Lecture II: parton energy loss at high pT

Marco van LeeuwenUtrecht University

Jyväskylä Summer School 2008

2

Hard probes of QCD matter

Use the strength of pQCD to explore QCD matter

Use ‘quasi-free’ partons from hard scatterings

to probe ‘quasi-thermal’ QCD matterInteractions between parton and medium:-Radiative energy loss-Collisional energy loss-Hadronisation: fragmentation and coalescence

Sensitive to medium density, transport properties

Calculable with pQCD

Quasi-thermal matter: dominated by soft (few 100 MeV) partons

3

Energy loss in QCD matter

radiated gluon

propagating parton

2QCD bremsstrahlung(+ LPM coherence effects)

Density of scattering centers:

Nature of scattering centers, e.g. mass: radiative vs elastic loss

Or no scattering centers, but fields synchrotron radiation?

1

2

ˆ q

2ˆ~ LqE Smed

Transport coefficient

Energy loss

Energy loss probes:

4

STARSTAR

Relativistic Heavy Ion Collider

PHENIX STAR

Au+Au sNN= 200 GeV

RHIC: variety of beams: p+p, d+Au, Au+Au, Cu+CuTwo large experiments: STAR and PHENIX

Smaller experiments: PHOBOS, BRAHMS decomissioned

Recent years: Large data samples, reach to high pT

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STAR and PHENIX at RHIC

PHENIXSTARSTAR

(PHOBOS, BRAHMS more specialised)

PHENIX

2 coverage, -1 < < 1 for tracking + (coarse) EMCal

PID by TOF, dE/dx (STAR), RICH (PHENIX)

Partial coverage 2 x 0.5, -0.35 < < 0.35Finely segmented calorimeter

+ forward muon arm

Optimised for acceptance (correlations, jet-finding)

Optimised for high-pt 0, , e, J/(EMCal, high trigger rates)

6

Hadron production in p+p and pQCD

NLO calculations: W. Vogelsang

Star, PRL 91, 172302Brahms, nucl-ex/0403005

0 and charged hadrons at RHIC in good agreement with NLO pQCD

PRL 91, 241803

Perturbative QCD ‘works’ at RHIC energies

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Nuclear geometry: Npart, Nbin, L,

b Npart: nA + nB (ex: 4 + 5 = 9 + …)Nbin: nA x nB (ex: 4 x 5 = 20 + …)

Two limits:- Complete shadowing, each nucleon only interacts once, Npart

- No shadowing, each nucleon interact with all nucleons it encounters, Nbin

Soft processes: long timescale, large tot Npart

Hard processes: short timescale, small , tot Nbin

Transverse view

Eccentricity

Path length L, mean <L>

Density profile : part or coll

22

22

xy

xy

x

y

L

8

Centrality examples

This is what you really measure... and this is what you see in a presentation

centralmid-centralperipheral

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Centrality dependence of hard processes

d/dNch

200 GeV Au+Au

Rule of thumb for A+A collisions (A>40) 40% of the hard cross section

is contained in the 10% most central collisions

Binary collisions weight towards small impact parameter

Total multiplicity: soft processes

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Direct photons: no interactions

PHENIX

Direct spectra

Scaled by Ncoll

PHENIX, PRL 94, 232301

ppTbin

AuAuTAA dpdNN

dpdNR

/

/

Direct in A+A scales with Ncoll

Centrality

A+A initial state is incoherent superposition of p+p for hard probes

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Testing Ncoll scaling II: Charm

PRL 94 (2005)

NLO prediction:m ≈ 1.3 GeV, reasonably hard scale at pT=0

Total charm cross section scales with Nbin in A+A

Scaling observed in PHENIX and STAR – scaling error in one experiment?

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0 RAA – high-pT suppression

Hard partons lose energy in the hot matter

: no interactions

Hadrons: energy loss

RAA = 1

RAA < 1

0: RAA ≈ 0.2

: RAA = 1

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Two extreme scenarios

p+p

Au+Au

pT

1/N

bin

d2 N/d

2 pT

Scenario IP(E) = (E0)

‘Energy loss’

Shifts spectrum to left

Scenario IIP(E) = a (0) + b (E)

‘Absorption’

Downward shift

(or how P(E) says it all)

P(E) encodes the full energy loss process

RAA not sensitive to details of mechanism

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Energy loss spectrum

BrickL = 2 fm, E/E = 0.2E = 10 GeV

Typical examples with fixed L

E/E> = 0.2 R8 ~ RAA = 0.2

Different theoretical approximation (ASW, WHDG) give different results – significant?

Significant probability to lose no energy (P(0))

Broad distribution, large E-loss (several GeV, up to E/E = 1)

Theory expectation: mix of partial transmission+continuous energy loss– Can we see this in experiment?

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Parton energy loss and RAA modeling

Qualitatively:

)/()( , jethadrTjetshadrT

EpDEPdEdN

dpdN

`known’ from e+e-knownpQCDxPDF

extract

Parton spectrum Fragmentation (function)Energy loss distribution

This is what we are after

Need deconvolution to extract P(E)Parton spectrum and fragmentation function are steep non-trivial relation between RAA and P(E)

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Determining the medium densityPQM (Loizides, Dainese, Paic),Multiple soft-scattering approx (Armesto, Salgado, Wiedemann)Realistic geometry

GLV (Gyulassy, Levai, Vitev), Opacity expansion (L/), Average path length

WHDG (Wicks, Horowitz, Djordjevic, Gyulassy)GLV + realistic geometry

ZOWW (Zhang, Owens, Wang, Wang) Medium-enhanced power corrections (higher twist) Hard sphere geometry

AMY (Arnold, Moore, Yaffe) Finite temperature effective field theory (Hard Thermal Loops)

For each model:

1. Vary parameter and predict RAA

2. Minimize 2 wrt data

Models have different but ~equivalent parameters:

• Transport coeff. • Gluon density dNg/dy• Typical energy loss per L: 0

• Coupling constant S

q̂

PHENIX, arXiv:0801.1665,J. Nagle WWND08

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Medium density from RAA

PQM <q> = 13.2 GeV2/fm +2.1- 3.2

^

GLV dNg/dy = 1400 +270- 150

WHDG dNg/dy = 1400 +200- 375

ZOWW 0 = 1.9 GeV/fm +0.2- 0.5

AMY s = 0.280 +0.016- 0.012

Data constrain model parameters to 10-20%

Method extracts medium density given the model/calculation Theory uncertainties need to be further evaluated

e.g. comparing different formalisms, varying geometry

But models use different medium parameters– How to compare the results?

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Some pocket formula results

Large differences between models

GLV/WHDG: dNg/dy = 1400

2

1)(

Rdy

dN g

3

0 fm4.12)fm1( 32

202.116T

T(0) = 366 MeV

PQM: (parton average) /fmGeV2.13ˆ 2q

32202.172

ˆ Tq s

T = 1016 MeV

AMY: T fixed by hydro (~400 MeV), s = 0.297

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Di hadron correlations

associated

trigger

8 < pTtrig < 15 GeV

pTassoc > 3 GeV

Use di-hadron correlations to probe the jet-structure in p+p, d+Au

Near side Away side

and Au+Au

Combinatorialbackground

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Naive picture for di-hadron measurements

PT,jet,1

PT,jet,2

Fragment distribution(fragmentation fuction)

Out-of-cone radiation:PT,jet2 < PT,jet1

jetT

hadrT

P

pz

,

,

dzdN

Ref: no ElossIn-cone radiation:PT,jet2 = pT,jet1

Softer fragmentation

Naive assumption for di-hadrons: pT,trig measures PT,jet

So, zT=pT,assoc/pT,trig measures z

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Di hadron yield suppression

No suppressionSuppression byfactor 4-5 in central Au+Au

Away-side: Suppressed by factor 4-5 large energy loss

Near side Away side

STAR PRL 95, 152301

8 < pT,trig < 15 GeV

Yield of additional particles in the jet

Yield in balancing jet, after energy loss

Near side: No modification Fragmentation outside medium?

Note: per-trigger yields can be same with energy-loss

Near sideassociated

trigger

Away side associated

trigger

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d-Au

Au-Au

Medium density from di-hadron measurement

IAA constraintDAA constraintDAA + scale uncertainty

J. Nagle, WWND2008

associated

trigger

0=1.9 GeV/fm single hadrons

Medium density fromaway-side suppression

and single hadron suppression agree

Theory: ZOWW, PRL98, 212301

Data: STAR PRL 95, 152301

8 < pT,trig < 15 GeV

zT=pT,assoc/pT,trig

(Experiment and theory updates in the works)

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Conclusion so far

• Hard probes experimentally accessible at RHIC– Luminosity still increasing, so more to come?

• Ncoll scaling seen for , total charm xsec

• Large suppression of light hadrons parton energy loss

We have a dense, strongly interacting system in Heavy Ion collisions at RHIC

But how dense? All models say: T > 300 MeV, but large spread

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Path length dependence I

Centrality

Au+Au

Cu+Cu

In-plane

Out of plane

<L>, density increase with centralityVary L and density independently by changing Au+Au Cu+Cu

Change L in single system in-plane vs out of plane

Collision geometry

2ˆ~ LqE Smed

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Path length I: centrality dependence

Modified frag: nucl-th/0701045 - H.Zhang, J.F. Owens, E. Wang, X.N. Wang

6 < pT trig < 10 GeV

Away-side suppressionRAA: inclusive suppression

B. Sahlmüller, QM08

O. Catu, QM2008

Inclusive and di-hadron suppression seem to scale with Npart

Some models expect scaling, others (PQM) do not

Comparing Cu+Cu and Au+Au

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Npart scaling?

PQM - Loizides – private comunication

Geometry (thickness, area) of central Cu+Cu similar to peripheral Au+Au

PQM: no scaling of with Npartcollq ˆ q̂

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Path length II: RAA vs LPHENIX, PRC 76, 034904

In Plane

Out of Plane

3<pT<5 GeV/c

L

RAA as function of angle with reaction plane

Suppression depends on angle, path length

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RAA L Dependence

Au+Au collisions at 200GeV

Phenomenology: RAA scales best with L

Little/no energy loss for L< 2 fm ?

0-10%

50-60%

PH

EN

IX, P

RC

76

, 03

49

04

29

Modelling azimuthal dependenceA. Majumder, PRC75, 021901

RAA

pT (GeV) pT (GeV)

RAA

RAA vs reaction plane sensitive to geometry model

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RAA vs reaction plane angle

Azimuthal modulation, path length dependence largest in ASW-BDMPS

Data prefer ASW-BDMPS

C. V

ale

, PH

EN

IX, Q

M0

9

But why? – No clear answer yet

31

Path length III: ‘surface bias’

Near side trigger, biases to small E-loss

Away-side large L

Away-side suppression IAA samples different path-length distribution than inclusives RAA

32

L scaling: elastic vs radiativeT. Renk, PRC76, 064905

RAA: input to fix density Radiative scenario fits data; elastic scenarios underestimate

suppression

Indirect measure of path-length dependence: single hadrons and di-hadrons probe different path length distributions

Confirms L2 dependence radiative loss dominates

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Summary of L-dependence

• Centrality, system size dependence as expected ( Npart)

• Angle-dependence under studymore subtle, needs work

• RAA vs IAA indicates L2 dependence radiative E-loss

2ˆ~ LqE Srad

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Heavy quark suppressionP

HE

NIX

nucl-ex/0611018, ST

AR

nucl-ex/0607012

Djordjevic, Phys. Lett. B632, 81

Armesto, Phys. Lett. B637, 362

Measured suppression of non-photonic electrons larger than

expected

Using non-photonic electrons

light

M.D

jordjevic PR

L 94

Wicks, H

orowitz et al, N

PA

784, 426

Expected energy loss

Expect: heavy quarks lose less energy due to dead-cone effect

Most pronounced for bottom

Radiative (+collisional) energy loss not dominant? E.g.: in-medium hadronisation/dissociation (van Hees, et al)

35

Light flavour reference

Armesto, Cacciari, Salgado et al.

Note again: RAA and IAA fit same density

36

Heavy Quark comparison

No minimum – Heavy Quark suppression too large for ‘normal’ medium density

37

B

DX.Y. Lin, hep-ph/0602067

e h rBe hB (1 rB )e h

D

rB eB /(eD eB )

Charm/bottom separation

Idea: use e-h angular correlations to tag semi-leptonic D vs B decay

D → e + hadrons

B peak broader due to larger mass

Extract B contribution by fitting:

38

RAA eB

AA eCAA

Nbin (eBpp eC

pp )

eBAA

NbineBpp

eBpp

(eBpp eC

pp )

eC

AA

NbineCpp

eCpp

(eBpp eC

pp )

rB RAAeb (1 rB )RAA

ec

rB eBpp /(eB

pp eCpp )

Charm/bottom separation

Combine rB and RAA to extract RAA for charm and bottom

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I: Djordjevic, Gyulassy, Vogt and Wicks, Phys. Lett. B 632 (2006) 81; dNg/dy = 1000II: Adil and Vitev, Phys. Lett. B 649 (2007) 139III: Hees, Mannarelli, Greco and Rapp, Phys. Rev. Lett. 100 (2008) 192301

pT > 5 GeV/c

RAA for c e and b eB

.Biritz Q

M09

Combined data show:electrons from bothB and D suppressed

Large suppression suggestsadditional energy loss mechanism

(resonant scattering, dissociative E-loss)

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• Use e-K invariant mass to separate charm and bottom

• Signal: unlike-sign near-side correlations

• Subtract like-sign pairs to remove background

• Use Pythia to extract D, B yields

arXiv:0903.4851 hep-ex

D/B from e-K correlations

B → e + D D → e + KD → e + K

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Charm-to-Bottom Ratio

PHENIX p+p measuments agree with pQCD (FONLL) calculation

arXiv:0903.4851 hep-ex

42

Equalibration of rare probes

• Rare probes: not chemically equilibrated in the jet spectrum.• Example 1: flavor not contained in the medium, but can be produced

off the medium (e.g. photons)

– Need enough yield to outshine other sources of Nrare.

• Example 2: flavor chemically equilibrated in the medium

– E.g. strangeness at RHIC– Coupling of jets (flavor not equilibrated) to the equilibrated medium should

drive jets towards chemical equilibrium.

L

N

NN

dt

dN

jet

excess rare,jet

rare

1

gssg e.g. %50

for RHIC GeV 10 @ %5

mediumce

jetjet

du

sw

du

sw

dug ,,

dug ,, s

R. Fries, QM09

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Equilibration process: jet conversion

W. Liu, R.J. Fries, Phys. Rev. C77 (2008) 054902 hard

parton

path length L

Quark

gluon

Flavour of leading parton changesthrough interactions with medium

44

RAA for , K and p

pT (GeV)

STAR preliminary

RAA(K) ~ 0.4 at high pT > 5.0 GeV

Consistent with jet conversion calculations

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Summary

• Large suppression of high-pT hadron production partons lose energy

• 4 different theoretical frameworks (radiative E-loss)– Can all describe single hadron suppression (and often di-

hadron suppression)– T = 300 - 1000 MeV

• Path length dependence– RAA vs reaction plane not fully understood?

– RAA, IAA simultaneous fit: Strong indication of L2 dependence radiative dominates

• Heavy quarks– Expected to lose less energy (dead cone effect)

Not observed

‘A lot of ins, a lot of outs’ – The Dude

46

Extra slides

47

Transport and medium properties

Broad agreement between different observables, and with theory

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2ˆ qpQCD:

2.8 ± 0.3 GeV2/fmq̂

(Baier)

23 ± 4 GeV/fm3

T 400 MeV

Transport coefficient

Total ETViscosity

10.008.0ˆ

25.13

q

T

s

(model dependent)

= 0.3-1fm/c

~ 5 - 15 GeV/fm3 T ~ 250 - 350 MeV

(Bjorken)

From v2

(see previous talk: Steinberg)dy

dE

RV

E T

02

1

GeV580

dy

dET1.0s

(Majumder, Muller, Wang)

Lattice QCD:/s < 0.1

A quantitative understanding of hot QCD matter is emerging

(Meyer)

48

Kaons in p+p

Charged and neutral kaons are extended up to 15 GeV/c in p+p collisions.

Charged and neutral kaons are consistent.

Phys. Rev. C 75 (2007) 64901

STAR preliminary STAR preliminary

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Quark vs gluon energy loss

Energy Loss when jet pass the medium, which is characterized by

Color charge effect of parton energy loss in heavy ion collisions.

ddpdddpNd

NR

Tpp

TAB

binAB /

/12

2

QM08

arXiv: 0804.4760

STAR preliminary

Eg

Eq

~ 9/4In pQCD:

Suppression for proton >

hardparton

path length L

Quark

Quark

50