Understanding strongly coupled quarkgluon plasma s QGP Israeli

Understanding strongly coupled quark-gluon plasma (s. QGP) (Israeli Physical Soc. Rehovot, Dec. 2007) Edward Shuryak Stony Brook

The emerging theory of s. QGP Manybody theory Flux tubes -> Plasma physics Stronly coupled cold trapped atoms Quantum mechanics Quasiparticles Potentials correlators Bound states Bose-Einstein of EQP and MQP Condensation J/psi, mesons, baryons, calorons -> confinement Hydrodynamics s. QGP Molecular dynamics Energy loss, Collective modes Mach cones Transport properties Lattice simulations Eo. S RHIC data Monopoles E/M duality Ad. S/CFT duality String theory Gauge theories, SUSY models

l RHIC findings: collective flows and jet quenching l Fundamental questions: Why quark-gluon plasma (s. QGP) 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 s. QGP? Does Ad. S/CFT duality explain RHIC results? q Viscosity and diffusion constant from Ad. S/CFT, New meaning of dissipation q Electric and magnetic quasiparticles (EQPs and MQPs) are fighting for dominance q q (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, PRC 74, 044908, 044909 (2006), J. F. Liao, ES, hep-ph/0611131, PRC 07): q q transport summary; two dualities -Ad. S/CFT and s. QGP with monopoles - seem to work. Summary: Are they related? ? ? LHC will tell

RHIC findings l Strong radial and elliptic flows are very well described by ideal hydro => ``perfect liquid” l Strong jet quenching, well beyond p. QCD gluon radiation rate, same for heavy charm quarks (b coming) l Jets destroyed and their energy goes into hydrodynamical ``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 s 1/4 • 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 Þ ES+Hung, prc 57 (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 nonperturbative 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… 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, s. QGP

Contrary to expectations of most, hydrodynamics does work at RHIC! Elliptic flow How does the system respond to initial spatial anisotropy? is it macro or microscopic? )

The coolest thing on Earth, T=10 n. K or 10^(-12) e. V can actually produce a Micro-Bang ! (O’Hara et al, Duke ) Elliptic flow with ultracold trapped Li 6 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”

2001 -2005: hydro describes radial and elliptic flows for all secondaries , pt<2 Ge. V, centralities, rapidities, A (Cu, Au)… Experimentalists were very sceptical but were convinced and ``near-perfect liquid” is now official, =>AIP declared this to be discovery #1 of 2005 in physics proton v_2=<cos(2 phi)> pion 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)

So it is even less than presumed Lower bound (Son et al) <1/4 ! Why it may be possible, read Lublinsky, ES hep-ph 0704. 1647

One more surprise from RHIC: strong jet quenching and flow of heavy quarks nucl-ex/0611018 Heavy quark quenching as strong as for light gluon-q jets! Radiative energy loss only fails to reproduce v 2 HF. Heavy quark elliptic flow: v 2 HF(pt<2 Ge. V) is about the same as for all hadrons! => Small relaxation time t or diffusion coefficient DHQ inferred for charm.

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 ``diffuson” a sound

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

Ad. S/CFT duality from gravity in Ad. S 5 to strongly coupled CFT (N=4 SYM) plasma what LHC people dream about -- a black hole formation -does happen, in each and every RHIC Au. Au event ! thermalization, All info is lost except the overall entropy=area of newly formed b. h. horizon

viscosity from Ad. S/CFT (Polykastro, Son, Starinets 03) Kubo formula <Tij(x)Tij(y)>=> • • • Left vertical line is Ad. S boundary (our 4 d 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) does Both viscosity and entropy are proportional to b. h. horizon, thus such a simple asnwer

Heavy quark diffusion J. Casalderrey+ D. Teaney, hep-ph/0605199, hep-th/0701123 One quark (fisherman) is In our world, The other (fish) in Antiworld (=conj. amplitude) String connects them and conduct waves in one direction through the black hole A N T I W O R L D

subsonic supersonic Left: P. Chesler, L. Yaffe Up- from Gubser et al Both groups made Amasingly detailed Description of the conical flow from Ad. S/CFT=> not much is diffused

Electric/magnetic duality and transport in s. QGP E and M couplings run in opposite directions! magnetically charged (monopoles and dyons) Quasiprticles in s. QGP EQP and MQP repel each other At T<Tc they somehow (? ) make a “dual superconductor” =>confinement.

Note norm. monopole density grows to Tc Correlations are liquid-like even at 2. 87 Tc

Electric and magnetic scrrening Masses, Nakamura et al, 2004 My arrow shows the ``self-dual” E=M point Me<Mm Magnetic Dominated At T=0 magnetic Screening mass Is about 2 Ge. V (de Forcrand et al) (a glueball mass) Other data (Karsch et al) better show Me Vanishes at Tc Me>Mm Electrric dominated ME/T=O(g) ES 78 MM/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) <- n=2 adjoint 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

So why is such plasma a good liquid? Because of magnetic-bottle trapping: static e. Dipole+MPS Note that Lorentz force is O(v)! E+ + M V E- - Monopole rotates around the electric field line, bouncing off both charges (whatever the sign)

We found that two charges play pingpong by a monopole without even moving! Chaotic, regular and escape trajectories for a monopole, all different in initial condition by 1/1000 only! Dual to Budker’s magnetic bottle

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 M 50=50% etc again diffusion decreases indefinitely, viscosity does not It matters: 50 -50 mixture makes the best liquid, as it creates ``maximal trapping

short transport summary log(inverse viscosity s/eta)- vs. log(inverse heavy q diffusion const D*2 pi. T) (avoids messy discussion of couplings) ->Stronger coupled -> • • RHIC data: very small viscosity and D vs theory - Ad. S/CFT and MD(soon to be explained) Most perfect liquid 4 pi MD results, with specified monopole fraction Weak coupling end => (Perturbative results shown here) Both related to mean free path 50 -50% E/M is the most ideal liquid

From RHIC to LHC: (no answers, only 1 bn$ questions) (I don’t mean the price of LHC but ALICE) l Will ``perfect liquid” be still there? l Is jet quenching as strong, especially for c, b quark jets and much larger pt? l Is matter response (conical flow at Mach angle) similar? (This is most sensitive to viscosity…)

From SPS to LHC • lifetime of QGP phase nearly doubles, but v 2 grows only a little, to a universal value corresponding to Eo. S 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 above from S. Bass)

Conclusions Strongly coupled QGP is produced at RHIC T=(1 -2)Tc l This is the region where transition from magnetic to electric dominance happen l at T<1. 4 Tc still Lots of magnetic objects => E-flux tubes l l. Good liquid because of magneticbottle trapping l. Classical MD is being done, the lowest viscosity for 50 -50% electric/magneti c plasma Ad. S/CFT => natural applications of string theory, N=4 SYM is not QCD: nonconfining and Strongly coupled, s. QGP is OK l RHIC data on transport l (eta, D), ADS/CFT and classical MD all qualitatively agree! l Are these two pictures related?

reserve

Effective coupling is large! alphas=O(1/2 -1) (not <0. 3 as in p. QCD applications) t. Hooft lambda=g 2 Nc=4 pi. Nc=O(20)>>1 -1 Bielefeld-BNL lattice group: Karsch et al

Strong coupling in plasma physics: Gamma= <|Epot|>/<Ekin> >>1 gas => liquid => solid This is of course for +/- Abelian charges, l But ``green” and ``anti -green” quarks do the same! l • 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 s. QGP)

Gelman, ES, Zahed, nuclth/0601029 With a non-Abelian color => Wong eqn Gas, liquid solid

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) l Feynman theory (for liquid He 4): polygon jumps BEC if exp(-∆S(jump))>. 16 or so (1/Nnaighbours) We calculated ``instantons” for particles jumping paths in a liquid and solid He 4 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 monopoles have masses M about 3 T exp(3)<<1 is our classical parameter (Boltzmann statistics is good enough) l At T=Tc monopoles presumably go into Bose. Einsetein condensation => new semiclassical theory of it for strongly interacting Bose gases, tested on He 4 l (M. Cristoforetti, ES, in progress) l

Bose condensation versus repulsive scattering length

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(d 2+(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 Me. V