(I): Matter in Extremis

威海 2007

Xin-Nian Wang - LBNL 1

(I): Matter in Extremis

Lawrence Berkeley National Laboratory

Xin-Nian Wang

高能物理前沿暑期论坛威海 July 31 – August 7, 2006

QCD and Heavy Ion Physics

威海 2007


Phases of Matter

火水土(gas) (liquid) (solid)

Bose-Einstein condensate, fermionic condensate, superfluids, supersolids, paramagnetic,

ferromagnetic, liquid crystals, …

Quark-gluon Plasma (QGP)

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Quark-gluon Plasma (QGP)

Discovery of asymptotic freedom of QCD: Gross, Wilczek and Politzer (1973)

Weakly interacting quarks at high density and temperature

First concept of QGP in early universe, neutron star coreand change of the vacuum structure at high temperature

Lee and Wick,(1974); Collins and Perry (1975);Baym and Chin (1976)

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QCD Theory

• SU(3) gauge symmetry (non-Abelian)• Asymptotic freedom at short distance

• Confinement at long distance

• Scale invariance and anomaly• Chiral symmetry and its spontaneous

breaking• Goldstone boson and chiral condensate

• UA(1) symmetry and anomaly

22 3

2 2

4 /(11 )( )

ln( / )f

sQCD

nQ

Q

,1

1( )

2 4

fna

QCD a a af a

L i gA m F F

0

0F F

0F F

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Scale Anomaly and invariance at high T

( ) 3 0T x P

( ) ( )scaleJ x x T x

( ) ( )12s

ac l

sa aeJ x T x F F

BFF aas 4

12

2 40.015 GeVs F

Scale anomaly Break scale invariance

2s

Pc

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EOS in Lattice QCD

MeVTc 817031.7 0.3 /c GeV fm

F. Karsch ‘2001 SB limit

25%

Quasi-particle with dispersion given by HTL resummation

Blaizot, Iancu, Rebhan ‘2001

Super Yang-Mills 2 3/ 20

3 15/ 1 (3)(2 )

4 8SYM YMS S g N

Guber, Klebanov, Tseytlin ‘1998

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Confinement-deconfinement

Karsch, Laermann and Peikert 2001

( ) + V r rr

SU(3) non-Abelian gauge interaction confinement

Heavy quark potential:

J/ suppression

Q Q

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QCD Phase Diagram

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Strong coupling near Tc

( ) 312

asaF FT x P

2s

Pc

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Resonances in QGP above Tc?

J/ survives up to T=1.6Tc

Hatsuda et al

Could there be many other resonances? Shuryak & Zahed ‘04

dpAK

xdeJxJpD xpi

),(),(

)0,0(),(T),( 3

Maximum entropy method (MEM)

Hatsuda et al, 2004

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Cerenkov gluon radiation in near Tc?

Koch, Majumder & XNW’05

1cos

( )c

p

Dielectric constant

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Chiral Symmetry

Spontaneously broken:

0

Goldstone bosons (,K,)

(3) (3) (3)L RSU SU SU

F. Karsch ‘2001

MeVTc 8170

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QCD Phase Diagram

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Quark Matter in Neutron Stars

Spin-down

Spin-up

N. Glendenning ‘2000

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Heavy-ion Collisions

RHIC BNL

Au+Au up to 200 GeV/n

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Medium Response

41( ) (0) ( )

4iq x em emW q d xe A j j x A

1( )BF xqp

qxB

2

2

Dynamic System:

Hard probes: Medium response to strong interactionJet quenching

EM emission: Medium response to EM interaction

production, J/ suppression

Soft hadrons: Bulk properties of medium, collective behavior

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Energy Density in Heavy-ion Collisions

20

1energy desnity: TdE

dy R

540 GeVTdE

dy3

0( 1.0 fm/ ) 4.5 GeV/fmc

Above the critical density from lattice QCD

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Chemical equilibrium at freeze-out

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Non-central Heavy Ion Collisions

x

z

y

EZDC

ET

Centrality of the collisions

Impact Parameter (b)

EZDC

ET

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Elliptic Flow

Ideal Hydro calculation

2cos2 v

Pressure gradient anisotropy

)2cos2cos1( 210

vvNd

dNch

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A perfect fluid?

1 fm/cth

Constraint on thermalization time

Heinz ‘04

/ 0.1s

Constraint on shear viscosity:

Teaney ‘03

H2O : / 10s

0T

Ideal Hydrodynamic

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Shear viscosity

3

3 0( ) ( , )

(2 ) 2

d kT x k k f x k

k

( )P u u Pg

2( )

3ij i j j i ij k k ij k ku u u u

0

1lim ( , ), (0,0)

2i t

xy xydtdx e T t x T

Kubo relation

Energy-momentum tensor in microscopic picture

( , ) ([ ])u f x k C f Transport:

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?

Kapusta, Csernai & McLerran

Viscosity of QCD Matter

• Hadron gas at low temperature:

– Chiral perturbation theory:

• QGP at high temperature:

– Perturbative QCD2

0.022/

log(1/ )S S

s

Arnold,

Moore,Yaffe

4

4

15

16

f

s T

Prakash et al

Chen & Nakano

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OH2

Phase transition or strong coupling?

1/

4s

Small viscosity in SYM Policastro, Son & Starinets ‘02

Is it possible to measure /s from experiments?

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Quark Coalescence

n = number of constituent quarks

Rec. ModelsHwa & YangFries, Muller, BassKo et al

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Bifurcation of Spectra

Constituent quark recombination promote baryon production

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Shock Wave or Cherenkov Radiation

PHENIX

1cos

( )c

p

cos /M sc c

Velocity of sound:Index of refraction

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Orbital angular momentum

x

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Quark Polarization

4 ( )qq

pP

E E m

20 12 2 2

ˆ( )4 ( ) ( )

( )T

T s T TT T T q

d d d p x nC K x K x

d x d x d x E E m

Polarized cross section:xT

p

n

pf

Zuo-tang Liang & XNW PRL 94(2005)

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STAR Preliminary

Au+Au @ 200GeV (20-70%)

Au+Au @ 62GeV (0-80%)

Tp (GeV/c)

P

STAR Preliminary

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Summary

• Broken symmetries and their restoration at high T accompanied by phase transitions

• Intriguing properties of QGP near the critical point

• Study of soft hadrons from RHIC experiments:– High initial energy density above Tc reached– Chemical equilibrium at freeze-out– Strong collective flow indicating fluid property with low viscosity

• Partonic degree of freedom before hadronization

• Many other effects such a global quark polarization provide additional information

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威海 2007


(II): Hard Probes of Dense Matter

Lawrence Berkeley National Laboratory

Xin-Nian Wang

高能物理前沿暑期论坛威海 July 31 – August 7, 2006

QCD and Heavy Ion Physics

威海 2007


Medium Response

41( ) (0) ( )

4iq x em emW q d xe A j j x A

1( )BF xqp

qxB

2

2

Dynamic System:

Hard probes: Medium response to strong interactionJet quenching

EM emission: Medium response to EM interaction

Soft hadrons: Bulk properties of medium, collective behavior

威海 2007


Jets in heavy-ion collisions

q

q

leadingparticle

leading particle

pQCD

Bjorken’82, XNW & Gyulassy’92

威海 2007


Jet Tomography

Calibrated source

Absorptionproperties

Compute assisted

Correction

pQCDp+p, p+A

dE/dx Expansion dynamics QGP

威海 2007


LPM interference in EM Radiation

EM field carried by afast moving electronv

EM Radiation by scattering:Interference between initialand final state radiation

Initial rad.

Final rad.

22 2

2

( )

4

( )i f

fi

k k v

k

d I e

d

k

vv

k

d

v

k

(

22

1 )2

21

( ) ( )

4i ii i

i i i

i t k rk k v k k vd I e

d d ke

v k v

Landau-Pomeranchuck-Midgal interference(1 cos ) /i i fL L

2

2f

Formation time

威海 2007


Radiation in QCD: Colors matter

pi pf

ka

c

k

pi pf

pfpi

k

Gluon multiple scattering (BDMP’96)

accaS TTTTk

kR

2

)1( 2

caS TTkq

kqR ,

)(

)(22

)2(

dy

dN

y0

QCD

dy

dN

y0

QED

威海 2007


Modified Jet Fragmentation

(Guo & XNW’00)

0 ( ) ( , ),h a h aD z D z E

Suppression of leading particles (Huang, XNW’96)

威海 2007


DIS off Nucleie-

, )) (( ,( )qh

q h hHdW

d f x p q Dxd

zz

x

pypedy

xf yixpBq )()0(

2

1

2)(

/( ) 0 (0) , , ( ) 02 2 2

h hip y zhq h h q h h q

S

z dyD z e Tr p S p S y

Frag. Func.

22 )(2)(2

1),,( xpqxpqpTreqpxH q

威海 2007


Parton energy loss: A twisted story

e-

4

( , , ) () )( q h h

D

qh h twist

H x p qdW dW

dxd

f xz d

D zz

( ), () ( , ) q hq

hH x D zx px qfd

2 2 2( , ) ( , ) ( , )h h hD z Q D z Q D z Q Modified frag. function

威海 2007


Modified fragmentation function

22 2

40

( , )21( ) ( ) (virtual)

2 1 ( )

Aqg Lh s sT

q h q h AT c A

T x xzdz z dD z D C g h

z z z N q x

1 2

_2 1

1 2 2 1( ) ( )

(1

)2

( , ) (0) ( ) ( ) ( )2 2

1 1 ( ) ( )

B L T

L L

i x x p y ix p y y

ix p y ix p

L

y y

Aqg

dyT x x dy dy A F y F y y Ae

e y y ye

2 1 22

40 0

1 (1 ) ( , )

( )

Q

s

Aqg L

s Aq

TT

E zd dz

E

T x x

f x

2 ( , )2

( )

Aqg B Ts

Tc A B

T x xq

N q x

Quark energy loss

pT broadening (Guo’98)

Guo & XNW(2000)

威海 2007


Single hadron suppression

NNAB

ABAB

NR

binary

威海 2007


Centrality Dependence

威海 2007


Dihadron suppression

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Energy Loss in Cold Nuclear Matter

0.5 GeV/fmdE

dx

in Au nuclei

e-Enke Wang & XNW (2000)

威海 2007


Suppression of away-side jet

0

13.8 3.9 GeV/fmdE

dx

cold matter

0.5 GeV/fmdE

dx

0 0.2 fm/c

Initial Density about 30 times of that in a Cold Au Nucleus

威海 2007


Cherenkov radiation or shock wave

PHENIX

cos /M sc c

Velocity of sound:

1cos

( )c

p

Index of refraction

威海 2007


Degrees of freedom in sQGP?

2 223 3 BS

BSS

BS B SC

S S

Quark-gluon plasma: s quark has both B and S B & S strongly correlated, CBS=1

Hadron gas:K meson has B=0 B-S correlation is more complicated

Koch, Majumder & Randrup ‘05

Bound state QGP or hadronic gas

Ideal quarks

Gavai & Gupta ‘05

威海 2007


Other Important Developments

• Gluon Saturation in heavy nuclei at small x (parallel 4: Kharzeev; Gay Ducati)

• High baryon density physics at lower energies (parallel 4: Bravina)

• Microscopic picture of strongly interacting QGP (parallel 4: Levai)

• Elastic versus radiative energy loss

• Heavy quark energy loss & quarkonium suppression (parallel 4: Armesto)

• Hard probes at LHC (parallel 4: Lokhtin, Kodolova, Safarik)

威海 2007


Outlook: an example

• Direct -tagged events:

E~Ejet

• Measure directly Dh/a(z)• Azimuthal anisotropy

jet

X.-N.W&HuangPRC55(97)3047

威海 2007


Summary

• Heavy-ion collisions can test many properties of QCD– Deconfinement phase transition– Chiral symmetry restoration

• Current RHIC data indicate formation of strongly interacting QGP– High energy density 20 GeV/fm (t0=1 fm/c)

from jet quenching, dN/dy, radial flow– Elliptic flow early thermalization, low viscosity– Parton recombination partonic matter– J/ suppression deconfinement

• Microscopic picture of sQGP– Quasi-particle, bound states?

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Back up slides

威海 2007


UA(1) Anomaly

U(1) and UA(1) Symmetry:5, ii

AU e U e

(Classically) conserved current:0V 0 5A

Spontaneous chiral symmetry breaking 9th Goldstone boson (0)

A0 not a conserved current UA(1) is broken in

quantum theory: Chiral anomaly0

2

16f a

s a

nA F F

Alder&Jackiw

0

22 4

2

20 | ( ), (0) | 0

16f s

YM

nm i d x T FF x FF

f

Topological susceptibility2

YM

威海 2007


Partial restoration of UA(1)

Z. Huang & XNW

UA(1) restored phase could lead to false vacuum 0 Massive parity violation Kharzeev & Pisarski

威海 2007


Chiral Symmetry

Chirality of massless quarks: 5

1(1 )

2L 5

1(1 )

2R

Chiral symmetry: LiL Le

Ri

R Re

Conserved currents: 2

aaV 5 2

aaA

Spontaneously broken: 0

Goldstone bosons (,K,)(3) (3) (3)L RSU SU SU

Or alternatively: 5 / 2/ 2 , iiV AU e U e

威海 2007


Running of s(Q)

S Bethke J.Phys. G26 (2000) R27

22 2 23

4( )

(11 ) ln( / )sf QCD

Qn Q

Gross,Wilczek;Politzer (73)

SU(3) Gauge SymmetryNon-abelian interaction

Anti-screening of color

Asymptotic freedom

威海 2007


Ideal Gas Approximation

• Leading orders inperturbation (Kapusta)

• Failure of simple perturbation: (non-convergenceg g~1)(Arnold & Zhai ’94)

– Expand contributions from soft modes k~ gT in terms of g.

1/3

0

[ ]exp ( )T

Z d d d xL

)4

151(

3016 4

2

sT

g

ssfqq TTn

2

184

1

21

501

120

76

2

4224

2

432

0 2ln013.0007.0ln09.012.0095.01 g

TgggPP

威海 2007


Resummation of HTL

• Resummation of Hard Thermal Loops (Braaten & Pisarski)

– Effective theory integrating out “hard” (k~T) loops

– Resummation of HTP

)(

)(

)(

)()(

22 pp

pe

pp

pepD

HTLL

LHTLT

T

xix

xxxD

HTLL 21

1ln

21)1( 22

)1(41

1ln)1(

4222

22 xxi

x

xx

xxD

HTLT

(Weldon’94)

p

px 0

= + + …

222 )6/1( Tgn fD

Debye mass

威海 2007


Quasi-partciles & Self-consistent Resummation

• Quasi-particles with dispersion given by HTL

• Self-consistentresummation:

• Dyson’s equation

-1 -10 0 0

1 1Tr lnD Tr ln D

2 2HTL THL

)(10

1 DDD

威海 2007


Scale Anomaly

• Scale invariance (massless quarks)

• QCD interaction renormalization of g()

– Break scale invariance scale anomaly

3/ 2( ) ( )

( ) ( )

x x

A x A x

( ) ( )scaleJ x x T x

( ) ( ) 0scaleJ x T x

Classically conserved dilation current

12as

aT F F

BFF aas 4

12

2 40.015 GeVs F

Gluon condensate

0 0, PB B

Bag constant

威海 2007


QCD Phase transition

• Ideal quark and gluon gas

• Massless pion gas

• First order phase transition:

2416

30T

g

247

6120q q fn T

243

30T

3

P

( ) ( )q g c cP T P T

1/ 40.72cT B ( 0)

P

T4

T4

4B

Tc4

Tc4

,q g B ,

1

3 q gP B

威海 2007


Azimuthal anisotropy I

0 1 2(1 cos 2 cos 2 )chdNN v v

d

Single hadron

威海 2007


Flavor of Jet Quenching

Parton recombination -> Partonic degrees of freedom

威海 2007


Elliptic Flow

py

px

Coordinate space: initial asymmetry

Momentum space: final asymmetry

)2cos2cos1( 210

vvNd

dNch

2cos2 v Pressure gradient diff

Hydro-dynamics calc.

威海 2007


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(I): Matter in Extremis

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