marco van leeuwen, marta verweij, utrecht university energy loss in a realistic geometry

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

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

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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

~