Download Energy loss in a realistic geometry

Energy loss in a realistic geometry
Marco van Leeuwen,
Marta Verweij,
Utrecht University
Soft QCD matter and hard probes
Heavy-ion collisions produce
‘quasi-thermal’ QCD matter
Dominated by soft partons
p ~ T ~ 100-300 MeV
Hard-scatterings produce ‘quasi-free’ partons
 Initial-state production known from pQCD
 Probe medium through energy loss
Use the strength of pQCD to explore QCD matter
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 Problem
Gluon(s)
w
kT
Compare energy-loss in a well-defined model system:
Fixed-length L (2, 5 fm)
Density T, q
Quark, E = 10, 20 GeV
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Energy loss models

Multiple soft scattering approximation ASW-MS
Phys.Rev.D68 014008

Opacity expansions (OE)

ASW-SH

(D)GLV
Nucl.Phys.A784 426
AMY, HT only in brick part
(discussed at JET symposium)
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Some (overly) simple arguments
p0 spectra
Nuclear modification factor
PHENIX, PRD 76, 051106, arXiv:0801.4020
This is a cartoon!
Hadronic, not partonic energy loss
No quark-gluon difference
Energy loss not probabilistic P(DE)
Ball-park numbers: DE/E ≈ 0.2, or DE ≈ 2 GeV
for central collisions at RHIC
Note: slope of ‘input’ spectrum changes with pT: use experimental reach to exploit this
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Energy loss distributions
‘Typical for RHIC’
Not a narrow distribution:
 Significant probability for DE ~ E
 Conceptually/theoretically difficult
ASW: Armesto, Salgado, Wiedemann
WHDG: Wicks, Horowitz, Dordjevic, Gyulassy
TECHQM ‘brick problem’
L = 2 fm, DE/E = 0.2
E = 10 GeV
Significant probability
to lose no energy P(0) = 0.5 – 0.6
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RAA with DE/E= 0.2
Quarks only
Spread in DE reduces suppression
(RAA~0.6 instead of 0.2)
〈DE/E〉not very relevant for RAA at RHIC
Large impact of P(0); broad distribution
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Rn to summarize E-loss
1
Rn   dx (1  x) n P( x)
0
n: power law index
n ~ 8 at RHIC
 R8 ~ RAA
(Brick report uses R7,
numerical differences small)
Use Rn to characterise P(DE)
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Suppression vs q̂
Gluon gas Nf = 0
For all models:
TECHQM
preliminary
Use temperature T to set all inputs
R7 = 0 . 2 5
L = 2 fm
qha t ( Ge V^ 2 / f m )
BD M PS
WHDG rad
ASW - SH
23.1
17.8
8.4
AM Y
2.7
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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 the
same suppression factor
R7
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
TECHQM
preliminary
Suppression factor R7
dominated by:

ASW-MS: partons w/o energy loss

OEs: p0 and soft gluon radiation
Continuous part of energy loss distribution more relevant for OE than MS
Can we measure this?
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Geometry
Density profile
Space-time evolution
Density along parton path
Wounded Nucleon Scaling
with optical Glauber
Longitudinal expansion 1/t
dilutes medium
 Important effect
Formation time: t0 = 0.6 fm
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Effective medium parameters
PQM:
ASW-MS: wc, R
GLV, ASW-OE:
GLV, ASW-OE
Generalisation m, l:
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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

Now: Partons in all directions from all positions

Medium characterized by wc and L
ASW-MS
DGLV
Different treatment of large angle radiation cut-off: qperp<E
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Medium as seen by parton

Medium characterized by typical gluon energy wc and path
length L
Radially inward
from surface
Radially
outward
from
surface
ASW-MS
DGLV
Radially outward
from intermediate R
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Medium as seen by parton
ASW-MS
DGLV
R7
isolines
There is no single ‘equivalent brick’ that captures the full geometry
Some partons see very opaque medium (R7 < 0.05)
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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
Single hadron
Trigger
Associate
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Surface bias I
DE < E: Surviving partons
22%
surviving
partons
ASW-MS
48%
surviving
partons
WHDG rad
OE more surviving partons → more fractional energy loss
OE probe deeper into medium
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Surface bias II: Ltrig vs Lassoc
Leff [fm]
Leff [fm]

For RAA and IAA different mean path length.

Pt Trigger > Pt Assoc

Triggers bias towards smaller L

Associates bias towards longer L
Leff [fm]
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RAA vs IAA: Trigger bias
IAA: conditional yield
Need trigger hadron
with pT in range  DE < E
IAA selects harder
parton spectrum
Parton spectra resulting in hadrons with
8<pthadron<15 GeV for without (vacuum)
and with (ASW-MS/WHDG) energy loss.
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RAA and IAA at RHIC


Models fitted to RAA using
modified c2 analysis
1s uncertainty band
indicated
q0 for multiple-soft approx 4x opacity expansion (T0 factor 1.5)
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Brick vs full geometry
Brick:
Full geometry
Factor between MS and OE
larger in full geom than brick
OE give larger suppression at large L
NB: 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
Using medium density from RHIC
50 < pt,Trig < 70 GeV
RAA increases with pT at LHC
larger dynamic range
DE/E decreases with pT
IAA: decrease with pT,assoc
Slopes differ between models
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RAA and IAA at LHC
Density 2x RHIC
50 < pt,Trig < 70 GeV
Reduced pT dependence
Slope similar for different models
IAA < RAA
Some pT dependence?
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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(DE | 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? g-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 Factor
in a brick

Hadron spectrum if each parton loses energy:
pt' = (1- ) pt
Weighted average energy loss:
For RHIC: n=7

R7 approximation for RAA.
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Multi gluon spectrum



Nmax,gluon = (2*Ngluon+1) Iterations
Ngluon follows Poisson
distribution –
model assumption
Normalize to get a
probability distribution.
Poisson convolution of
single gluon to multi
gluon spectrum
1
2
3 4
5 6
7 = Nmax,gluon
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Geometry of HI collision

Woods-Saxon profile

Wounded Nucleon Scaling with optical Glauber

Medium formation time: t0 = 0.6 fm

Longitudinal Bjorken Expansion 1/t

Freeze out temperature: 150 MeV
Temperature profile
dN
dN
=
°P ΔE °D  pt,hadr / pt,parton 
dpt,hadr dpt,parton
Measurement Input parton Energy loss
spectrum
geometry
Known
medium
LO pQCD
Fragmentation
Factor
Known
from e+e36
Opacity Expansion


Few hard
interactions.

Calculation of
parameters through
All parameters scale
with a power of T:
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Schematic picture of energy loss
mechanism
in hot dense matter
path length L
kT
l
Outgoing quark
xE1x)E
Radiated energy
ExE
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Model input parameters
~
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