppression vs
For all models:
Use temperature T to set all inputs
TECHQM preliminary
R7 = 0 .2 5
BD M PS W H D G r a d ASW - SH AM Y
23.1 17.8 8.4 2.7
qha t ( Ge V^ 2 / f m )
L = 2 f m
Gluon gas Nf = 0
q̂
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Single gluon spectrum
For all models this is the starting point
P(∆E) originates from spectrum of radiated gluons
Models tuned to thesame suppression factorR
7
Gluon spectrum different for ASW-MS and OE TECHQM
preliminary
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Energy loss probability
P(∆E) is generated by a Poisson convolution of the single gluon spectrum:
3 distinct contributions:
p0 = probability for no energy loss = e-⟨Ngluons>
p(∆E) = continuous energy loss = parton loses ∆E
∆E > E: parton is absorbed by the medium
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Outgoing quark spectrum
Outgoing quark spectrum:
xE = 1 - ∆E/E
xE = 0: Absorbed quarks
xE = 1: No energy loss
Suppression factor R7
dominated by:
ASW-MS: partons w/o energy loss
OEs: p0 and soft gluon radiation
TECHQM preliminary
Can we measure this?
Continuous part of energy loss distribution more relevant for OE than MS
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GeometryDensity profile Density along parton path
Longitudinal expansion 1/dilutes medium Important effect
Space-time evolution
Wounded Nucleon Scalingwith optical Glauber
Formation time: 0 = 0.6 fm
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Effective medium parameters
PQM:
ASW-MS: c, R
Generalisation , :
GLV, ASW-OE:
GLV, ASW-OE
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Medium as seen by parton
Path average variables which characterize the energy loss.
Exercise:
Parton is created at x0 and travels radially through the center of the
medium until it leaves the medium or freeze out has taken place.
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Medium as seen by parton
Different treatment of large angle radiation cut-off: qperp<E
Now: Partons in all directions from all positions
Medium characterized by c and L
ASW-MS DGLV
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Medium as seen by parton Medium characterized by typical gluon energy c and path
length L
Radially outward fromsurface
Radially outward from intermediate R
Radially inward from surface
ASW-MS DGLV
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Medium as seen by parton
ASW-MS DGLV
There is no single ‘equivalent brick’ that captures the full geometry
Some partons see very opaque medium (R7 < 0.05)
R7
isolines
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Why measure IAA
?
Bias associated particle towards longer path length
Probe different part of medium
Trigger to larger parton pt
Probe different energy loss probability distribution
Associate
Trigger
Single hadron
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Surface bias I
ASW-MS WHDG rad22% surviving partons
48% surviving partons
OE more surviving partons → more fractional energy loss
OE probe deeper into medium
E < E: Surviving partons
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Surface bias II: Ltrig
vs Lassoc
For RAA
and IAA
different mean path length.
Pt Trigger > P
t Assoc
Triggers bias towards smaller L
Associates bias towards longer L
Leff
[fm] Leff
[fm] Leff
[fm]
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RAA
vs IAA
: Trigger bias
Parton spectra resulting in hadrons with 8<p
thadron<15 GeV for without (vacuum)
and with (ASW-MS/WHDG) energy loss.
IAA: conditional yield
Need trigger hadron with pT in range E < E
IAA selects harder
parton spectrum
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RAA
and IAA
at RHIC
Models fitted to RAA using
modified 2 analysis
1 uncertainty band indicated
q0 for multiple-soft approx 4x opacity expansion (T0 factor 1.5)
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Brick vs full geometryBrick:
Full geometry
Factor between MS and OE larger in full geom than brick
OE give larger suppression at large LNB: large L R7 < 0.2 in full geom
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RAA
and IAA
at RHIC
RAA – fitted IAA – predicted
Measured IAA (somewhat) larger than prediction
Differences between models small; DGLV slightly higher than others
IAA < RAA due to larger path length – difference small due to trigger bias
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RAA
and IAA
at LHC
50 < pt,Trig
< 70 GeV
Using medium density from RHIC
RAA increases with pT at LHC
larger dynamic rangeE/E decreases with pT
IAA: decrease with pT,assoc
Slopes differ between models
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RAA
and IAA
at LHC
Reduced pT dependence
Slope similar for different modelsIAA < RAA
Some pT dependence?
50 < pt,Trig
< 70 GeV
Density 2x RHIC
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LHC estimates
RHIC best fits
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Conclusion
Energy loss models (OE and MS) give different suppression at same density
For R7 = 0.25, need L=5, T=300-450 MeV or L=2, T=700-1000 MeV
Full geometry:
Large paths, large suppression matter
Surface bias depends on observable, energy loss model
Measured IAA above calculated in full geometry
At LHC: pT-dependence of RAA sensitive to P(E | E)
Only if medium density not too large
RAA, IAA limited sensitivity to details of E-loss mode (P(E))Are there better observables?
Jets: broadening, or long frag? -hadron
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Extra slides
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Where does the log go?
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Single gluon spectrum
P(∆E) originates from spectrum of radiated gluons. ASW-MS and ASW-SH the same at large .
WHDG smooth cutoff depending on Eparton
.
Opacity expansions more soft gluon radiation than ASW-MS.
Ngluons,ASW-SH
~ Ngluons,WHDG
⟨⟩ASW-SH
> ⟨⟩WHDG
Ngluons,ASW-MS
< Ngluons,OE
TECHQM preliminary
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Suppression Factorin a brick
Hadron spectrum if each parton loses energy:
Weighted average energy loss:
For RHIC: n=7
R7 approximation for R
AA.
pt' = (1-) p
t
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Multi gluon spectrum
1
2
3 45 6
7 = Nmax,gluon
Poisson convolution of single gluon to multi gluon spectrum
Nmax,gluon
= (2*Ngluon
+1) Iterations
Ngluon
follows Poisson
distribution – model assumption
Normalize to get a probability distribution.
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Geometry of HI collision Woods-Saxon profile
Wounded Nucleon Scaling with optical Glauber
Medium formation time: 0 = 0.6 fm
Longitudinal Bjorken Expansion 1/ Freeze out temperature: 150 MeV
Temperature profile
Input parton spectrumKnown
LO pQCD
Fragmentation FactorKnown
from e+e-
Energy loss
geometry
medium
partont,hadrt,partont,hadrt,
pp°DΔE°PdpdN
=dpdN
/
Measurement
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Opacity Expansion
Calculation of parameters through
Few hard interactions.
All parameters scale with a power of T:
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Schematic picture of energy loss mechanismin hot dense matter
path length L
kT
Radiated energyx
Outgoing quarkxx)
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Model input parameters
~