Understanding strongly coupled quark-gluon plasma (sQGP)

Understanding strongly coupled quark-gluon plasma (sQGP)

(SIS program,(SIS program,Cambridge, Aug.2007)Cambridge, Aug.2007)

Edward ShuryakEdward ShuryakStony BrookStony Brook

(SIS program,(SIS program,Cambridge, Aug.2007)Cambridge, Aug.2007)

Edward ShuryakEdward ShuryakStony BrookStony Brook

The emerging theory of sQGP

sQGP

Plasma physics

Manybody theory

Lattice simulations

Gauge theories,SUSY models

String theory

AdS/CFT

Monopoles

Quantum mechanics

QuasiparticlesPotentialscorrelators

Bound states of EQP and MQPJ/psi,mesons,baryons,calorons

Stronly coupledcold trappedatoms

Moleculardynamics

Transport properties

E/M duality

EoSHydrodynamics

Energy loss,Collective modesMach cones

Flux tubes->

Bose-EinsteinCondensation->confinement RHIC

data

OutlineOutlineQs: Why do we have strongly coupled quark-gluon plasma

(sQGP) at RHIC? Is it related to deconfinement (T=(1-1.5)Tc) or quasi-conformal behaviour at $T>1.5Tc? What is the role of magnetic objects? Can one explain RHIC results using AdS/CFT? A picture is emerging…

RHIC findings: collective flows and jet quenching

Viscosity and diffusion constant from AdS/CFT, complete gravity dual?

Phase diagram and lattice. Electric and magnetic quasiparticles (EQPs and MQPs) are fighting for dominance (J.F.Liao,ES, hep-ph/0611131,PRC 07) Flux tube existence/dissolution (J.F.Liao,ES, 0706.4465[hep-ph]) the magnetic bottle effect

molecular dynamics (MD) of Non-Abelian plasma with monopoles(B.Gelman, I.Zahed,ES, PRC74,044908,044909 (2006), J.F.Liao,ES, hep-ph/0611131,PRC 07):

transport summary; From RHIC to LHC Summary: are two explanations related???

Qs: Why do we have strongly coupled quark-gluon plasma (sQGP) at RHIC? Is it related to deconfinement (T=(1-1.5)Tc) or quasi-conformal behaviour at $T>1.5Tc? What is the role of magnetic objects? Can one explain RHIC results using AdS/CFT? A picture is emerging…

RHIC findings: collective flows and jet quenching

Viscosity and diffusion constant from AdS/CFT, complete gravity dual?

Phase diagram and lattice. Electric and magnetic quasiparticles (EQPs and MQPs) are fighting for dominance (J.F.Liao,ES, hep-ph/0611131,PRC 07) Flux tube existence/dissolution (J.F.Liao,ES, 0706.4465[hep-ph]) the magnetic bottle effect

molecular dynamics (MD) of Non-Abelian plasma with monopoles(B.Gelman, I.Zahed,ES, PRC74,044908,044909 (2006), J.F.Liao,ES, hep-ph/0611131,PRC 07):

transport summary; From RHIC to LHC Summary: are two explanations related???

RHIC findingsRHIC findings

Strong radial and elliptic flowsStrong radial and elliptic flows are very are very well described by ideal hydro => well described by ideal hydro => ``perfect liquid``perfect liquid””

Strong jet quenchingStrong jet quenching, well beyond , well beyond pQCD gluon radiation rate, same for pQCD gluon radiation rate, same for heavy charm quarks (b coming) heavy charm quarks (b coming)

Jets destroyed and their energy goes Jets destroyed and their energy goes into hydrodynamical into hydrodynamical ``conical flow``conical flow” ”

Strong radial and elliptic flowsStrong radial and elliptic flows are very are very well described by ideal hydro => well described by ideal hydro => ``perfect liquid``perfect liquid””

Strong jet quenchingStrong jet quenching, well beyond , well beyond pQCD gluon radiation rate, same for pQCD gluon radiation rate, same for heavy charm quarks (b coming) heavy charm quarks (b coming)

Jets destroyed and their energy goes Jets destroyed and their energy goes into hydrodynamical into hydrodynamical ``conical flow``conical flow” ”

From Magdeburg hemispheres (1656) to dreams of 1970’s…

•“We cannot pump out complicated objects populating the QCD vacuum, but we can pump in something else, namely the Quark-Gluon Plasma, and measure explosion”

(QGP in 1970’s was expected to be just a simple near-ideal quark-gluon gas, to ``fill the bag”)

QCD vacuum isso compicated…

One may have an absolutely correct theory and still

make accidental discoveries…

One may have an absolutely correct theory and still

make accidental discoveries…Columbus believed if he goes west he should eventually come to India

But something else was on the way…

We believed if we increase the energy density, we should eventually get weakly interacting QGP. But something else was found on the way, sQGP

How Hydrodynamics Works at RHIC

How Hydrodynamics Works at RHIC

Elliptic flowElliptic flowHow does the system respond to initial spatial How does the system respond to initial spatial

anisotropy?anisotropy?

)

Dense or dilute?Dense or dilute?If dense, thermalization?If dense, thermalization?

If thermalized, EoS?If thermalized, EoS?

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 resonanceSimilar 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 )

2001-2005: hydro describes radial and elliptic flows for all secondaries , pt<2GeV, centralities, rapidities, A (Cu,Au)…

Experimentalists were very sceptical but wereconvinced and ``near-perfect liquid” is now official,

=>AIP declared this to be discovery #1 of 2005 in physics v_2=<cos(2 phi)>

PHENIX,

Nucl-ex/0410003

red lines are for ES+Lauret+Teaney done before RHIC data, never changed or fitted, describes SPS data as well! It does so because of the correct hadronic matter /freezout via (RQMD)

proton pion

One more surprise from RHIC: strong jet quenching and flow of heavy quarks

Heavy quark quenching as strong as for light gluon-q jets!

Radiative energy loss only fails to reproduce v2

HF.

Heavy quark elliptic flow: v2

HF(pt<2GeV) is about the same as for all hadrons!=>Small relaxation time or diffusion coefficient DHQ

inferred for charm.

nucl-ex/0611018

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

• the energy deposited by jets into liquid-like strongly coupled QGP must go into conical shock waves

• 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

Wake effect or “sonic boom”

Two hydro modes can be excited(from our linearized hydro solution):

a a ``diffuson” a ``diffuson” a soundsound

2 Mach cones in strongly coupled plasmas

(thanks to B.Jacak)

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

The most peripheral bin, here no matter

AdS/CFTfrom gravity in AdS5 to strongly coupled CFT (N=4 SYM) plasma

AdS/CFTfrom gravity in AdS5 to strongly coupled CFT (N=4 SYM) plasma what people dream about for LHCwhat people dream about for LHCexperments -- a black hole formation -- experments -- a black hole formation --

does happen, does happen, in each and every RHIC in each and every RHIC AuAu event =>AuAu event =>

thermalization, All info is lost except thermalization, All info is lost except the overall entropy=area of newly the overall entropy=area of newly formed b.h.horizonformed b.h.horizon

what people dream about for LHCwhat people dream about for LHCexperments -- a black hole formation -- experments -- a black hole formation --

does happen, does happen, in each and every RHIC in each and every RHIC AuAu event =>AuAu event =>

thermalization, All info is lost except thermalization, All info is lost except the overall entropy=area of newly the overall entropy=area of newly formed b.h.horizonformed b.h.horizon

viscosity from AdS/CFT (Polykastro,Son, Starinets 03)

Kubo formula <Tij(x)Tij(y)>=>

• Left vertical line is our 4d Universe, (x,y are on it)

• Temperature is given by position of a horizon (vertical line, separationg

• From interier of``black brane” T=T(Howking radiation) (Witten 98)

• Correlator needed is just a graviton propagator G(x,y)

• Blue graviton path does not contribute to Im G, but

the red graviton path (on which it is absorbed) does

Both viscosity and entropy are proportional to b.h. horizon, thus such a simple asnwer

€

η /s =1/4π

€

η /s = hbar /4π

€

η /s = hbar /4π

Heavy quark diffusion J.Casalderrey+ D.Teaney,hep-ph/0605199,hep-th/0701123

WORLD

ANTIWORLD

One quark (fisherman) isIn our world,The other (fish) in Antiworld (=conj.amplitude)String connects them and conduct waves in one direction through the black hole

Left: P.Chesler,L.YaffeUp- from Gubser et al

Both groups made Amasingly detailedDescription of the conical flow from AdS/CFT=> not much is diffused

subsonic

supersonic

Gravity dual to the whole collision: “Lund model” in AdS/CFT

• Expanding/cooling fireball= departing Black Hole

(Nastase 03, Sin,ES and Zahed 04,Janik-Peschanski 05…)

If colliding objects made of heavy quarks • Stretching strings -- unlike Lund model those are

falling under the AdS gravity and don’t break (Lin,ES hep-ph/0610168)

• The falling membrane is created which separate two regions of two different metrics: it is becoming a b.h. horizon

Now linearized version in progress (field from a static Maldacena string recently done

Lin,ES arXiv:0707.3135, T00 ->1/r7 )

AdS5

Center=

Extremal b.h.

AdS/CFT suggests completely new

pictures of gauge theory topology • Instantons = D-1 brane=point in the bulk,

at large Nc coalesce together (Mattis,Khose,Dorey 90’s)

• Monopoles = endpoints of D1 (string-like) branes

• Electric-magnetic duality includes duality between baryons and calorons (finite T instantons) as Nc monopoles (known before ads <= Kraan,van Baal ….)

Explaining transport in sQGP:electric/magnetic fight“Classical QGP” and its Molecular Dynamics

Explaining transport in sQGP:electric/magnetic fight“Classical QGP” and its Molecular Dynamics

Electrons have the same charge -e all the time,

but our quasiparticles (quarks, gluons,…) have colors

which is changing in time

Fraction of quasiparticles are magnetically Charged (monopoles and dyons) whichfight each other At T<Tc they somehow (?) make a “dual superconductor”=>confinement.

An example of ``dyonic baryon”=finite T instanton

top.charge Q=1 config.,dyons identified via fermionic zero modes

Berlin group - Ilgenfritz et al

Red, blue and green U(1) fields

3 dyons with corresp.Field strengths, SU(3),Each (1,-1,0) charges

Electric and magnetic scrreningMasses, Nakamura et al, 2004

My arrow shows the ``self-dual” E=M point

Me>MmElectrricdominated

Me<MmMagneticDominated

At T=0 magneticScreening massIs about 2 GeV(de Forcrand et al)(a glueball mass)

Other data (Karsch et al) better show how MeVanishes at Tc

ME/T=O(g)ES 78MM/T=O(g^2)Polyakov 79

New (compactified) phase diagram

describing an electric-vs-magnetic competition Dirac condition (old QED-type units e^2=alpha, deliberately no Nc yet)

Thus at the e=g line

Near deconfinement line g->0 in IR (Landau’s U(1) asymptotic freedom)

=> e-strong-coupling because g in weak! Why is this diagram better? =>

There are e-flux tubes in all blue region, not only in the confined phase! In fact, they are maximally enhanced at Tc

<- n=2 adjoint

Energy and entropy associated with 2

static quarksis very large near Tc

from lattice potntials Bielefeld-BNL

• R->infinity means there are 2 separate objects

• Entropy=20 implies exp(20) states

• At R=(.3-1.2)fm both are about linear in R <=

What object is that?

pQCD predictsa negative U

Energy and entropy associated with 2

static quarksis very large near Tc

from lattice potntials Bielefeld-BNL

• R->infinity means there are 2 separate objects

• Entropy=20 implies exp(20) states

• At R=(.3-1.2)fm both are about linear in R <=

What object is that?

pQCD predictsa negative U

e-flux tubes above Tc?(with J.F.Liao, archive 0706.4465 [hep-ph])

• Dual superconductivity at T<Tc as a confinement mechanism (‘tHooft, Mandelstam 1980’s) => monopole Bose condensation => electric flux tubes (dual to Abrikosov-Nielsson-Olesen vortices)

• Can uncondenced MQPs do the same at T>Tc ? MQPs are reflected from a region with E field =>

pressure => flux tubes compression in plasma• We solve quantum mechanics of motion in each partial wave

magnetic flux tubes at the Sun,(work without any superconductor!): so we need

to work out the exact conditions where classical electrons rotate

around it • B: about 1 kG, • Lifetime: few months

Classical and quantum mechanics of the flux tube

Red trajectory A => nu=0(velocity at large r directed to the center)Black one B => m=0 (which goes through the center because no m^2/r^2 barrier)

Self-consistent solution => stability condition of the flux tube

Z=exp(-mu/T)

dissolution of the tube roughly at T>1.4Tc

(lattice Bielefeld-BNL)

• Assuming this is the case and using our criterion we get density of magnetic QPs=>

• n(magnetic,T=1.3Tc)=(4-6)fm-3

• Twice less than about 10 fm^-3 at T=0 (Bali et al, from vacuum confining strings)

Is sQGP full of flux tubes?

evolution with T:• T=0, dual Meissner =>ANO• At T<Tc complicated shape can produce

entropy=o(L) but it is Nc independent => no electric objects, no color changed

• At T>Tc heavy gluon (and quark) quasiparticles first appear as ``beads” S=(L/a)log7+(L/b)log(Nc)

• As T grows further => less monopoles of higher energy => no electric field flux suppression

=>``electric polymers” • Very high T => wQGP, electric plasma, no bound

states

(Presumably gluons-in-the-tube correspond to AdS/CFTMinahan string solutions and are also dual to monopoles-in-the-tube solutions recentlyWorked out by Tong et al,Shifman et al)

Bose-Einstein condensation of interacting

particles (=monopoles) (with M.Cristoforetti,Trento)

• Feynman theory (for liquid He4): polygon jumps BEC if exp(-∆S(jump))>.16 or so (1/Nnaighbours)

We calculated ``instantons” for particles jumping paths in a liquid and

solid He4 incuding realistic atomic potentials and understood 2 known effects:

(i) Why Tc grows with repulsive interaction<= because a jump proceeds faster under the barrier

(ii) no supersolid He => density too large and action above critical

Marco is doing Path Integral simulations with permutations numerically, to refine conditions when BEC transitions take place

Jumping paths:Feynman,interacting

BEC (confinement) condition for monopoles

For charged Bose gas (monopoles) the action for the jump can be calculated similarly, but relativistically; jumps in space d and in time

Comparable)

∆S=M sqrt(d2+(1/Tc)2)+ ∆S(interaction) = Sc =1.65-1.89

(first value from Einstein ideal gas, second from liquid He)

provides the monopole mass M at Tc

M Tc approx 1.5 => M as low as 300 MeV

Strong coupling in plasma physics: Gamma= <|Epot|>/<Ekin> >>1

gas => liquid => solid• This is of course for

+/- Abelian charges,• But ``green” and

``anti-green” quarks do the same!

•local order would be preserved in a liquid also,

as it is in molten solts (strongly coupled TCP with <pot>/<kin>=O(60), about 3-10 in sQGP)

Wong eqn can be rewritten as x-p canonical pairs, 1 pair for SU(2), 3 for SU(3), etc. known as Darboux variables. We did SU(2) color => Q is a unit vector on O(3)

Gas, liquid solid

Gelman,ES,Zahed,nucl-th/0601029

With a non-Abelian color => Wong eqn

So why is such plasma a good liquid? Because of magnetic-bottle trapping:

static eDipole+MPS

+

-

MV

E+

E-

Note that Lorentz force is O(v)!

We found that two charges play ping-pong by a monopole without even

moving!

Dual to Budker’s

magnetic bottle

Chaotic, regular and escape trajectories for a monopole, all different in initial condition by 1/1000 only!

MD simulation for plasma with monopoles (Liao,ES hep-ph/0611131)

monopole admixture M50=50% etcagain diffusion decreases indefinitely, viscosity does not

€

D∝1/Γ^(0.6 − 0.8)It matters: 50-50 mixture makes the best liquid, as itcreates ``maximal confusion”

short transport summary log(inverse viscosity s/eta)- vs. log(inverse heavy q

diffusion const D*2piT) (avoids messy discussion of couplings)

• RHIC data: very small viscosity and D• vs theory - AdS/CFT and MD(soon to be

explained)

Weak coupling end =>(Perturbative results shown here)Both related to mean free path

MD results, with specifiedmonopole fraction

->Stronger coupled ->

Most perfect liquid

50-50% E/M is the most ideal liquid

4pi

From RHIC to LHC:(no answers, only 1bn$ questions)From RHIC to LHC:(no answers, only 1bn$ questions)

Will Will ``perfect liquid``perfect liquid” be still there?” be still there? Is Is jet quenchingjet quenching as strong, especially for as strong, especially for

c,b quark jets and much larger pt?c,b quark jets and much larger pt? Is matter response (conical flow at Is matter response (conical flow at

Mach angle) similar? Mach angle) similar? (This is most (This is most sensitive to viscosity…)sensitive to viscosity…)

Will Will ``perfect liquid``perfect liquid” be still there?” be still there? Is Is jet quenchingjet quenching as strong, especially for as strong, especially for

c,b quark jets and much larger pt?c,b quark jets and much larger pt? Is matter response (conical flow at Is matter response (conical flow at

Mach angle) similar? Mach angle) similar? (This is most (This is most sensitive to viscosity…)sensitive to viscosity…)

From SPS to LHCFrom SPS to LHC

• lifetime of QGP phase nearly doubles, but v2 grows only a little, to a universal value corresponding to EoS p=(1/3)epsilon• radial flow grows by about 20% => less mixed / hadronic phase (only 33% increase in collision numbers of hadronic phase in spite of larger multiplicity)

(hydro abovefrom S.Bass)

ConclusionsConclusions

StronglyStrongly coupled coupled QGP is produced QGP is produced at RHIC T=(1-2)Tcat RHIC T=(1-2)Tc

This is the region This is the region where transition where transition from magnetic to from magnetic to electric electric dominance dominance happenhappen

at T<1.4 Tc at T<1.4 Tc still Lots of still Lots of magnetic magnetic objects => objects =>

E-flux tubesE-flux tubes

StronglyStrongly coupled coupled QGP is produced QGP is produced at RHIC T=(1-2)Tcat RHIC T=(1-2)Tc

This is the region This is the region where transition where transition from magnetic to from magnetic to electric electric dominance dominance happenhappen

at T<1.4 Tc at T<1.4 Tc still Lots of still Lots of magnetic magnetic objects => objects =>

E-flux tubesE-flux tubes

RHIC data on RHIC data on transport (eta,D), transport (eta,D), ADS/CFT and ADS/CFT and classical MD all classical MD all qualitatively agree qualitatively agree !!

Are these two Are these two pictures pictures related? related?

RHIC data on RHIC data on transport (eta,D), transport (eta,D), ADS/CFT and ADS/CFT and classical MD all classical MD all qualitatively agree qualitatively agree !!

Are these two Are these two pictures pictures related? related?

Good liquid Good liquid because of because of magnetic-bottle magnetic-bottle trappingtrappingClassical MD Classical MD is being done,is being done, lowest lowest viscosity for viscosity for 50-50% 50-50% electric/magnetic electric/magnetic plasmaplasma•AdS/CFT => natural AdS/CFT => natural applications of applications of string theorystring theoryN=4 SYM is N=4 SYM is nonconfining andnonconfining andStrongly coupled!Strongly coupled!

•

reservereserve

Effective coupling is large! alphas=O(1/2-1) (not <0.3 as in pQCD applications)

tHooft lambda=g2Nc=4piNc=O(20)>>1-1

Effective coupling is large! alphas=O(1/2-1) (not <0.3 as in pQCD applications)

tHooft lambda=g2Nc=4piNc=O(20)>>1-1

Bielefeld-BNL lattice group: Karsch et al

At e=m line both effective gluons and At e=m line both effective gluons and monopoles have masses M about 3T exp(-monopoles have masses M about 3T exp(-3)<<1 is our classical parameter3)<<1 is our classical parameter

(Boltzmann statistics is good enough)(Boltzmann statistics is good enough) At T=Tc monopoles presumably go into Bose-At T=Tc monopoles presumably go into Bose-

Einsetein condensation => new semiclassical Einsetein condensation => new semiclassical theory of it for strongly interacting Bose theory of it for strongly interacting Bose gases, tested on He4gases, tested on He4

(M.Cristoforetti, ES, in progress)(M.Cristoforetti, ES, in progress)

At e=m line both effective gluons and At e=m line both effective gluons and monopoles have masses M about 3T exp(-monopoles have masses M about 3T exp(-3)<<1 is our classical parameter3)<<1 is our classical parameter

(Boltzmann statistics is good enough)(Boltzmann statistics is good enough) At T=Tc monopoles presumably go into Bose-At T=Tc monopoles presumably go into Bose-

Einsetein condensation => new semiclassical Einsetein condensation => new semiclassical theory of it for strongly interacting Bose theory of it for strongly interacting Bose gases, tested on He4gases, tested on He4

(M.Cristoforetti, ES, in progress)(M.Cristoforetti, ES, in progress)