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

12

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

13

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

16

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.

17

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

18

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

19

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

20

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

21

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

22

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)

25

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

26

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

28

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

30

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

~