How should we How should we probeprobeaa Strongly Coupled Strongly Coupled QGP?QGP?

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

Not to be discussed in detail• Hydro => good description for ..• sQGP seem to be the most perfect fluid known

/s= .1-.2<<1• Relation to other strongly coupled systems,

from atomic experiments to string theory To be discussed• how strong is strong? => When bound states

occure (ES+Zahed,2003)• Zero binding lines =>large cross sections =>

explains small mean free path ?• Many colored bound states => solution toseveral lattice puzzles =>high mutual concistency

of lattice data: masses, potentials, EoS

Outline cont: new ideas

• Jet quenching due to ``ionization” of new bound states(I.Zahed+ES)

• Conical flow from quenched jets (Casalderrey, ES,Teaney)

Bound states (,,) and a near-threshold bump in QGP => dileptons => quasiparticle masses and their interaction (Jorge Casalderrey +ES)

Reminder 1: EOS of QCD is such that cs^2 is not a Reminder 1: EOS of QCD is such that cs^2 is not a constconstp/e(e) = EoS along fixed np/e(e) = EoS along fixed nBB/s lines (Hung,ES,hep-ph/9709264).:/s lines (Hung,ES,hep-ph/9709264).:

<= RHIC

A gas of Relativistic pions =>

Relativisitc QGP=>

The softest point

QGP pressure is nearly balanced by the vacuum QGP pressure is nearly balanced by the vacuum pressure: p=p(QGP)-Bpressure: p=p(QGP)-B

55

Magdeburg hemispheres Magdeburg hemispheres 16561656

•We cannot pump the QCD vacuum out, but we can pump in something else, namely the Quark-Gluon Plasma –arguments from 1970’s

• QGP was looked at as a much simpler thing, to be described by pQCD. We now see it is also quite complicated matter, sQGP…

hydro describes both radial and elliptic flows (from Jacak’s talk)

proton pion

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

Hirano(3d)

Kolb

Huovinen(w/& w/oQGP)

nucl-ex/0410003

Why is v2 so sensitive to the initial time?

The maximal v2is at rather peripheral bin => a ``thin almond”.

Reminder 2: The beginning of sQGP: a

New QCD Phase Diagram, in which ``zero

binding lines” first appeared

(ES+I.Zahed hep-ph/030726, PRC)

it had one colored state, qq already

T

The lines marked RHIC and SPS show the adiabatic cooling paths

Chemical potential B

Why is hydro description so Why is hydro description so good ? =>good ? => marginal states with near zero marginal states with near zero

binding provide largebinding provide large cross sections? cross sections? (ES+Zahed,03, same)(ES+Zahed,03, same)

Well, can it work ?

Elliptic flow with ultracold trapped Li6 atoms, a=> infinity regime via the so called Feshbach resonance

The system is extremely dilute, but it still goes into a hydro regime, with an elliptic flow: cross section changes by about 10^6 or so!

Is it a good liquid? How good?

It works for cold atoms!

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

•New development: Hydro works for up to New development: Hydro works for up to 1000 oscillations1000 oscillations! ! agrees with hydro agrees with hydro (red star)(red star) at at resonance within resonance within better than a percent!better than a percent! Viscosity has a strong Viscosity has a strong minimum thereminimum there

B.Gelman, ES,I.Zahed nucl-th/0410067Quantum viscosityhbar n).3 seem to be reached at the experimental minimum.

About as perfect as sQGP!

New hydro New hydro phenomenon:phenomenon:a ``conical” flowa ``conical” flow

J.Casalderey-J.Casalderey-SolanaSolana,Edward Shuryak ,Edward Shuryak and and Derek Teaney,hep-Derek Teaney,hep-ph/04…..ph/04…..

Sonic boom from quenched jets

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

• We solved relativistic hydrodynamics and got the flow picture

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

Distribution of radial velocity v_r (left) and modulus v (right).

(note tsunami-like features, a positive and negative parts of the wave)

How to observe it?

• the direction of the flow is normal to Mach cone, defined entirely by ratio of the speed of sound to the speed of light

• Unlike the (QCD) radiation, the angle is not shrinking 1/ with increase of the momentum of the jet but is the same for all jet momenta

• At high enough pt a punch through expected, filling the cone

Is such a sonic boom already observed?

M.Miller, QM04

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

+/-1.1=2.0,4.2

PHENIX jet pair distribution (from B.Jacak)Away-side jets

have a ~2 dip at – 1.1 is a Mach peak around hard parton, for all bins but the most peripheral one

Note: it is only projection, shoud be seen better in d

So, one can determine the speed of sound (=>EoS), but at what time?

• At kinetic freezeout, =12-15 fm/c, and that is why we used cs

2=.16-.2 for resonance gas

• That was because we considered central collisions (to awoid complications with elliptic flow subtraction) in which a jet has to go about a diameter of Au

• One can use semi-peripheral and play withJet orientation relative to collision plane and

change timing

Back to jets: Back to jets: dE/dx of dE/dx of two typestwo types Radiative eloss is largeRadiative eloss is large but but

energy is going into gluons which energy is going into gluons which are still moving relativistically are still moving relativistically with v=cwith v=c

Heating and ionization lossesHeating and ionization losses: this : this energy goes into matter. energy goes into matter.

The The second type lossessecond type losses should be should be equal to equal to hydro drag forcehydro drag force calculated for the conical flowcalculated for the conical flow

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

Calculation of the ionization rateES+Zahed, hep-ph/0406100

• Smaller than radiative loss if L>.5-1 fm

• Is there mostly near the zero binding lines,

• Thus it is different from both radiative and elastic looses, which are simply proportional to density

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

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

Lattice puzzles and Lattice puzzles and ``new spectroscopy”``new spectroscopy”

Two Two lattice puzzleslattice puzzles

Matsui-Satz: l Matsui-Satz: l J/J/,,cc dissolves in QGP dissolves in QGP (thus it (thus it

was a QGP signal), and yet it is now found was a QGP signal), and yet it is now found (Asakawa-Hatsuda,Karsch et al) that they seem (Asakawa-Hatsuda,Karsch et al) that they seem to exist to exist up to T=2Tup to T=2Tcc. or more. Why????. or more. Why????

How can How can pressure be highpressure be high at at T=(1.5-2)TT=(1.5-2)Tcc

while q,g while q,g quasiparticles are quite heavy? quasiparticles are quite heavy? MM»» 3T, exp(-3)<<1 3T, exp(-3)<<1

(it gets parametric in the N=4 SYM as quasiparticles in (it gets parametric in the N=4 SYM as quasiparticles in strong coupling are infinitely heavy mstrong coupling are infinitely heavy m»» (g (g22Nc)Nc)1/21/2TT

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 not, about 2T

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

• Since q and g quasiparticles are heavy,

M about 3T, they are bound as well !

Digression :Relativistic Klein-Gordon eqn has a critical Coulomb coupling for falling onto the center (known since 1920’s)

• (4/3)s=1/2 is too strong, a critical value for Klein-Gordon (and it is 1 for Dirac).

New ``free energies” for static quarks (from Bielefeld)

•Upper figure is normalized at small distances: one can see that there is large ``effective mass” for a static quark at T=Tc.

•Both are not yet the potentials!

•The lower figure shows the effective coupling constant

Fitting F to screened Coulomb

• Fit from Bielefld group hep-lat/0406036

Note that the Debye radius corresponds to``normal” (still enhanced by factor 2) coupling, while the overall strength of the potential is much larger

New potentials should have the entropy term is subtracted,

which makes potentials deeper still

this is how potential I got look like for T = 1; 1.2; 1.4; 2; 4; 6; 10Tc,from right to left, from ES,Zahed hep-ph/0403127

Here is the binding and |psi(0)|^2 is indeed bound till nearly 3 Tc

E/2MVs T/Tc

J ψ

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

• In QGP there is no confinement =>

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

The pressure The pressure puzzle puzzle p/p(SB)=.8 from about .3 GeV

to very large value. Interpreted as an argument that interaction is relatively weak (0.2) and can be resumed, although pQCD series are bad…

BUT: we recently learned that storng coupling result in N=4 SYM leads to about 0.8 as well at g2N» 10

•This turned out to be the most misleading picture we had, fooling us for nearly 20 years

Well known lattice prediction, Karsch et al

the pressure as a function of T

(normalized to that for free quarks and gluons)

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

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

``Polymerization of sQGP?Multibody bound states

(Casalderrey and ES, in progress)

• Qbar - g - g - g -…- g - Q

• color convoluted inside naturally

• ``Polymeric chains” are better bound than pairs because instead of m(reduced)=m/2 in relative motion in binaries there is nearly the full mass for polymers

Can we verify existence of bound states at T>Tc experimentally?

Dileptons from sQGP:

A near-threshold enhancement (``bump”)

should exist at any T• Why bump?

Because attraction between anti-q q in QGP enhances annihilation

Example: pp(gg) -> t t at Fermilab has a bump near threshold (2mt) due to gluon exchanges. The nonrelat. Gamow parameter for small velocity z= (4/3)s/v > 1,Produces a bump: theFactor z/(1-exp(-z))Cancels v in phase space

dilepton rate: a nonrelativisticapproach with realistic potentials (Jorge Casalderrey +ES,hep-ph/0408128)

The annihilation rate divided by that for free massless quarks using non-rel. Green

function, for lattice-based potential (+ instantons)

Im(M) for T=1.2,1.4,1.7, 3 Tc

Asakawa-Hatsuda, T=1.4Tc

Karsch-Laerman, T=1.5 and 3 Tc

The widths of these states are being calculated… But one sees these peaks on the lattice!

Summary Summary

New hydro New hydro phenomenon => phenomenon => Conical flowConical flow

many mesons many mesons survive at T>Tcsurvive at T>Tc

plus hundreds of plus hundreds of exotic colored exotic colored binary states.binary states.

Polymers?Polymers? Lattice potentials, Lattice potentials,

masses and EoS masses and EoS are all are all consistent ! consistent ! Puzzles resolvedPuzzles resolved

• vectorsvectors above Tc above Tc can be observed can be observed via via dileptonsdileptons: the bound: the bound vectors vectors plus aplus a near- near-threshold bump. threshold bump. •Most likely in the Most likely in the region 1.5 GeV, region 1.5 GeV, where 2Mq stays the where 2Mq stays the same same in a wide T in a wide T interval.interval. The The widthwidth issue is being issue is being studiedstudied

Now we are ready to Now we are ready to move to move to N=4 SUSY YM at finite TN=4 SUSY YM at finite TWhy this theory is so special? Why this theory is so special? Copling does not run and can be Copling does not run and can be

large (or small) at all distances.large (or small) at all distances. AdS/CFT correspondence!!!AdS/CFT correspondence!!!

A complete ``gravity A complete ``gravity dual” for RHIC from 10-d dual” for RHIC from 10-d GR?GR? Black Holes + Howking rad. Is Black Holes + Howking rad. Is

used to mimic the finite Tused to mimic the finite T How How black hole is producedblack hole is produced can be can be

calculated from GR (tHooft … calculated from GR (tHooft … Nastase)Nastase)

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

MovingMoving brane => hydro expansion brane => hydro expansion(ES,Sin,Zahed, in progress)(ES,Sin,Zahed, in progress)

Classical QED plasmaClassical QED plasma

(ze)^2/aT>>1(ze)^2/aT>>1 is a strongly coupled is a strongly coupled regime: e.g. molted soltsregime: e.g. molted solts

Molecular dynamicsMolecular dynamics of 1970’s found of 1970’s found that diffusion is going down but that diffusion is going down but viscosity reaches a minimumviscosity reaches a minimum when when this param.is about 10 and then this param.is about 10 and then grow toward a ``glass” and finally a grow toward a ``glass” and finally a solid (at param. about 300)solid (at param. about 300)