Understanding strongly coupled quark-gluon plasma (sQGP)

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

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

3. 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 fromAdS/CFT, New meaning of dissipation • Electric andmagneticquasiparticles (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

4. RHIC findings • Strong radial and elliptic flows are very well described by ideal hydro => ``perfect liquid” • Strong jet quenching, well beyond pQCD gluon radiation rate, same for heavy charm quarks (b coming) • Jets destroyed and their energy goes into hydrodynamical ``conical flow”

5. 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…}

6. 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

7. 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)

8. 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”)

9. One may have an absolutely correct asymptotic theory and stillmake 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

10. 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? )

11. The coolest thing on Earth, T=10 nK or 10^(-12) eV can actually produce a Micro-Bang ! (O’Hara et al, Duke ) 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”

12. proton pion 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 physicsv_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)

13. So it is even less than presumed Lower bound (Son et al) <1/4! Why it may be possible, read Lublinsky,ES hep-ph0704.1647

14. 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 v2HF. Heavy quark elliptic flow: v2HF(pt<2GeV) is about the same as for all hadrons! => Small relaxation time t or diffusion coefficient DHQinferred for charm.

15. Wake effect or “sonic boom” Sonic boom from quenched jetsCasalderrey,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

16. Two hydro modes can be excited(from our linearized hydro solution): a ``diffuson” a sound

17. 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

18. AdS/CFTdualityfrom gravity in AdS5 to strongly coupled CFT (N=4 SYM) plasma what LHC people dream about -- a black hole formation -- does happen, in each and every RHIC AuAu event ! thermalization, All info is lost except the overall entropy=area of newly formed b.h.horizon

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

20. Heavy quark diffusion J.Casalderrey+ D.Teaney,hep-ph/0605199,hep-th/0701123 W O R L D 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

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

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

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

25. Electric and magnetic scrreningMasses, Nakamura et al, 2004My arrow shows the ``self-dual” E=M point Me<Mm Magnetic Dominated At T=0 magnetic Screening mass Is about 2 GeV (de Forcrand et al) (a glueball mass) Other data (Karsch et al) better show how Me Vanishes at Tc Me>Mm Electrric dominated ME/T=O(g) ES 78 MM/T=O(g^2) Polyakov 79

26. An example of ``dyonic baryon”=finite T instantontop.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

27. New (compactified) phase diagramdescribing 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 allblue region, not only in the confined phase! In fact, they are maximally enhanced at Tc

28. So why is such plasma a good liquid? Because of magnetic-bottle trapping: static eDipole+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)

29. We found that two chargesplay ping-pong 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

30. Another example: a monopole in a “grain of solt”Liao and ES, in progree

31. Dimensionless coupling for classical plasmas:

32. MD simulation for plasma with monopoles (Liao,ES hep-ph/0611131)monopole admixture M50=50% etcagain diffusion decreases indefinitely, viscosity does not It matters: 50-50 mixture makes the best liquid, as it creates ``maximal trapping”

33. short transport summarylog(inverse viscosity s/eta)- vs. log(inverse heavy q diffusion const D*2piT) (avoids messy discussion of couplings) ->Stronger coupled -> • RHIC data: very small viscosity and D • vs theory - AdS/CFT and MD(soon to be explained) Most perfect liquid 4pi 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

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

35. From 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 above from S.Bass)

36. Strongly coupled QGP is produced at RHIC T=(1-2)Tc This is the region where transition from magnetic to electric dominance happen at T<1.4 Tc still Lots of magnetic objects => E-flux tubes AdS/CFT => natural applications of string theory, N=4 SYM is not QCD: nonconfining and Strongly coupled, sQGP is OK RHIC data on transport (eta,D), ADS/CFT and classical MD all qualitatively agree! Are these two pictures related? Conclusions • Good liquid because of magnetic-bottle trapping • Classical MD is being done, the lowest viscosity for 50-50% electric/magnetic plasma

37. reserve

38. 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

39. Strong coupling in plasma physics: Gamma= <|Epot|>/<Ekin> >>1gas => 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)

40. Gelman,ES,Zahed,nucl-th/0601029 With a non-Abelian color => Wong eqn Gas, liquid solid

41. 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)

42. 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: 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

43. At e=m line both effective gluons and monopoles have masses M about 3T exp(-3)<<1 is our classical parameter (Boltzmann statistics is good enough) • At T=Tc monopoles presumably go into Bose-Einsetein condensation => new semiclassical theory of it for strongly interacting Bose gases, tested on He4 • (M.Cristoforetti, ES, in progress)

44. Bose condensation versus repulsive scattering length

45. 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