Theoretical Challenges from RHIC Dublin 29 July 2005

1. A Nearly Perfect Ink !?Theoretical Challengesfrom RHIC Dublin - 29 July 2005 LATTICE 2005 Berndt Mueller (Duke University)

2. Hint: A perfect ink… • Is brilliantly dark and opaque • Yet flows smoothly and easily • A painful challenge to fountain pen designers • A delightful challenge to physicists: • Are the two requirements really compatible?

3. STAR The road to the quark-gluon plasma …Is hexagonal and 2.4 miles long

4. A wealth of … A wealth of … Challenges Challenges Challenges Challenges Challenges Challenges Challenges Challenges Challenges Challenges Challenges Challenges D A T A Two wealths

5. Cornerstone results from RHIC • Anisotropic transverse flow • “Jet” suppression • Baryon/meson enhancement

6. Semiperipheral collisions y Coordinate space: initial asymmetry Momentum space: final asymmetry px x Signals early equilibration (teq 0.6 fm/c) Azimuthal anisotropy v2 py

7. PHENIX Data: Identified p0 No quenching d+Au Quenching! Au+Au Jet quenching in Au+Au

8. RCP baryons mesons pT (GeV/c) f behaves like meson ? (also h-meson) Baryons vs. mesons

9. Overview • QCD Thermodynamics • What are the dynamical degrees of freedom? • Is there a critical point, and where is it? • Thermalization • How can it be so fast? • Transport in a thermal medium • Viscosity, energy loss, collective modes • Hadronization • Recombinationvs. fragmentation

10. T Critical endpoint ? Quark- Gluon Plasma RHIC Chiral symmetry restored Hadronic matter 1st order line ? Color superconductor Chiral symmetry broken B Nuclei Neutron stars QCD phase diagram

11. Bjorken formula teq Space-time picture Pre-equil. phase

12. Stages of a r.h.i. collision • Initial collision ≈ break-up of the coherent gluon field (“color glass condensate”) • Pre-equilibrium: the most puzzling stage • Equilibrium (T > Tc): hydrodynamic expansion in longitudinal and transverse directions • Hadronization: are there theoretically accessible domains in pT ? • Hadronic stage (T < Tc): Boltzmann transport of the hadronic resonance gas

13. ~ 1/Q2 Initial state: Gluon saturation Gribov, Levin, Ryskin ’83 Blaizot, A. Mueller ’87 McLerran, Venugopalan ‘94 “Color glass condensate (CGC)” Details of space-time picture depend on gauge!

14. CGC dynamics Initial state occupation numbers ~ 1/as 1 → classical fields generated by random color sources on light cone: Boost invariance → Hamiltonian gauge field dynamics in transverse plane (x,t). 2-dim lattice simulation shows rapid equipartitioning of energy (teq ~ Qs-1). Krasnitz, Nara & Venugopalan; Lappi (hep-ph/0303076 ) Challenge: (3+1) dim. simulation without boost invariance

15. Kharzeev & Levin Pseudorapidity h = - ln tan q Rapidity y = ln tanh(E+pL)/(E-pL) Saturation and dN/dh Assume nucleus is “black” for all gluons with kT Qs: Qs(x) → Qs(y) with x = Qse-|Y-y| . Also predicts beam energy dependence of dN/dy. Challenge: How much entropy is produced by simple decoherence, how much during the subsequent full equilibration?

16. The(rmalization) mystery • Experiment demands: tth 0.6 fm/c • “Bottom up” scenario (Baier, A. Mueller, Schiff, Son): • “Hard” gluons with kT ~ Qs are released from the CGC; • Released gluons collide and radiate thermal gluons; • Thermalization time tth ~ [as13/5Qs]-1≈ 2-3 fm/c • Perturbative dynamics among gluons does not lead to rapid thermalization. • Quasi-abelian instability (Mrowczynski;Arnold et al; Rebhan et al): • Non-isotropic gluon distributions induce exponentially growing field modes at soft scale k ~ gQs ; • These coherent fields deflect and isotropize the “hard” gluons.

17. After thermalization… ... matter is described by (relativistic) hydrodynamics ! Requires lf L and small shear viscosity h. HTL pert. theory (nf=3): Dimensionless quantity h/s. Classical transp. th.: h≈ 1.5rTlf, s ≈ 4r→ h/s ≈ 0.4Tlf. (Baym…; Arnold, Moore & Yaffe)

18. Semiperipheral collisions y Coordinate space: initial asymmetry Momentum space: final asymmetry px x Signals early equilibration (teq 0.6 fm/c) Azimuthal anisotropy v2 py

19. h – How small can it be? D. Teaney Boost invariant hydro with T0t0 ~ 1 requires h/s ~ 0.1. N=4 SUSY Yang-Mills theory (g1): h/s = 1/4p (Kovtun, Son, Starinets). Absolute lower bound on h/s ? h/s = 1/4p implies lf≈ (5 T)-1 ≈ 0.3 d QGP(T≈Tc) = sQGP Challenge: (3+1) dim. relativistic viscous fluid dynamics

20. Nakamura & Sakai Method: spectral function repr. of Gb and Gret, fit of spectral fct. to Gb. Related (warm-up?) problem: EM conductivity s ≈ q2rlf/2T. nf = 3 QGP → h/s≈ 20 T2. Caveat: lf(glue)  lf(quarks) SU(3) YM First attempts Challenge: Calculate h/s for real QCD

21. 20% QCD equation of state Challenge: QCD e.o.s. with light domain wall quarks Challenge: Devise method for determining n from data Challenge: Identify the degrees of freedom as function of T Is the (s)QGP a gaseous, liquid, or solid plasma ?

22. A possible method BM & K. Rajagopal, hep-ph/0502174 Eliminate T from e and s : Lower limit on n requires lower limit on s and upper limit on e.

23. Measuring e and s • Entropy is related to produced particle number and is conserved in the expansion of the (nearly) ideal fluid: dN/dy → S→ s = S/V. • Energy density is more difficult to determine: • Energy contained in transverse degrees of freedom is notconserved during hydrodynamical expansion. • Focus in the past has been on obtaining a lower limit on e; here we need an upper limit. • New aspect at RHIC: parton energy loss. dE/dx is telling us something important – but what exactly?

24. Entropy • Two approaches: • Use inferred particle numbers at chemical freeze-out from statistical model fits of hadron yields; • Use measured hadron yields and HBT system size parameters as kinetic freeze-out (Pratt & Pal). • Method 2 is closer to data, but requires more assumptions. • Good news: results agree within errors: • dS/dy = 5100 ± 400 for Au+Au (6% central, 200 GeV/NN) → s = (dS/dy)/(pR2t0) = 33 ± 3 fm-3

25. PHENIX Data: Identified p0 No quenching d+Au Quenching! Au+Au Jet quenching in Au+Au

26. High-energy parton loses energy by rescattering in dense, hot medium. q q Scattering power of the QCD medium: “Jet quenching” = parton energy loss Radiative energy loss: L Scattering centers = color charges q q Density of scattering centers g Range of color force

27. Data suggest large energy loss parameter: Eskola, Honkanen, Salgado & Wiedemann Dainese, Loizides, Paic RHIC pT = 4.5–10 GeV Energy loss at RHIC

28. ˆ ˆ ˆ q q q RHIC data sQGP QGP Pion gas The Baier plot • Plotted against e, is the same for a p gas and for a perturbative QGP. • Suggests that is really a measure of the energy density. • Data suggest that may be larger than compatible with Baier plot. • Nonperturbat. calculation is needed. Cold nuclear matter Challenge: Realistic calculation of gluon radiation in medium

29. x quark x - a b + Eikonal formalism Kovner, Wiedemann x Gluon radiation: x = 0

30. Eikonal form. II Challenge: Compute F+i(x)F+i(0) for x2 = 0 on the lattice Not unlike calculation of gluon structure function, maybe moments are calculable using euclidean techniques.

31. Where does Eloss go? STAR p+p Au+Au Away-side jet Trigger jet Lost energy of away-side jet is redistributed to rather large angles!

32. Angular distribution depends on energy fraction in collective mode and propagation velocity T. Renk & J. Ruppert Wakes in the QGP J. Ruppert and B. Müller, Phys. Lett. B 618 (2005) 123 Mach cone requires collective mode with w(k) < k: • Colorless sound • Colored sound = longitudinal gluons • Transverse gluons

33. RCP baryons mesons pT (GeV/c) f behaves like meson ? (also h-meson) Baryons vs. mesons

34. Fragmentation Recombination Hadronization mechanisms

35. Baryons compete with mesons Recombination wins… … for a thermal source Fragmentation dominates for a power-law tail

36. Quark number scaling of v2 In the recombination regime, meson and baryon v2 can be obtained from the quark v2 :

37. D D fragmentation recombination Hadronization RHIC data (Runs 4 and 5) will provide wealth of data on: • Identified hadron spectra up to much higher pT (~10 GeV/c); • Elliptic flow v2 up to higher pT with particle ID; • Identified di-hadron correlations; • Spectra and v2 for D-mesons…. Challenge: Unified framework treating recombination as special case of QCD fragmentation “in medium”. A. Majumder & X.N. Wang, nucl-th/0506040

38. Some other challenges • Where is the QCD critical point in (m,T)? • What is the nature of the QGP in Tc < T < 2Tc ? • How well is QCD below Tc described by a weakly interacting resonance gas? • Thermal photon spectral function r(m2,T). • Are there collective modes with w(k) < k ? • Can lattice simulations help understand the dynamics of bulk (thermal) hadronization?

39. Don’t be afraid… “Errors are the doors to discovery” James Joyce

40. Back-up slides

41. Hard-soft dynamics Nonabelian Vlasov equations generalizing “hard-thermal loop” effective theory. Can be defined on (spatial 3-D) lattice with particles described as test charges or by multipole expansion (Hu & Müller, Moore, Bödeker, Rummukainen). Poss. problem: short-distance lattice modes have wrong w(k). k ~ gQs k ~ Qs Challenge: Full (3+1) dim. simulation of hard-soft dynamics

42. Quark distribution function at “freeze-out” For a thermal distribution, the hadron wavefunctions can be integrated out, eliminating the model dependence of predictions. Remains exactly true even if higher Fock states are included! Reco: Thermal quarks Relativistic formulation using hadron light-cone frame:

43. Heavy quarks • Heavy quarks(c, b) provide a hard scale via their mass. Three ways to make use of this: • Color screening of (Q-Qbar) bound states; • Energy loss of “slow” heavy quarks; • D-, B-mesons as probes of collective flow. RHIC program: c-quarks and J/Y; LH”I”C program: b-quarks and . • RHIC data for J/Y are forthcoming (Runs 4 & 5).

44. Quenched lattice simulations, with analytic continuation to real time, suggest Td 2Tc ! S. Datta et al. (PRD 69, 094507) Karsch et al. J/Y suppression ? Vqq is screened at scale (gT)-1  heavy quark bound states dissolve above someTd. Color singlet free energy Challenge: Compute J/Y spectral function in unquenched QCD

45. J/Y RHIC LHC RHIC  LHC C-Cbar kinetics J/Y,  can be ionized by thermal gluons. If resonances persist above Tc, J/Y and  can be formed by recombination in the medium: J/Y may be enhanced at LHC! Challenge: Multiple scattering theory of heavy quarks in a thermal medium Analogous to the multiple scattering theory for high-pT partons, but using methods (NRQCD etc.) appropriate for heavy quarks.