1. Introduction to heavy ion physics (NPII_06) lect.3 Edward Shuryak Department of Physics and Astronomy State University of New York Stony Brook NY 11794 USA

2. Why study the heavy ion physics? A ``Bang” like other magnificent explosions like Supernova or Big Bang New form of matter formed, the Quark-Gluon Plasma It is different from the QCD vacuum phase New spectroscopy, in spite of deconfinement and With restored chiral symmetry Relation to other fields: plasma physics, strongly coupled atoms, string theory

3. The theoretical tools we will need Finite T field theory Finite T QCD and lattice formulation Hydrodynamics Transport phenomena (freezeout) and coefficients (viscosity) Jet quenching: dE/dx and its origin

4. Cooling of the Universe (in the inverse order in time) T>1 ev ( or 10^4 K) time< 300000 years: atoms cannot exist. After atoms are created, the photons propagate unscattered till today, and we see them as T=2.7K “background radiation” T=1-0.05 MeV: time=few mins, size of Universe is about a Solar system. Light nuclei (d,He…Li^7) are created T>170 MeV: time 10^(-5) sec, Universe size about 3 km. Before that there was no “elementary particles” such as protons, neutrons, pions, and the matter was in a Quark-Gluon Plasma phase T>200 GeV quarks,leptons and W,Z get massless: the last phase transition we think we understand. We will not discuss electroweak phase transition in these lectures.

5. The Big vs the Little Bang Big Bang is an explosion which created our Universe. Entropy is conserved because of slow expansion Hubble law v=Hr for distant galaxies. H is isotropic. “Dark energy” (cosmological constant) seems to lead to accelrated expansion Little Bang is an explosion of a small fireball created in high energy collision of two nuclei. Entropy is also conserved Also Hubble law, but H is anisotropic The ``vacuum pressure” works against QGP expansion (And that is why it was so difficult to produce it)

6. Two main phases of Quantum Chromodynamics (QCD) The vacuum phase: Quarks and gluons cannot propagate free but are confined into hadrons (mesons and baryons) with zero total color. Color charges are “confined” Attempts to separate them lead to creation of a string between charges and a potential V=Kr Another feature of the vacuum: quark pairs are condensed, like Cooper pairs in superconductor => Broken chiral symmetry by a ``quark condensate” In QGP phase quarks and gluons are deconfined and they can propagate as “quasiparticles”. The color charges are “screened” at large distances (ES,1978), while also being antiscreened at small ones (Politzer, Gross and Wilczek 1973) New spectroscopy: Recently we learned that at not too high T=(1-4)T c quasiparticles can also be bound in pairs, but in this case a nonzero color is allowed and such states in fact dominate High density phases of color superconductivity we will not discuss

7. The vacuum vs QGP, continued The vacuum is very complicated, dominated by ``topological objects” Vortices, monopoles and instantons Among other changes it shifts its energy down compared to an “empty” vacuum, known as The Bag terms: p=#T 4 -B  =3#T 4 +B The QGP, as any plasma, screens them, and is nearly free from them So, when QGP is produced, the vacuum tries to expel it (recall here pumped out Magdeburg hemispheres By von Guericke in 1656 we learned at school)

8. Magdeburg hemispheres 1656 We cannot pump the QCD vacuum out, but we can pump in something else, namely the Quark- Gluon Plasma

9. Diquarks as a Feshbach resonance Point S has the maximal Tc/Mu Line of qq marginal stability befurkates Line with point D is de- binding of Cooper pairs

10. Our map: the QCD Phase Diagram T The lines marked RHIC and SPS show the paths matter makes while cooling, in Brookhaven (USA) and CERN (Switzerland) Chemical potential mu Theory prediction (numerical calculation, lattice QCD, Karsch et al) the pressure as a function of T (normalized to that for free quarks and gluons)

11. The zigzags on the phase diagram Both bar.charge and entropy are conserved: n_b/s=const(t) In resonance gas and QGP different formulae: curves do not meet at the critical line Of course they are connected inside the mixed phase –heating while expanding due to latent heat A decade old plot From C.M.Hung and ES, hep-ph/9709264,PRC

12. Crude zigzags start to appear, but far from being accurate enough… Effective eos along the line s/n_b=const also have a minimum at e=1 GeV/fm^3

13. Macro theory expects 3 special points in an energy scan, not 1! (Macro theory=collision of very large nuclei, so hydro is valid without doubt…) Focusing effect See below longest expansion, K/pi V2 stops rising, Elab about 5 GeV*A

14. The same thing in log(s)-log(n) coordinates (now the cooling lines are simple, but the thermodynamics is tricky) Black=true

15. RHIC : a view from space A dedicated collider for (i)Heavy ion collisions, AuAu 100+100 GeV/N (ii) Polarized pp, 250+250 GeV

16. Relativistic Heavy Ion Collider Two counter rotating beams in two rings, 6 crossing points Multiple magnets of the ring are all At the liquid He Temperature – the main Expence during the runs

17. Two large experiments +2 small PHENIX 2 e and 2 muon arms STAR Large tracking TPC

18. One of the first RHIC events at STAR detector, The average multiplicity at AuAu 200 GeV/N Is about 5000

19. Many measurements (up to high p T !) from all 4 detectors

20. Main findings at RHIC Partciles are produced from matter which seems to be well equilibrated (by the time it is back in hadronic phase), N1/N2 =exp(- (M_1-M_2)/T) Very robust collective flows, well described by ideal hydro with Lattice-based Equation of state (EoS). This indicates very strong interaction even at early time => sQGP Jet quenching: Quarks and gluons with high energy (jets) do not fly away freely but are mostly (up to 90%) absorbed by the matter. The released energy partly go to hydrodynamical ``conical flow” or sound waves rather than gluons.

21. Most importantly, we definitely produced ``matter”: (while many skeptics predicted otherwise) The main condition for that: l << L (the micro scale) << (the macro scale) (the mean free path) << (system size) (relaxation time) << (evolution duration) I the zeroth order in l/L is ideal hydro with a local stress tensor. Viscosity appears as a first order correction l/L, it has velocity gradients. (Note that it is inversely proportional to the cross section and thus is the oldest strong coupling expansion)

22. If so, Hydrodynamics is simple! Static EoS from Lattice QCD Finite T,  field theory Critical phenomena Dynamic Phenomena Expansion, Flow Space-time evolution of thermodynamic variables Once we accept local thermalization, life becomes very easy. Why and when the equilibration takes place is a tough question one has to answer Local Energy-momentum conservation: Conserved number:

23. Example of Hydro (with Jet Quenching) Color: parton density Plot: mini-jets Au+Au 200AGeV, b=8 fm transverse plane@midrapidity Fragmentation switched off hydro+jet model Hydro+Jet model (T.Hirano & Y.Nara (’02)) x y

24. How Hydrodynamics Works at RHIC Explosion goes in all directions Radial and especially Elliptic flow The red almond-shaped region is where the dense matter is. Yellow region shows “spectators” which fly by without interaction The so called “jet tomography” of the initial shape of the matter

25. “elliptic flow” works as a barometer which measures the pressure of QGP Origin: spatial anisotropy of the system when created, followed by multiple scattering of particles in the evolving system spatial anisotropy  momentum anisotropy v 2 : 2 nd harmonic Fourier coefficient in azimuthal distribution of particles with respect to the reaction plane Almond shape overlap region in coordinate space

26. More on Elliptic Flow See recent reviews, P.Huovinen (QM2002), nucl-th/0305064; P.Kolb and U.Heinz, nucl-th/0305084; E.Shuryak, hep-ph/0312227 Hydro: P.Kolb et al.(’99) (Note: Hydro+RQMD gives a better description. D.Teaney et al.(’01)) STAR, PRC66(’02)034904 Hydro: P.Huovinen et al.(’01) PHENIX, PRL91(’03)182301.

27. Viscosity of QGP QGP at RHIC seem to be the most ideal fluid known, viscosity/entropy =.1 or so water would not flow if only a drop with 1000 molecules be made viscous corrections 1 st order correction to dist. fn.: :Sound attenuation length Velocity gradiants Nearly ideal hydro !? D.Teaney(’03)

28. What is needed to reproduce the magnitude of v 2 ? Huge cross sections!!

29. How to get 50 times pQCD  gg ? quark bound states don’t all melt at Tc all q,g have strong rescattering qqbar  meson Resonance enhancements (Zahed and ES,2003) Huge cross section due to resonance enhancement causes elliptic flow of trapped Li atoms

30. 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” The coolest thing on Earth, T=10 nK or 10^(-12) eV can actually produce a Micro-Bang !

31. 3 more strongly coupled systems N=4 Supersymmetric Yang-Mills Cold trapped atoms in Feshbach resonance (a=>1) Classical plasma with  =(Ze) 2 /RT>>1 is a very good liquid, up to 300, with very small viscosity at  » 10 where it has a deep minimum