The The strongly coupled strongly coupled Quark-Gluon PlasmaQuark-Gluon Plasma

Edward ShuryakEdward ShuryakDepartment of Physics and AstronomyDepartment of Physics and Astronomy

State University of New YorkState University of New York

Stony Brook NY 11794 USAStony Brook NY 11794 USA

Outline: Outline: The Little Bang, not a firework of minijetsThe Little Bang, not a firework of minijets Collective flows: radial and elliptic, Collective flows: radial and elliptic,

systematics: => systematics: => viscosityviscosity Where the energy of jets go? A ``sonic Where the energy of jets go? A ``sonic

boom” boom” What does the ``strong coupling” mean?What does the ``strong coupling” mean? Quasiparticles and Potentials at T>TcQuasiparticles and Potentials at T>Tc The phase diagram and few puzzlesThe phase diagram and few puzzles Hadronic bound states at T>TcHadronic bound states at T>Tc ColoredColored bound state and EoS bound state and EoS Strongly coupled atomsStrongly coupled atoms Strongly coupled N=4 SUSY YM and Strongly coupled N=4 SUSY YM and

AdS/CFT correspondenceAdS/CFT correspondence

The Big vs the Little The Big vs the Little BangBang Big Bang is an Big Bang is an

explosion which explosion which created our Universe. created our Universe.

Entropy is conserved.Entropy is conserved. Hubble law v=Hr forHubble law v=Hr for distant galaxies. H is distant galaxies. H is

isotropic. isotropic. ““Dark energy”Dark energy”

(cosmological (cosmological constant) seems to constant) seems to lead to accelerated lead to accelerated expansionexpansion

Little Bang is an Little Bang is an explosionexplosion

of a small fireball of a small fireball created in created in high energy high energy collisioncollision of two nuclei. of two nuclei.

Also entropy is well Also entropy is well conservedconserved

Hubble law, but Hubble law, but anisotropic (see below)anisotropic (see below)

The ``The ``vacuum vacuum pressurepressure” works against ” works against expansionexpansion

(And that is why it was (And that is why it was soso

difficult to produce it)difficult to produce it)

The vacuum vs the The vacuum vs the QGPQGP The vacuum is very The vacuum is very

complicated, dominated complicated, dominated by ``topological by ``topological objects”objects”

Vortices, monopolesVortices, monopoles and and instantonsinstantons

Among other changes it Among other changes it shifts its energy shifts its energy downdown compared to ancompared to an

““empty” vacuum, known empty” vacuum, known asas

The Bag terms, The Bag terms, p=#T^4-Bp=#T^4-BEpsilon=#T^4+BEpsilon=#T^4+B

The QGP, as any The QGP, as any plasma, screens them, plasma, screens them, and is nearly free from and is nearly free from themthem

So, when QGP is So, when QGP is produced, produced, the vacuum the vacuum tries to expel ittries to expel it

(recall here pumped out (recall here pumped out Magdeburg Magdeburg hemisphereshemispheres

By von Guericke in 1656 By von Guericke in 1656 we learned at school)we learned at school)

Magdeburg hemispheres 1656

We cannot pump the QCD vacuum out, but we can pump in something else, namely the Quark-Gluon Plasma

The map: the QCD Phase The map: the QCD Phase DiagramDiagram

T

The lines marked RHIC and SPS show the paths matter makes while cooling, in Brookhaven (USA) and CERN (Switzerland)

Chemical potential mu

Theory prediction (numerical calculation, lattice QCD, Karsch et al) the pressure as a function of T (normalized to that for free quarks and gluons)

p= #T^4 – B, the vacuum pressure

Collective flows: bits Collective flows: bits of historyof history

Early days

• L.D.Landau, 1953 => first use of hydrodynamics• L.D.Landau, S.Z.Belenky 1954 Uspechi => compression shocks => resonance gas (Delta just discovered)• G.A.Milekhin 1958 => first numerical solution for the

transverse flow

My hydro

• Hydro for e+e- as a spherical explosion PLB 34 (1971) 509

=> killed by 1976 discovery of jets in e+e-• Looking for transverse flow at ISR,

ES+Zhirov, PLB (1979) 253 =>Killed by apparent absence of flow in pp ES+Hung, prc57 (1998) 1891, radial flow

at SPS with correct freezeout surface, Tf vs centrality dependence predicted

QM99 predictions for v2(with D.Teaney)

RQMD

HIJING

Our hydro/cascade

Main findings at RHICMain findings at RHIC

Partciles are produced from matter which Partciles are produced from matter which seems to be seems to be well equilibratedwell equilibrated (by the time it is (by the time it is back in hadronic phase), N1/N2 =exp(-(M_1-back in hadronic phase), N1/N2 =exp(-(M_1-M_2)/T)M_2)/T)

Very robust Very robust collective flowscollective flows were found, were found,

indicating very strongly coupled Quark-Gluon indicating very strongly coupled Quark-Gluon Plasma Plasma (sQGP)(sQGP)

Strong quenching of large pt jetsStrong quenching of large pt jets: they do : they do not fly away freely but are mostly (up to 90%) not fly away freely but are mostly (up to 90%)

absorbed by the matter. The deposited energy absorbed by the matter. The deposited energy seemseem

To go into To go into hydrodynamical motion (conical flow) hydrodynamical motion (conical flow)

TμTμ

Tμ/2

/)(

/)(

ee

e

p

pE

E

ReminderReminderStatistical Model Statistical Model

Works well with just two parametersWorks well with just two parameters

ReminderReminderStatistical Model Statistical Model

Works well with just two parametersWorks well with just two parameters

Hadro-chemistry seems to be all done at the critical lineHadro-chemistry seems to be all done at the critical line

Hydrodynamics is simple Hydrodynamics is simple and very predictive, but and very predictive, but one has to understand few one has to understand few things,things,and so not all hydros are and so not all hydros are the samethe same EoS from Lattice QCD

Dynamic Phenomena •Expansion, Flow•Space-time evolution of thermodynamic variables

Caveat: Why and when the equilibration takes place is a tough question to answer

Local Energy-momentum

conservation:Conserved number:

Thinking About EoSThe Latent Heat and the ``softest point”

(Hung, ES 1995)

4T

T

T

4T

P

partonichadronic

LH T

P

0.2

0.33

Understanding of the freezeouts(which some hydro groups forgot)

• Chemical freezeout at Tch means that atT<Tch hadronic matter is indeed chemically

frozen => different EoS with nonzero mu’s• Kinetic freezout at fixed Tf is wrong: the

larger systems cool to LOWER Tf, one has to calculate the freezeout surface (Hung,ES) or use afterburner (RQMD) (Teaney, ES)

hydro describes both radial and elliptic hydro describes both radial and elliptic

flowsflows (from Phenix) v_2=<cos(2 phi)>(from Phenix) v_2=<cos(2 phi)>proton pion

Hydro models:Teaney(w/ & w/oRQMD)

Hirano(3d)

Kolb

Huovinen(w/& w/oQGP)

nucl-ex/0410003

V2 systematics:V2 systematics:it depends on many variablesit depends on many variables

• Particle type => y_t^2 m scalingParticle type => y_t^2 m scaling

• Collision energy s –dependenceCollision energy s –dependence

• (pseudo) rapidity (eta) y-dependence(pseudo) rapidity (eta) y-dependence

• Pt: rapid growth with saturationPt: rapid growth with saturation

• Centrality => v2/s2 scalingCentrality => v2/s2 scaling

A Hydrodynamic A Hydrodynamic Description of Heavy Ion Description of Heavy Ion Collisions at the SPS and Collisions at the SPS and RHICRHICD. Teaney,D. Teaney, J. Lauret,J. Lauret, and and E.V. ShuryakE.V. Shuryaknucl-th/0110037 v2 6 Dec nucl-th/0110037 v2 6 Dec 20012001

The dependence on The dependence on dN/dydN/dyhas a growing trend, with has a growing trend, with a saturationa saturation

More on Elliptic FlowMore on Elliptic Flow

See recent reviews, P.Huovinen (QM2002) , nucl-th/0305064; P.Kolb and U.Heinz, nucl-th/0305084; E.Shuryak, hep-ph/0312227

Hydro: P.Kolb et al.(’99)(Note: Hydro+RQMD

gives a better description.D.Teaney et al.(’01))

STAR, PRC66(’02)034904

Hydro: P.Huovinen et al.(’01)

PHENIX, PRL91(’03)182301.

The (pseudo)rapidity distribution of v2 (from PHOBOS) is not the same as that

of the particles

v2 vs eta PHOBOS

0

0.01

0.02

0.03

0.04

0.05

0.06

-6 -4 -2 0 2 4 6

eta

v2

19.6 GeV

62.4 GeV

130 GeV

200 GeV

Particle distribution over Particle distribution over (pseudo) rapidity(pseudo) rapidity

• Number of charged particles Number of charged particles per unit of pseudorapidityper unit of pseudorapidity

200 GeV Au-Au PHOBOS

0

100

200

300

400

500

600

700

-6 -4 -2 0 2 4 6

eta

dN

/d_

eta

: 0 to 6 %

: 6 to 15 %

: 15 to 25

: 25 to 35

: 35 to 45

130 GeV AU-AU PHOBOS

0

100

200

300

400

500

600

700

-6 -4 -2 0 2 4 6

eta

dN

/d_

eta

0 - 6 %

6 - 15 %

15 - 25 %

25 - 35 %

35 - 45 %

45 - 55 %

19.6 Gev Au-Au PHOBOS

0

100

200

300

400

500

600

700

-6 -4 -2 0 2 4 6

eta

dN

/d_e

ta

: 0 - 6 %

: 6 - 15

: 15 - 25

: 25 - 35

: 35 - 45

But the trend roughly follows the But the trend roughly follows the (BJ-like) hydro predictions, (BJ-like) hydro predictions, which which is is also about s-independentis is also about s-independent

v2 vs. dn_deta

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0 100 200 300 400 500 600 700 800

dN/d_eta

v2

200 GeV central

130 GeV central

19.6 GeV central

TLS LH8 EOS

TLS LH8 Hydro Only

LH16 EOS

LH_inf

Are Are the fine structure the fine structure of vof v22 hydrodynamical hydrodynamical for all secondaries? for all secondaries? (PHENIX, R.Lacey)(PHENIX, R.Lacey) Scaling from (nucl-th/0402036)Scaling from (nucl-th/0402036)

12

0

( )

( )

I wv

I w

22 0 3 01 2

20 1 1

~ 1 ..T

T k Tk kv y m

T k m k m

22 0 3 01 2

20 1 1

~ 1 ..T

T k Tk kv y m

T k m k m

2fsT m Ty k y m 2fsT m Ty k y m

we then define a “fine

structure” variable

The data scale as hydro:The data scale as hydro:2fs

T m Ty k y m 2fsT m Ty k y m

pT (GeV/c)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

v 2

0.00

0.05

0.10

0.15

0.20

0.25

pK

s 200 GeVNNAu Au

0 1 2 3

v 2

0.00

0.05

0.10

0.15

0.20

s 200 GeVNNAu Au

p

fsTy

5 < Centrality < 30 %

K

(PHENIX)

(PHENIX)

(PHENIX)

0.0 0.5 1.0 1.5 2.0 2.5

v 2

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

fsTy

Kp

Hydro

Au Au data look like hydro!

Kolb, et al

Sonic boom from Sonic boom from quenched jets quenched jets Casalderrey,ES,Teaney, hep-ph/0410067; Casalderrey,ES,Teaney, hep-ph/0410067; H.Stocker…H.Stocker… the energy deposited the energy deposited

by jets into liquid-like by jets into liquid-like strongly coupled QGP strongly coupled QGP must go into must go into conical conical shock wavesshock waves, similar , similar to the well known to the well known sonic boom from sonic boom from supersonic planes.supersonic planes.

We solved relativistic We solved relativistic hydrodynamics and hydrodynamics and got the flow picture got the flow picture

If there are start and If there are start and end points, there are end points, there are two spheres and a two spheres and a cone tangent to bothcone tangent to both

Distribution of radial Distribution of radial velocity v_r (left) and velocity v_r (left) and modulus v (right).modulus v (right).(note tsunami-like features, a (note tsunami-like features, a positive and negative parts of the positive and negative parts of the wave)wave)

Is such a sonic boom already Is such a sonic boom already observed?observed?Mean Cs=.33 time average over 3 stages=>Mean Cs=.33 time average over 3 stages=>

M.Miller, QM04

flow of matter normal to the Mach cone seems to be observed! See data from STAR,

+/-1.23=1.91,4.37

PHENIX jet pair distribution PHENIX jet pair distribution

Note: it is only projection of a cone on phi

Note 2: more

recent data from

STAR find also a minimum in

<p_t(\phi)> at

180 degr., with

a value

Consistent with background

Away <pAway <pTT> vs > vs centralitycentrality

Away core <pT> drops with centrality faster than corona <pT>.Core hadrons almost identical to medium in central collisions.A punch-though at the highest trigger?

STAR,Preliminary

away <pT> dependence on away <pT> dependence on angle angle (STAR,preliminary)(STAR,preliminary)

Preliminary

<pT> (phi) has a dip structure in central AA.

Mach shock wave?

Collective flows Collective flows =>collisional regime =>collisional regime

=> hydrodynamics=> hydrodynamicsThe main assumption:The main assumption:

l << Ll << L(the micro scale) << (the macro scale)(the micro scale) << (the macro scale)

(the mean free path) << (system size)(the mean free path) << (system size)

(relaxation time) << (evolution (relaxation time) << (evolution duration) duration)

II

In the zeroth order in l/L it is ideal hydro with a local stress tensor. Viscosity appears as a first order correction l/L, it has velocity gradients. Note that it is inversely proportional to the cross section and thus is (the oldest) strong coupling expansion

Viscosity of QGPViscosity of QGPQGP at RHIC seem to be the most idealfluid known, viscosity/entropy =.1 or so water would not flow if only a drop with 1000 molecules be made

• viscous corrections1st order correction to dist. fn.:

:Sound attenuation length

Velocity gradients

Nearly ideal hydro !? D.Teaney(’03)

Theory and Theory and phenomenology of phenomenology of sQGPsQGP

How to get 20 times How to get 20 times pQCD pQCD ??

(Zahed and ES,2003)(Zahed and ES,2003)

Quark-antiquark bound states don’t all Quark-antiquark bound states don’t all melt at Tc (charmonium from lattice melt at Tc (charmonium from lattice known prior to that…) known prior to that…)

Many more colored channelsMany more colored channels all q,g have strong rescattering qqbar all q,g have strong rescattering qqbar

mesonmesonResonance enhancementsResonance enhancements Huge cross section due to resonance Huge cross section due to resonance

enhancement causes enhancement causes elliptic flow of elliptic flow of trapped trapped Li atomsLi atoms

Scattering amplitudesScattering amplitudesfor quasiparticlesfor quasiparticlesM. Mannarelli. and R. Rapp hep-ph/05050080

Elliptic flow with ultracold trapped Li6 atoms, a=> infinity regime

The system is extremely dilute, but can be put into a hydro regime, with an elliptic flow, if it is specially tuned into a strong coupling regime via the so called Feshbach resonance

Similar mechanism was proposed (Zahed and myself) for QGP, in which a pair of quasiparticles is in resonance with their bound state at the “zero binding lines”

The coolest thing on Earth, T=10 nK or 10^(-12) eV can actually produce a

Micro-Bang ! (O’Hara et al, Duke )

Hydro works for up to Hydro works for up to 1000 oscillations1000 oscillations! ! The z mode frequency agrees with hydro The z mode frequency agrees with hydro (red star) at resonance, with universal (red star) at resonance, with universal EoS EoS Viscosity has a strong minimum thereViscosity has a strong minimum there

``Quantum viscosity”``Quantum viscosity” <= universality <= universality

• There is no need There is no need to specify to specify constituents or a constituents or a mean free path:mean free path:

• Hydro: Hydro: damping damping of sound wavesof sound waves can provide a can provide a definitiondefinition

•For cold T=0 atoms ``quantum viscosity”

• =hbar n

Should be the universal dimensionless constant•Scattering rate must be -1= const hbar/F

So what is the viscosity?

• B.Gelman, ES,I.Zahed

nucl-th/0410067

• At the minimum alpha_eta is about .5+- .3 or so =>

• This liquid is about as perfect as sQGP at RHIC!

Bound states in sQGPBound states in sQGP

The map: the QCD Phase Diagram

T

The lines marked RHIC and SPS show the paths matter makes while cooling, in Brookhaven (USA) and CERN (Switzerland)

Chemical potential mu

Theory prediction (numerical calculation, lattice QCD, Karsch et al) the pressure as a function of T (normalized to that for free quarks and gluons)

p/psb=0.8 weak or strong coupling?

How strong is strong?For a screened Coulomb potential, Schr.eqn.=>a simple

condition for a bound state

• (4/3)s (M/MDebye) > 1.68

• M(charm) is large, MDebye is about 2T

• If (Md) indeed runs and is about ½-1, it is large enough to bind charmonium till about T=3Tc (above the highest T at RHIC)

• Since q and g quasiparticles are heavy,

M about 3T, they all got bound as well !

Fitting F to screened Coulomb

• Fit from Bielefld group hep-lat/0406036

•Note that the Debye radius corresponds to

``normal” (enhanced by factor 2) coupling, while the overall strength of the potential is much larger •It becomes still larger if V is usedinstead of F, see later

Here is the binding and |psi(0)|^2

E/2MVs T/Tc

Solving for binary bound statesES+I.Zahed, hep-ph/0403127

• In QGP there is no confinement =>

• Hundreds of colored channels should have bound states as well!

The pressure puzzle is resolved!Masses, potentials and EoS from lattice are

mutually consistentM/Tc vc T/Tc and p/pSB vs T/Tc

Can we verify existence of Can we verify existence of bound states at T>Tc bound states at T>Tc experimentally?experimentally?Dileptons from sQGP:Dileptons from sQGP:

Jet quenching by Jet quenching by ``ionization”``ionization”of new bound states in QGP?of new bound states in QGP?

Calculation of the ionization Calculation of the ionization raterateES+Zahed, hep-ph/0406100ES+Zahed, hep-ph/0406100• Smaller than Smaller than radiative radiative

lossloss if if L>.5-1 fmL>.5-1 fm• Is there mostly near Is there mostly near

the zero binding lines,the zero binding lines,• Thus it is different from Thus it is different from

both both radiative radiative and and elasticelastic looses, which looses, which are simply proportional are simply proportional to densityto density

• Relates Relates to non-trivial to non-trivial energy dependence of energy dependence of jet quenchingjet quenching (smaller (smaller at 62 and near absent at 62 and near absent at SPS)at SPS)

dE/dx in GeV/fm vs T/Tc for a gluon 15,10,5 GeV. Red-elastic, black -ionization

Theoretical sQGP in Theoretical sQGP in N=4 SUSY YM and N=4 SUSY YM and AdS/CFTAdS/CFT

A gift by the A gift by the stringstring theorists: AdS/CFT theorists: AdS/CFT correspondencecorrespondence

The viscosity/entropy => 1/4Pi is very small and about as observed at RHIC (D.Son et al 2003)

QCD vs CFT: let us start with EoS

(The famous .8 explained!)

Bound states in AdS/CFT(ES and Zahed, PRD 2004)

• The quasiparticles are heavy

M_q =O(sqrt(lambda) T) >> T

• But there are light binary bound states with the mass = O(M_q/sqrt(lambda))=O(T)

Out of which the matter is made of!

A complete ``gravity dual” for RHIC from 10-d GR? (ES,Sin,Zahed, in progress)

• Black Holes + Howking rad. Is used to mimic the finite T

• How black hole is produced can be calculated from GR (tHooft … Nastase)

• Entropy production => black hole formation, falling into it is viscosity

• Moving brane => hydro expansion

ConclusionsConclusions

QGP as a “matter” in QGP as a “matter” in the usual sense, not the usual sense, not a bunch of particles, a bunch of particles, has been produced has been produced at SPS/RHICat SPS/RHIC

It shows very robust It shows very robust collective flows. The collective flows. The EoS is as expected: EoS is as expected: the vacuum pressure the vacuum pressure of about .5 GeV/fm3 of about .5 GeV/fm3 observed.observed.

QGP seems to be the QGP seems to be the most ideal fluid most ideal fluid known known

eta/hbar s=.1-.2 <<1eta/hbar s=.1-.2 <<1

All of this hints that All of this hints that QGP is a liquidQGP is a liquid, in a , in a strong coupling strong coupling regimeregime

Interesting Interesting analogies with other analogies with other strongly coupled strongly coupled systems systems

``quantum gases”``quantum gases” AdS/CFTAdS/CFT Strongly coupled Strongly coupled

e/m plasmas e/m plasmas