marco van leeuwen, marta verweij, utrecht university energy loss in a realistic geometry
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Marco van Leeuwen,Marta Verweij,
Utrecht University
Energy loss in a realistic geometry
2
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
3
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
4
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
5
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)
6
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
7
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
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
9
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)
10
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
11
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
14
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
15
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]
23
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
24
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
27
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
29
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
31
Extra slides
32
Where does the log go?
33
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
34
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
35
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.
36
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
37
Opacity Expansion
Calculation of parameters through
Few hard interactions.
All parameters scale with a power of T:
38
Schematic picture of energy loss mechanismin hot dense matter
path length L
kT
Radiated energyx
Outgoing quarkxx)
39
Model input parameters
~
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