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Magnetic side of Strongly coupled Quark-Gluon Plasma

Magnetic side of Strongly coupled Quark-Gluon Plasma. (GGI program, June 2008) Edward Shuryak Stony Brook. Collaborators: Jinfeng Liao, Marco Cristoforetti. outline. Map and main questions Electric-magnetic duality and couplings (fight,competition…) on the QCD phase diagram

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Magnetic side of Strongly coupled Quark-Gluon Plasma

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  1. Magnetic side of Strongly coupled Quark-Gluon Plasma (GGI program, June 2008) Edward Shuryak Stony Brook Collaborators: Jinfeng Liao, Marco Cristoforetti

  2. outline • Map and main questions • Electric-magnetic duality and couplings (fight,competition…) on the QCD phase diagram • Lattice monopoles behave like the usual particles: lattice correlators vs MD • Novel plasmas with both electric and magnetic particles: MD => transport • Stable and metastable flux tubes • BEC condensation criterium for interacting gases • conclusions

  3. Prologue: multiple views on sQGP (which forced us to learn a lot in the last few years…) Quantum mechanics Stronly coupled cold trapped Atoms: 2nd best liquid 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, Entropy generation Plasma physics E/M duality Collective modes Energy loss, Mach cones AdS/CFT duality Gauge theories, SUSY models Black hole physics, String theory

  4. The only hydro slide (P.Kolb) • 3 stages take about the same time at RHIC; • QGP, ``mixed phase”, hadronic phase • News is that mixed phase= magnetic plasma

  5. Deconfinement and Electric-magnetic fight/competition in sQGP . “Magnetic plasma” monopoles and dyons Assumed dominant at 0.9<T< 1.5Tc

  6. Magnetic objects and their dynamics: classics • ‘t Hooft and Polyakov discovered monopoles in Non-Abelian gauge theories • ‘t Hooft and Mandelstamm suggested “dual superconductor” mechanism for confinement • Seiberg and Witten shown that it does work in N=2 Super YangMills theory

  7. Recent developments • Liao+ES; running coupling => magnetic liquid near Tc • Chernodub+Zakharov=> high monopole density near Tc, e-3p from monopoles • D’Ellia+D’Alessandro => monopole density and spatial correlators • Liao+ES => correlators are the same as in the Coulomb liquid

  8. Liao,ES hep-ph/0611131 electric/magnetic couplings (e/g) run in the opposite directions! s(electric) s(magnetic)=1 Old good Dirac condition (in QED-type units e2= s) s(el) at the e=g “equilibrium line” s(el)=s(mag)=1 (the best liquid there?) s(mag) monopoles must get sufficently weakly coupled before BEC= deconfinement, also they are much lighter/denser than gluons/quarks =>s(mag) smaller thans(el) how small can s(mag)be?

  9. Electric and magnetic screening from the lattice Nakamura et al, 2004 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 lattice data -Karsch et al- show how Me Vanishes at Tc better) Me>Mm Electrric dominated ME/T=O(g) ES 78 MM/T=O(g^2) Polyakov 79 Why is QGP getting magnetic as T=>Tc?

  10. Strong coupling regime in plasma physics: Gamma= <|Epot|>/<Ekin> >>1gas => liquid => solid • Strongly compressed matter inside Jupiter etc when electrons gets collective • ``dusty plasmas’ at International Space Station • 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)

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

  12. Lattice SU(2) gauge theory, monopoles found and followed by Min.Ab.gauge DeTar 1980’s, Kanazawa and ITEP group… • x-Correlations • give Coulomb like MM potential • First lattice sighting of a liquid! Recent results +- monopole density strongly grows as T=> Tc ++

  13. Our MD for 50-50 MQP/EQP

  14. s(electric) and s(magnetic)do run in opposite directions! • Squares: fitted magnetic coupling, circles: its inverse compared to asymptotic freedom (dashed) • Effective plasma parameter (here for magnetic) • So, the monopoles are never really weakly coupled!

  15. V=F+TS ``potential energy” V(r,T) from Bielefeld/BNL lattice group (Karsch…) • ``tension” nearly 5 times that at T=0 (black line)

  16. Two potentials - two tensions

  17. two types of flux tubes • Stable with supercurrent (no dissipation), • metastable with normal current

  18. F=slow=all level crossing,V=F+TS fast=no level crossing (ES+Zahed,03) • Landau-Zener formula (1932),for transition when 2 levels are crossing with the velocity v12 • Creation of metastable flux tube is possible at and even above Tc

  19. We solve ellipsoidal bags with 2 charges at focal points • ``bag constant” related to potential at any T • This constant is made of two components, condenced and uncondeced monopoles

  20. Condences monopoles <=F

  21. Uncondenced monopoles <= V Direct observation of MAG monopoles wrapping around lattice (time)

  22. dE/dx=V <= Energy loss • v2=<cos2phi> • Nobody was able to get so large v2 if absorbtion is proportional to density • But we do ! • So main dE/dx seems to be near Tc?

  23. So why are collisions so often in sQGP making it the best liquid? Because of magnetic bottle effect: 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)

  24. Indeed, collisions are much more frequent than in cascades two chargesplay ping-pong with a monopole without even moving! Dual to Budker’s magnetic bottle

  25. MD simulation for novel plasma containing both charges and monopoles (Liao,ES hep-ph/0611131)monopole admixture up to M50=50% , 1000 particles, numerically solveddiffusion decreases indefinitely, viscosity does not 50-50 mixture makes the best liquid, as it creates ``maximal trapping”

  26. 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 diffusion • vs theory - AdS/CFT and our MD 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

  27. Understanding monopole dynamics further • Chernodub,V.Zakharov … monopole percolation on the lattice, monopole contribution to e-3p, etc • Claudia Ratti+ES: Higgsing<L(T)> for g,q, tHooft-Polyakov monopoles +lattice data (e.g n(mon,T)) =>masses of q,g,m and s(el,T),s(mag,T) • Marco Cristoforetti +ES: Bose-condensation in strongly interacting liquids => Monopole mass at Tc from Feynman condition

  28. Bose-Einstein condensation of strongly interacting particles(with M.Cristoforetti,now TU Munich) • Feynman theory polygon jumps BEC if ∆S(jump)<Sc (=1.65 for ideal gas, 1.44 from combinatorics of polygons • if used for He4 Tc=3.5K not 2.17 as observed) d • We calculated ``instantons” for particles jumping paths in a liquid and • solid He4 incuding realistic atomic potentials and confirmed by quantum 1-body path int. with/without permutations numerically, to refine conditions when BEC transitions take place Jumping paths: Feynman, interacting Liquid He4 is superfluid, But solid He4 is NOT supersolid,why? <= interacting stronger because of a bit higher density

  29. <=Potential in He4the whole row moves by a=>delta S/atom

  30. 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 =1.44 provides the monopole mass M at Tc M Tc approx 1.5 => M(monopoles) as low as 200 MeV (to be compared to 600-800 MeV for q,g and 1 gev for dyons)

  31. QGP= strongly coupled liquid with record low eta/s, diffusion, large dE/dx Large density of ``normal” (non-Bose-condensed) monopoles near Tc may be the reason (Is it also true in quasi-conformal regime T>2Tc? LHC will tell) Two tensions => two flux tubes => two components of the monopole ensemble, condenced and uncondenced This is the region where electric/magnetic couplings cross 1 Magnetic component is also a liquid! the “most perfect liquid” (because of the magnetic-bottle trapping) for 50-50% electric/magnetic plasma RHIC data on transport (dE/dx, eta/s,D), ADS/CFT and electric/magnetic QGP qualitatively agree! But why? Conclusions

  32. reserve

  33. Do we have Higgsing (<A0>) in QCD at T>Tc in AA collisions? <= its evolution is quite slow • At RHIC the QGP lifetime is about 5 fm/c • (Same for ``mixed phase, same for hadronic)

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