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High Momentum probes Nuclear Suppression Correlations Identified particle measurements (for theory see lecture 5). Hadronization in QCD (the factorization theorem). hadrons. Parton Distribution Functions. hadrons. Hard-scattering cross-section. leading particle. Fragmentation Function.

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High Momentum probes

Nuclear Suppression


Identified particle measurements

(for theory see lecture 5)

Hadronization in qcd the factorization theorem
Hadronization in QCD (the factorization theorem)


Parton Distribution Functions


Hard-scattering cross-section

leading particle

Fragmentation Function

High pT (> 2.0 GeV/c) hadron production in pp collisions:


Jet: A localized collection of hadrons which come from a fragmenting parton



Parton Distribution Functions

Hard-scattering cross-section

Fragmentation Function



“Collinear factorization”

Jet quenching parton energy loss

High-energy parton loses energy by

rescattering in dense, hot medium.



“Jet quenching” = parton energy loss

Described in QCD as medium effect on parton fragmentation:

Medium modifies perturbative fragmentation before final hadronization in vacuo. Roughly equivalent to an effective shift in z:

Important for controlled theoretical treatment in pQCD:

Medium effect on fragmentation process must be in perturbative q2 domain.

Induced gluon radiation
Induced Gluon Radiation

Modification according to Gyulassy et al. (nucl-th/0302077) attributable to radiative rather than collisional energy loss

Induced Gluon Radiation

  • ~collinear gluons in cone

  • “Softened” fragmentation

R aa and high pt suppression
RAA and high-pT suppression

STAR, nucl-ex/0305015

pQCD + Shadowing + Cronin



pQCD + Shadowing + Cronin + Energy Loss

Deduced initial gluon density at t0 = 0.2 fm/c dNglue/dy ≈ 800-1200

e≈ 15 GeV/fm3, eloss = 15*cold nuclear matter (compared to HERMES eA)(e.g. X.N. Wang nucl-th/0307036)

Energy dependence of r aa
Energy dependence of RAA

p 0


RAA at 4 GeV: smooth evolution with √sNN

Agrees with energy loss models

Two possible mechanisms of radiative e loss plus collisional e loss








Two possible mechanisms of radiative e-loss plus collisional e-loss

High energy limit: energy loss by gluon radiation. Two limits:

(a) Thin medium: virtuality q2 controlled by initial hard scattering (LQS, GLV)

(b) Thick medium: virtuality q2 controlled by rescattering in medium (BDMPS)

Trigger on leading hadron (e.g. in RAA) favors case (a).

Low to medium jet energies: Collisional energy loss is competitive!

Especially when the parent parton is a heavy quark (c or b).

Radiative energy loss in qcd

Baier, Schiff and Zakharov, AnnRevNuclPartSci 50, 37 (2000)

Radiative energy loss in QCD

BDMPS approximation: multiple soft collisions in a medium of static color charges

Transport coefficient:

Medium-induced gluon radiation


Total medium-induced energy loss:

DE independent of parton energy (finite kinematics DE~log(E))

DE  L2 due to interference effects (expanding medium DE~L)

What does qhat measure

~RHIC data




R. Baier, Nucl Phys A715, 209c

What does qhat measure?

  • Equilibrated gluon gas:

    • number density ~T3

    • energy density e~T4

qhat+modelling  energy density

Model uncertainties

  • pQCD result: c~2 (aS? quark dof? …)

  • sQGP (multiplicities+hydro): c~10

Q hat at rhic

RHIC data




Pion gas

Cold nuclear matter

q-hat at RHIC

Bdmps asw vs glv

Salgado and Wiedemann PRD68 (2003) 014008

Medium-induced radiation spectrum



Baier, Dokshitzer, Mueller, Peigne, Schiff, Armesto, Salgado, Wiedemann, Gyulassy, Levai, Vitev


Rough correspondence:

(Wiedemann, HP2006)

 30-50 x cold matter density

What do we learn from r aa
What do we learn from RAA?

GLV formalism

BDMPS formalism

~15 GeV

Wicks et al, nucl-th/0512076v2

Renk, Eskola, hep-ph/0610059

DE=15 GeV

Energy loss distributions very different for BDMPS and GLV formalisms

But RAA similar!

Need more differential probes

R aa for p 0 medium density i
RAA for p0: medium density I

I. Vitev

C. Loizides


W. Horowitz

Use RAA to extract medium density:

I. Vitev: 1000 < dNg/dy < 2000

W. Horowitz: 600 < dNg/dy < 1600

C. Loizides: 6 < < 24 GeV2/fm

Statistical analysis to make optimal use of data

Caveat: RAA folds geometry, energy loss and fragmentation

Application to heavy ion collisions initial results

Binary collision scaling

p+p reference

Application to Heavy Ion Collisions: Initial Results

Strong suppression in Au+Au collisions, no suppresion in d+Au:

Effect is due to interactions between the probe and the medium

Established use as a probe of the density of the medium

Conclusion (at the time): medium is dense (50-100x nuclear matter density)

PHENIX: Phys. Rev. Lett. 91 (2003) 072301

STAR: Phys. Rev. Lett. 91 (2003) 072304

PHOBOS: Phys. Rev. Lett. 91 (2003) 072302

BRAHMS: Phys. Rev. Lett. 91 (2003) 072303

The limitations of r aa fragility

Central RAA Data

Increasing density

The Limitations of RAA: “Fragility”

K.J. Eskola, H. Honkanken, C.A. Salgado, U.A. Wiedemann, Nucl. Phys. A747 (2005) 511

Surface bias leads effectively to saturation of RAA with density

Challenge: Increase sensitivity to the density of the medium

A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38(2005) 461

What can we learn about energy loss

PHENIX p0 Spectrum

What can we learn about Energy Loss?

Fractional effective energy loss: Sloss(MJT)

“Effective” because of surface bias when analyzing single particle spectra

PHENIX, nucl-ex/0611007

Renk and Eskola, hep-ph/0610059

8 < pT < 15 GeV/c

Calibrated interaction grey probes
Calibrated Interaction? Grey Probes

Wicks et al, nucl-ex/0512076

  • Problem: interaction with the medium so strong that information lost: “Black”

  • Significant differences between predicted RAA, depending on the probe

  • Experimental possibility: recover sensitivity to the properties of the medium by varying the probe

Interpreting correlations
Interpreting Correlations

T. Renk, nucl-ex/0602045

Geometric biases:Hadrons: surface

Di-hadrons: tangential, but depending on Eloss can probe deeply

Charm-hadron, and especially Beauty-hadron(B): depends on Eloss

Note: b and c produced in pairs, B and C decay into multiple hadrons

Gamma-hadrons: Precise kinematics, back to surface

Beyond reaction of probe to medium, also reaction of medium to probe

Di jets through hadron hadron correlations

Escaping Jet

“Near Side”

Lost Jet

“Far Side”

pedestal and flow subtracted

Di-Jets through Hadron-Hadron Correlations

“Disappearance of away-side jet” in central Au+Au collisions

4 < pT,trig< 6 GeV/c, 2< pT,assoc< pT,trig


STAR, PRL 90 (2003) 082302

IAA (Jet-correlated Yield in AA) / (Jet-correlated Yield in pp)

Evolution of jet structure

pedestal and flow subtracted

Evolution of Jet Structure

M. Horner, QM 2006

At higher trigger pT (6 < pT,trig < 10 GeV/c), away-side yield varies with pT,assoc

4 < pT,trig< 6 GeV/c, 2 < pT,assoc< pT,trig

For lower pT,assoc (1.3 < pT,assoc <1.8 GeV/c), away-side correlation has non-gaussian shape  becomes doubly-peaked for lower pT,trig

Reappearance of away side jet
“Reappearance of away-side jet”

With increasing trigger pT, away-side jet correlation reappears

STAR, Phys. Rev. Lett. 97 (2006) 162301

4 < pT,trig< 6 GeV/c, 2< pT,assoc< pT,trig

Dijets from dihadrons
Dijets from dihadrons

8 < pT(trig) < 15 GeV/c

pT(assoc)>6 GeV

STAR PRL 97 (2006) 162301


Au+Au 20-40%

Au+Au 0-5%

1/Ntrig dN/d(Df)

  • NOT background subtracted: no ambiguities from background model

  • At high trigger pT, high associated pT:

    • clear jet-like peaks seen on near and away side in central Au+Au

Surface bias of di jets
Surface Bias of Di-Jets?

STAR, Phys. Rev. Lett. 97 (2006) 162301

8 < pT,trig< 15 GeV/c

Renk and Eskola, hep-ph/0610059

8 < pT,trig< 15 , 4< pT,assoc< 6 GeV/c

Comparison of i aa to r aa
Comparison of IAA to RAA

D. Magestro, QM 2005

8 < pT(trig) < 15 GeV/c

 = Near-side IAA

 = Away-side IAA

IAA = Yield(0-5% Au+Au) Yield(d+Au)

In the di-jets where trigger pT is 8-15 GeV/c, the suppression is same as for single particles as a function of pT

Modification of clean signals
Modification of Clean Signals

Away-side yield strongly suppressed

(almost) to level of RAA

No dependence on zT in measured range

No modification in shape in transverse or longitudinal direction

The jets you can see cleanly are also in some sense the least modified

STAR PRL 97 (2006) 162301

Near side yields vs z t
Near-side Yields vs. zT

After subracting the Ridge

M. Horner, QM 2006

Away side yields vs z t
Away-side Yields vs. zT

M. Horner, QM 2006

Away side suppression as a function of p t trig
Away-side suppression as a function of pT,trig

Away-side suppression reaches a value of 0.2 for trigger pT > 4 GeV/c, similar to single-particle suppression

M. Horner, QM 2006

Away-side IAA

IAA (Jet-correlated Yield in AA) / (Jet-correlated Yield in pp)

Where does the energy go


STAR preliminary





pT (GeV/c)


Where does the energy go?

  • Lower the associated pT to search for radiated energy

  • Additional energy at low pT BUT no longer collimated into jets

    Active area: additional handles on the properties of the medium?

    Mach shocks, Cherenkov cones …

    e.g. Renk and Ruppert, Phys. Rev. C 73 (2006) 011901

PHENIX preliminary

0-12% 200 GeV Au+Au

STAR, Phys. Rev. Lett. 95 (2005) 152301

M. Horner, QM2006

Dh df correlations

d+Au, 40-100%

Au+Au, 0-5%

Dh-Df Correlations

Phys. Rev. C73 (2006) 064907

mid-central Au+Au

pt < 2 GeV

  • In Au+Au: broadening of the near-side correlation in 

  • Seen in multiple analyses

    • Number correlations at low pT

      • PRC73 (2006) 064907

    • PT correlations at low pT, for multiple energies

      • Major source of pT fluctuations

      • J. Phys. G 32, L37 (2006)

      • J. Phys. G 34, 451 (2007)

    • Number correlations at intermediate pT

      • PRC 75, 034901 (2007)

    • Number correlations with

      trigger particles up to 8 GeV/c

      • D. Magestro, HP2005

      • J. Putschke, QM2006


0.8< pt < 4 GeV

STAR PRC 75(2007) 034901

3 < pT(trig) < 6 GeV2 < pT(assoc) < pT(trig)

Near side correlation

Au+Au 20-30%

Near-side Correlation

J. Putschke, QM 2006

Au+Au 0-10%

STAR preliminary

Additional long-range correlation in Dh

the “ridge”

Coupling of high pT partons to longitudinal expansion -

Armesto et al, PRL 93 (2004)

QCD magnetic fields- Majumder et al, hep-ph/0611035

In recombination framework: Coupling of shower partons to thermal partons undergoing longitudinal expansion-

Chiu & Hwa Phys. Rev. C72:034903,2005

Radial flow + trigger bias –

S.A. Voloshin, Nucl. Phys. A749, 287 (2005)

Dh df two component ansatz
Dh-Df Two-Component Ansatz



3<pt,trigger<4 GeV

pt,assoc.>2 GeV

  • Study near-side yields

  • Study away-side correlated yields and shapes

  • Components

    • near-side jet peak

    • near-side ridge

    • v2 modulated background

Au+Au 0-10%


Strategy:Subtract  from  projection: isolate ridge-like correlation

Definition of “ridge yield”:

ridge yield := Jet+Ridge()  Jet()

Can also subtract large .

Extracting near side jet like yields

J = near-side jet-like corrl.

R = “ridge”-like corrl.








const bkg. subtracted

const bkg. subtracted



- (R)


flow (v2)






no bkg. subtraction

v2 modulated bkg. subtracted

Extracting near-side “jet-like” yields

J. Putschke, QM 2006

Au+Au 20-30%

The h ridge jet yield vs centrality

Jet+Ridge ()Jet ()





The h “Ridge” + “Jet” yield vs Centrality

Au+Au 0-10%

3<pt,trigger<4 GeV

pt,assoc.>2 GeV

Jörn Putschke, QM2006

“Jet” yield constant with Npart

Reminder from pT<2 GeV:

h elongated structure already in minbias AuAu

f elongation in p-p  to h elongation in AuAu.


STAR, PRC 73, 064907 (2006)

Jet spectrum vs ridge spectrum
“Jet” spectrum vs. “Ridge” spectrum

J. Putschke, QM 2006

STAR preliminary

STAR preliminary

STAR preliminary

“jet” slope

“ridge” slope

inclusive slope

Ridge yield
Ridge Yield

J. Putschke, QM 2006

pt,assoc. > 2 GeV

STAR preliminary

Ridge yield persists up to highest trigger pT and approximately constant yield

Particle production in jet distinctly different than in medium
Particle production in jet distinctly different than in medium



Associated particle production (B/M ratio) similar in ridge and medium

and about a factor 2-3 different than in the jet.

Ridge and medium have similar production mechanism ? Recombination ?

Extending the ridge correlations to dh 5
Extending the ridge: correlations to mediumDh=5

Trigger: 3<pTtrig<4 GeV/c, A.FTPC: 0.2<pTassoc< 2 GeV/c, A.TPC: 0.2<pTassoc< 3 GeV/c


AuAu 0-10%

AuAu 0-5%

AuAu 60-80%

STAR Preliminary

STAR Preliminary

Trigger on mid-h, associated particle high h (reverse of FMS)

Near-side correlation: consistent with zero (within large v2 errors)

Away-side correlations are very similar (when scaled)

Energy loss picture is the same for mid- and forward h?

Levente Molnar, QM2006

How to interpret shape modifications

STAR preliminary medium




mach cone


0-12% 200 GeV Au+Au



deflected jets

How to interpret shape modifications?

Hard-soft: away-side spectra approaching the bulk.

Deflected jets, Mach-cone shock waves, Cherenkov radiation, completely thermalized momentum conservation, or…?

  • M. Horner, QM2006

STAR Collaboration, PRL 95,152301 (2005)

Hard soft correlations

STAR preliminary medium




mach cone


0-12% 200 GeV Au+Au



deflected jets

Hard-soft correlations

4 < pT,trig< 6 GeV/c

Hard-soft: away-side spectra approaching the bulk.

Inclusive in top 5%?

  • Three-particle correlation – N.N. Ajitanand, J. Ulery

STAR, PRL 95,152301 (2005)

Three particle correlations

d+Au medium


0-12% Au+Au

0-12% Au+Au: jet v2=0


off-diagonal projection




Three particle correlations

  • Two Analysis Approaches:

  • Cumulant Method

    • Unambiguous evidence for true three particle correlations.

  • Two-component Jet+Flow-Modulated Background Model

    • Within a model dependent analysis, evidence for conical emission in central Au+Au collisions

pTtrig=3-4 GeV/c

pTassoc=1-2 GeV/c

C. Pruneau, QM2006

J. Ulery, HP2006 and poster, QM2006

What other handles do we have

4 < p mediumT,trig< 6 GeV/c, 2 < pT,assoc< pT,trig




STAR, Phys. Rev. Lett. 93 (2004) 252301

What other handles do we have?

Centrality, trigger and associated pT,…..

….Reaction plane

Another handle g jet

q medium


Another handle: g-jet

Wang et al., Phys.Rev.Lett. 77 (1996) 231-234

Increasing ratio of direct photons to decay photons with centrality due to hadron suppression at high pT

PHENIX, Phys. Rev. Lett. 94, 232301 (2005)

Photon-jet measurement is, in principle, sensitive to full medium

Bias to where away-side jet is close to surface?

Together with di-jet measurement for comparison

 Another differential observable

Another handle g jet1

q medium




Another handle: g-jet

Current Results from Run-4 Au+Au collisions:

T. Dietel, QM 2005

J. Jin, QM 2006

Summary medium

  • Limited information extracted from single-particle pT spectra

    • Effective fractional energy loss reaches 20% for most central collisions

    • Initial energy density ~ 15 GeV/fm3 from radiative energy loss models

  • Di-Jets (those that are observed) may have less surface bias

  • Photon-Jet Measurement will complement the di-jet for more complete probe

  • Heavy-flavor suppression not consistently described by theoretical models with light meson suppression – need elastic energy loss