Do We UnderstandInteractions of Hard Probes With Dense Matter ?

Joint EIC & Hot QCD Workshop on

Future Prospects of QCD at High EnergyBNL - 20 July 2006

Berndt Mueller (YITP Kyoto & Duke University)

It’s all about “Matter”

What’s the Matter? Probing the Matter Understanding the Matter

General comments

A young field: ~10 years of serious theory, 5 years of data! We are still in the conceptual phase.

A rich field – for theorists and experimentalists alike: Full of well defined questions and challenges.

An exciting field – new, unanticipated phenomena are discovered at a rapid pace in theory and experiment.

Part I

What’s the Matter?

QCD phase diagram

Saturation

Baryon density

Hadronicmatter

Critical end

point ?

Nuclei

Chiral symmetryrestored

Color SC

Neutron stars

Entropy

density Coexistence region

QGPRHIC

Color charge density

EIC

Chiral symmetrybroken

CEBAF

CGC

Past and future of QCD

The first 30 years of QCD were concerned (at the perturbative scale Q2) with single parton distributions: PDF’s, FF’s, GPD’s.

The future - exploration of multi-parton (N 2) correlations. These are generally:

Higher-twist effects (suppressed by powers of Q2).

Substantial effects in perturbative Q2 range require high parton densities:

A 1, x 0, dN/dy large.

Parton correlations

med( )

Initial-final state correlations

E.g., low opacity jet quenching

qq x FF ( )

Initial state correlations

E.g., double scatteri

')

n

(

g

qq x FF x

med med

Final state correlations

E.g., heavy quark recombination

qq qq

J/

x1

x1’

x2

Part II

Probing the matter

Theoretical tools: Factorization

1 2 1 22 2

ˆ ( )( ) ( )

ˆ

h cX hNN ab c h

a babcXT T h

d d D zdx dx f x f x

dy dp dy dp z

QCD factorization:

pp0

centralN

coll = 975 94

AuAu0

Medium modifies the fragmentation

function D(z)

“Higher twist”

High-energy parton loses energy by

rescattering in dense, hot medium.q

q

“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:

2 (med) 2 2

1 /( , ) ( , ) ,p h p h p h

E E

zD z Q D z Q D Q

Important for controlled theoretical treatment in pQCD:

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

Mechanisms

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).

q

q

L

q q

g

L

qq

Radiative energy loss:

2/ TdE dx L k

Radiative energy loss

Scattering centers = color chargesq q

g

L

2 22

2T

2

ˆf

dq kq dq

dq

Density of scattering centers

Range of color forceScattering power of the QCD medium:

Higher twist formalism

2

2

22 2

122

2

med,A2 1

A

2

2

with 2 (1 )( , ) ( , )

'( / ', )

2 '

(0) ( ) ( ) ( )( , , )

( ) (0) (

Medium eff

( , , ,

ect

)

( , )

, ,)

s

Lq h q h

q qg L

q qg

Q

sq h

z

qg TL

L

q

q x p q z zD z Q D z Q

dq dzD z z q qg gqz x

q z

F y F y yT x x

x q

z x xx

f x y

d

q

y

11 1

0

Integrated gluon density in

( ) ( ) 1

the medium

1L L

Lix p y ix p ydy F y F y y e e

Eikonal formalism

quark

x

x

- 0

( ) ( ; ) ( )

( ; ) exp ( , )L

q x W x L q x

W x L i dx A x x

P

Gluon radiation: + x = 0

x

Kovner Wiedemann

Radiation probablility ~ correlation function C along forward light cone

Gluonic energy density correlation length

†

2

2 †

0 0

2 2

Tr[ ( ; ) ( ; )]( , )

1

11 ( ) ( ) ( , ) ( ) ( , )

2

1ˆ

11 ( ) exp ( )

2 4

c

xLi

i

i

i F

W x L W y LC x y

N

x y dx dx F x W x x F x W x x

x y L xF F qy L

Nonperturbative definition of q-hat

q-hat in AdS/CFT

214

cl

ˆ( ) exp ( )

e (xp )

AT TW C qL x y

S C

horizon

(3+1)-D

world0

1r

T

x

C

L

cl Area of extremal worldsheet bounded ( ) by CS C

3 34 2 3

SYM 54

3/ 4ˆ2

,cq g N T s

Liu, Rajagopal, Wiedemann, hep-ph/0605178

Dynamic medium

(1) 12 s

2

2

2

4 2

(1) 12 s4 2

2ln

2l

Static medium:

1+1 dim boost inv. expansion:

n 9

f

gs

EE C

L

dN

L

LE

Ed

CLA y

Thin medium: opacity expansion (GLV) works well for leading hadron

22 9ˆ gs

f

dNq

A dy

assumes perturbative scattering and simplified evolution of the medium

Modeling sensitivity

Surface emission of leading hadrons

2/3

2/3~ exp

~

AA part

gpart

dNE LN

E A dy

R N

I. Vitev, hep-ph/0603010

Renk & Ruppert

Details of modeling of the medium and probability distribution P(E) of energy loss are very important.

Average interaction length L is not appropriate. Value of q-hat is very sensitive to modeling details.

Energy loss at RHIC

2ˆ 5 10 GeV /fmq Data suggest large energy loss parameter:

RHIC

Eskola et al.

pT = 4.5–10 GeV

Dainese, Loizides, Paic

Present calculations use simplified geometry and evolution models.

q-hat at RHIC

Pion gas

QGP

Cold nuclear matter

sQGP? ??

RHIC dataCaveat:

Details of medium evolution are important for quantitative extraction of q-hat from data!

A. Majumder – HT formalism with realistic evolution 2ˆ 2 3 GeV /fmq

The QGP is a “windy” place

Longitudinally and transversely flowing medium distorts jet cone

Along axis Off axis

T. Renk, J. Ruppert, PRC 72 (2005) 044901

Flat or rising RAA ?

Vitev et al (GLV)

LHC

Armesto et al (ASW)

Extrapolations to LHC energy vary widely due to modeling differences:

Charm energy loss

q_hat = 14 GeV2/fm

q_hat = 4 GeV2/fm

q_hat = 0 GeV2/fm

dNg/dy = 1000

Very surprising, b/c radiative energy loss of heavy quarks should be suppressed

Reconsider collisional energy loss mechanism (Mustafa & Thoma)

From “non-photonic” electrons:

S. Wicks et al nucl-th/0512076

Reaction plane correlations

Quenching effect in non-central collisions depends on direction of jet relative to the collision plane:

Allows for limited (!) test of L dependence!

LE

Back-to-back leading hadrons are quadratically suppressed!

Di-jet correlations

8 < pT(trig) < 15 GeV/c

Away-side jet

T. Renk

J. Ruppert

trigger

Photon tagged jets

“Golden” channel: q + g q + . Photon tags pT (and flavor - u/d quark!) of scattered parton.

Can be used to perform jet tomography (RAA does not work)

Important baseline and calibration for (opposite side) di-hadron tomography.

T. Renk, hep-ph/0607166

RAA does not discriminate ? -jet discriminates models

Medium-pT photons

Turbide, Rapp, Gale PRC 69 014903 (2004)0 = 0.33 fm/c, T = 370 MeV

Hard Probes 2006, June 15, 2006 – G. David, BNL

R.J. Fries, BM, D.K. Srivastava, PRL 90 (2003) 132301

2

2

s qed u s

dt s s u

gq

Jet induced contribution

Part III

Understanding the Matter

Where does the “lost” energy go?

p+p Au+Au

Lost energy of away-side jet is redistributed to rather large angles!

Trigger jetAway-side jet

Angular correlations

STAR Preliminary

PHENIX

2.5 < pT,trigger < 4.0 GeV1.0 < pT,assoc < 2.5 GeV

Backward peak of correlated hadrons shifts sideways when pT window of associated hadrons is lowered!

Deflection of primary backward parton – or extended shower of secondary particles associated with quenched backward parton?

Conical Flow vs Deflected Jets

Mediumaway

near

deflected jetsaway

near

Medium

mach coneJ. Ulery, Hard Probes 2006

STAR Data

* 0180

* 00.0

0110

Cent=0-5%

*

2

Theorists’ concepts

(Colorless or colorful) sonic shockwave:H. Stöcker, Nucl. Phys. A 750:121-147 (2005),J. Casalderrey-Solana & E. Shuryak, hep-ph/0411315,J. Ruppert & B.M., Phys. Lett. B 618:123-130 (2005),T. Renk & J. Ruppert, hep-ph/0509036

Localized heating of medium:A. Chaudhouri, U. Heinz, nucl-th/0503028

Large Angle Gluon Emission:Ivan Vitev, Phys.Lett.B630:78-84,2005Cherenkov (-like) radiation:A. Majumder & X. N. Wang, nucl-th/0507062,V. Koch et. al., nuclt-th/0507063,I. Dremin, hep-ph/0507167

Trigger jet

Trigger jet

Trigger jet

Collective QGP modes

Transverse modes

Signal: Cherenkov rings

“Colored” sound ?

Longitudinal (sound) modes

Normal sound

Signal: Mach cones

Mach cone phenomenology

Trigger jet

Away side jet

Heating

Sound wave

Fraction f of isentropic energy deposition into sound mode

Fraction (1-f) of dissipative energy deposition into heat – requires viscous, turbulent flow behind leading parton.

Thermal spectrum

Spectrum of sonic matter

Casalderrey et al., hep-ph/0602183

Dihadron correlations

Two-point velocity correlations among 1-2 GeV/c hadrons

away-side same-side

Parton correlations naturally translate into hadron correlations. Parton correlations likely to exist in the quasithermal regime,

created as the result of jet-medium interactions.

An explanation for compatibility dihadron correclations with recombination?

Fries, Bass, BM PRL 94, 122301 (2005)

Mach cone phenomenology II

Dijet rapidity correlation Trigger vertex distribution

Rapidity cut effects Flow effects on correlation

Renk - Ruppert, hep-ph/0605330

Renk, nucl-th/0607035

Wakes in the QGP

Mach cone requires collective mode with (k) < k.

Question: Is there a colored mode in this kinematic regime?

Or – can color field couple “superefficiently” to sound mode?

J. Ruppert and B. Müller, PLB 618 (2005) 123 Angular distribution depends

on energy fraction in collective mode and propagation velocity

Mach cone in AdS/CFT

2

2 2

2 2 2 2

22 2

3 v 1 v cos( )

2 1 3v cos

3v cos 2 v 1 3cos( )

2 1 3v cos

E

iQ k

k

O k

J.J. Friess et al. hep-th/0607022

N = 4 SYM

1

2 22 v

tan

c

dpg N T

k k

dt

Mach angle

The AdS5/CFT wake

Subsonic

Supersonic

Angular distributions for v = 0.95 and different k.

Summary

Jets are rich and discriminative probes of the medium: Strong energy loss agrees semi-quantitatively with theory; Probes of a well defined transport coefficient: q-hat; Quantitative determination of q-hat requires sophisticated and realistic description of medium evolution (transport); Rigorous, nonperturbative calculation of q-hat in QCD ? Relative weight of radiative and collisional energy loss ? Dependence on primary parton flavor ? Interaction of radiated energy with medium probes dissipation mechanisms and collective QGP modes.

Jet studies at the LHC will complement and greatly extend the RHIC measurements, but a lot remains to be explored at RHIC (heavy quarks, photon-jet correl’s, di- and multi-hadron correl’s with particle ID, etc.)