Understanding strongly coupled quark-gluon plasma (sQGP)

Understanding strongly coupled quark-gluon plasma (sQGP)

(Israeli Physical Soc.(Israeli Physical Soc.Rehovot, Dec.2007)Rehovot, Dec.2007)

Edward ShuryakEdward ShuryakStony BrookStony Brook

(Israeli Physical Soc.(Israeli Physical Soc.Rehovot, Dec.2007)Rehovot, Dec.2007)

Edward ShuryakEdward ShuryakStony BrookStony Brook

The emerging theory of sQGP

sQGP

Plasma physics

Manybody theory

Lattice simulations

Gauge theories,SUSY modelsString

theory

AdS/CFT duality

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

RHIC findings: collective flows and jet quenching Fundamental questions:

Why quark-gluon plasma (sQGP) at RHIC is such a good liquid? Is this related to deconfinement? What is the role of e/m duality of couplings? What is the role of magnetic objects in sQGP? Does AdS/CFT duality explain RHIC results?

Viscosity and diffusion constant from AdS/CFT, New meaning of dissipation Electric and magnetic quasiparticles (EQPs and MQPs) are

fighting for dominance (J.F.Liao,ES, hep-ph/0611131,PRC 07)

The trapping via 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; two dualities -AdS/CFT and sQGP with monopoles - seem to work.

Summary:Are they related??? LHC will tell

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” ”

Thermo and hydrodynamics: can they be used at a fm scale?

• Here are three people who asked this question first:

• Fermi (1951) proposed strong interaction leading to equilibration: <n>about s1/4

• Pomeranchuck (1952) introduced freezeout• Landau (1953) explained that one should use hydro in between, saving

Fermi’s prediction via entropy conservation {he also suggested it should work because coupling runs to strong at small distance! No asymptotic freedom yet in 1950’s…}

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

1970’s: QCD

• OK, QCD and weak coupling at small distances…but at large ones the coupling gets strong!

which makes the QCD vacuum so compicated… (instantons, monopoles, vortices and other non-perturbative beasts live there)

Can one at least measure the nonperturbative vacuum pressure/energy density?

(the ``true” bag constant)

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

•“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”

=> p(QGP)-p(vacuum)

(QGP in 1970’s was viewed as a simple near-ideal quark-gluon

gas, just ``needed to fill the bag”)

One may have an absolutely correct asymptotic theory and still

make accidental discoveries…

One may have an absolutely correct asymptotic 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

Contrary to expectations of most, hydrodynamics does

work at RHIC!

Contrary to expectations of most, hydrodynamics does

work at RHIC!Elliptic flowElliptic flow

How does the system respond to initial spatial How does the system respond to initial spatial anisotropy?anisotropy?

)

is it macro or microscopic?is it macro or microscopic?

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

So it is even less than presumedLower bound (Son et al) <1/4!Why it may be possible, readLublinsky,ES hep-ph0704.1647

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

PHENIX jet pair distribution

Note: it is only projection of a cone on phi

Note 2: there is also a minimum in

<p_t(\phi)> at

180 degr., with

a value

Consistent with

background

The most peripheral bin, here there is no QGP

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

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

what LHC people dream about what LHC people dream about -- a black hole formation -- -- 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 LHC people dream about what LHC people dream about -- a black hole formation -- -- 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 AdS boundary• (our 4d Universe, x,y are on it)• Temperature is given by position of

a horizon • T=T(Howking radiation) (Witten 98) graviton propagator G(x,y) dual to

sound• Blue graviton path does not

contribute to Im G, but the red graviton path (on which it is

absorbed) doesBoth viscosity and entropy are

proportional to b.h. horizon, thus such a simple asnwer

€

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

Electric/magnetic dualityand transport in sQGPElectric/magnetic dualityand transport in sQGP

E and M couplings run in opposite directions!

magnetically charged (monopoles and dyons)Quasiprticles in sQGPEQP and MQP repel each other At T<Tc they somehow (?) make a “dual superconductor”=>confinement.

Note norm. monopole density grows to TcCorrelations are liquid-like even at 2.87 Tc

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

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

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

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)!

Monopole rotates around the electric field line, bouncing off both charges (whatever the sign)

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!

Another example: a monopole in a “grain of solt”

Liao and ES, in progree

• Dimensionless coupling for classical plasmas:

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 trapping”

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)(I don’t mean the price of LHC but ALICE)

From RHIC to LHC:(no answers, only 1bn$ questions)(I don’t mean the price of LHC but ALICE)

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 sensitive to viscosity…)(This is most 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 sensitive to viscosity…)(This is most 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 still at T<1.4 Tc still Lots of 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 still at T<1.4 Tc still Lots of Lots of magnetic magnetic objects => objects =>

E-flux tubesE-flux tubes

AdS/CFT => natural AdS/CFT => natural applications of string applications of string theory, N=4 SYM is not theory, N=4 SYM is not QCD: nonconfining andQCD: nonconfining and

Strongly coupled, sQGP is OKStrongly coupled, sQGP is OK RHIC data on transport RHIC data on transport

(eta,D), ADS/CFT and (eta,D), ADS/CFT and classical MD all classical MD all qualitatively agree!qualitatively agree!

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

AdS/CFT => natural AdS/CFT => natural applications of string applications of string theory, N=4 SYM is not theory, N=4 SYM is not QCD: nonconfining andQCD: nonconfining and

Strongly coupled, sQGP is OKStrongly coupled, sQGP is OK RHIC data on transport RHIC data on transport

(eta,D), ADS/CFT and (eta,D), ADS/CFT and classical MD all classical MD all qualitatively agree!qualitatively agree!

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

Good liquid Good liquid because of because of magnetic-magnetic-bottle bottle trappingtrappingClassical Classical MD is being MD is being done,done, the lowest the lowest viscosity for viscosity for 50-50% 50-50% electric/magneelectric/magnetic plasmatic plasma

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

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

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

This is of course for This is of course for +/- Abelian charges+/- Abelian charges,,

But But ``green” and ``green” and ``anti-green”``anti-green” quarks quarks do the same!do the same!

This is of course for This is of course for +/- Abelian charges+/- Abelian charges,,

But But ``green” and ``green” and ``anti-green”``anti-green” quarks quarks do the same!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)

Gas, liquid solid

Gelman,ES,Zahed,nucl-th/0601029

With a non-Abelian color => Wong eqn

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)

Bose-Einstein condensation of interacting

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

Bose-Einstein condensation of interacting

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

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

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

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

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)

Bose condensation versus repulsive scattering lengthBose condensation versus repulsive scattering length

BEC (confinement) condition for monopolesBEC (confinement) condition for monopolesFor charged Bose gas (monopoles) the action for the jump can be calculated similarly, but For charged Bose gas (monopoles) the action for the jump can be calculated similarly, but

relativistically; jumps in space d and in timerelativistically; jumps in space d and in timeComparable)Comparable)

∆∆S=M sqrt(dS=M sqrt(d22+(1/Tc)+(1/Tc)22)+ ∆S(interaction) = Sc =1.65-1.89)+ ∆S(interaction) = Sc =1.65-1.89(first value from Einstein ideal gas, second from liquid He)(first value from Einstein ideal gas, second from liquid He)

provides the monopole mass M at Tcprovides the monopole mass M at Tc

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

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

Comparable)Comparable)

∆∆S=M sqrt(dS=M sqrt(d22+(1/Tc)+(1/Tc)22)+ ∆S(interaction) = Sc =1.65-1.89)+ ∆S(interaction) = Sc =1.65-1.89(first value from Einstein ideal gas, second from liquid He)(first value from Einstein ideal gas, second from liquid He)

provides the monopole mass M at Tcprovides the monopole mass M at Tc

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