Quark-Gluon Plasma From Concepts To “Precision” Science

1. Quark-Gluon PlasmaFrom ConceptsTo “Precision” Science Berndt Mueller RHIC Users Meeting BNL - March 28, 2008

2. Part 1… The Quest for the Quark-Gluon Plasma

3. T Critical point? RHIC Quark- Gluon Plasma Color superconductor quark-gluon plasma Chiral symmetry restored Hadronic matter 1st order line Chiral symmetry broken nucleons + mesons B Nuclei Neutron stars Melting nuclear matter QCD phase diagram

4. gluons quarks spin color spin color flavor 170 340 510 MeV RHIC Weak or strong coupling? Lattice QCD QCD equation of state

5. The QCD EoS (at =0) The precise value of Tc is still under debate: Tc = 170 ± 20 MeV with 20 - 30 MeV width. EoS near Tc is far from ideal ultrarelativistic gas! Sound velocity cs2 = P/ << 1/3.

6. pQGP Lattice - susceptibilities Eijiri Karsch Redlich QCD matter above Tc may be a highly correlated system, but what is correlated are quarks and not hadrons! (What about gluons?)

7. Part 2… The 6 Stages of the Collision

8. hadronic phase and freeze-out QGP and hydrodynamic expansion initial state pre-equilibrium hadronization teq Pre-equil. phase Liberation of saturated low-x glue fields (CGC) A multi-stage reaction

9. Stage 1 Decoherence of the initial state

10. None of these components of the baryon wave function are calculable… …but this one is, because it contains a large scale The initial state The Color Glass Condensate model is based on a brilliant idea: What applies to the proton (at high energy!), applies much better to a large nucleus, and at lower energy, because the gluon density per area is enhanced by a factor A1/3.

11. ~ 1/Q2 /sat x Gluon saturation Gribov, Levin, Ryskin ’83 Blaizot, A. Mueller ’87 McLerran, Venugopalan ‘94 Universal saturated state at small x: Qs >> QCD “Color glass condensate” (CGC) Evolution in x is described by BK or JIMWLK equations. Location of the onset of saturation is determined by fluctuations (Iancu, Peschanski,…) p A

12. CGC: Gluon production Krasnitz-Nara-Venugopalan, Lappi, Gelis Fields carried by moving sources interact non-linearly and generate classical spectrum of gluonic modes. This requires numerical solution of YM eqs. with CGC initial cond’s. Classical 2-particle rapidity correlations (Dumitru et al. ‘08) Simulation of T(x,t) possible.

13. Stage 2 Entropy: From 0 to (dS/dy=) 5000 in 0.000 000 000 000 000 000 000 002 seconds

14. Final entropy Phase space analysis (Pal & Pratt): Bjorken’s formula Chemical analysis (BM & Rajagopal): Assuming isentropic expansion up to Tch, averaging over R2 with R = 7 fm, and using lattice EOS: How is this entropy produced?

15. Decoherence Coherent state: Counting causally disconnected transverse domains: In D dimensions after equilibration: Clearly, fully 3-dimensional equilibration is essential - how and when?

16. 1/Qs From 2D to 3D Nielsen-Olesen instability of longitudinal color-magnetic field (Itakura & Fujii, Iwazaki)

17. r r v v Weibel instability

18. Exponential growth saturates when B2 > g2 T4. Turbulent power spectrum Color “turbulence” Wavelength and growth rate of unstable modes can be calculated perturbatively: kz ~ gQs , g ~ gQs < kz Mrowczynski Rebhan,Romatschke, Strickland Arnold, Moore, Yaffe Dumitru, Schenke

19. Color correlation length Time Non-abelian Quasi-abelian Noise Length (z) Turbulent color fields M. Strickland, hep-ph/0511212 Extended domains of coherent color field can create “anomalous” contributions to transport coefficients and accelerate equilibration (as in EM plasmas).

20. Stage 3 The (almost) perfect liquid

21. z Reaction plane y x • Elliptic flow (v2): • Gradients of almond-shape surface will lead to preferential expansion in the reaction plane • Anisotropy of emission is quantified by 2nd Fourier coefficient of angular distribution: v2 • prediction of fluid dynamics Collision Geometry: Elliptic Flow • Bulk evolution described by relativistic fluid dynamics, • assumes that the medium is in local thermal equilibrium, • but no details of how equilibrium was reached. • Input: e(x,ti), P(e), (h,etc.).

22. Mass splitting characteristic property of hydrodynamics v2(pT) vs. hydrodynamics

23. Elliptic flow “measures”hQGP Relativistic viscous hydrodynamics: Boost invariant hydrodynamics with T0t0 ~ 1 requires h/s ≤ 0.1 Small shear viscosity implies: The QGP is an almost perfect liquid Romatschke & Romatschke

24. String theory weighs in General argument [Kovtun, Son & Starinets, PRL 94 (2005) 111601] based on duality between thermal QFT and string theory on curved background with the “black-brane” metric: (3+1)-D world (t,x) (0,0) r0 horizon Dominated by absorption of (thermal) gravitons by the black hole:

25. An age-old problem solved! Unfortunately, this renders relativistic viscous hydrodynamics a-causal ! Solution, in principle: include time derivatives (Israel,Stewart, Müller - 1960s). Full second-order expression for shear stress in conformal limit finally given by Baier, Romatschke, Son, Starinets & Stephanov (arXiv:0712.2451):

26. Peq PT PL     Viscosity of RHIC R.J.Fries, BM, A. Schäfer, tbp

27. Stage 4 Hadronizing the Quark-Gluon Plasma

28. Failure of ideal hydrodynamics tells us how hadrons form v2(pT) vs. hydrodynamics

29. T,m,v Quark number scaling of v2 In the recombination regime, meson and baryon v2 can be obtained from the quark v2 : Emitting medium is composed of unconfined, flowing quarks.

30. CEP Observables After Freeze-out, no effect of final state interactions Critical point? T B • Observables that are not be sensitive to final state interactions Critical fluctuations, the primary signature of the CEP, are modified During expansion until chemical or kinetic freeze-out, in addition to being suppressed near CEP by critical slowing down. • usually assumed to be • momentum independent Chemical Freeze-out • but this is not right chemical freeze-out time is pT (or yT) dependent • Larger pT (or yT), earlier ch. Freeze-out

31. Emission Time Distribution Emission Time • Larger yT, earlier emission • To minimize resonance effect, • yT is used instead of pT • No CEP effect (UrQMD)

32. Focus on chemistry pT ratio near CEP falling with pT Tc Tc Asakawa, Bass, BM, Nonaka ‘08

33. RHIC can do it!

34. Part 3… Probing the structure of the Quark-Gluon Plasma

35. q q Scattering power of the QCD medium: Energy loss in QCD Radiative energy loss: Density of scattering centers Range of color force Nonradiative energy loss:

36. ASW HT AMY ~10 ~2 ~4 T3 ~20 ~4 3/4 Towards q-hat 3-D ideal hydrodynamics with radiative energy loss only Bass, Majumder, Qin, Renk et al. (tbp) Numbers change by up to factor of 2, depending on whether q-hat is scaled with T3, s, or 3/4 ! Other unresolved issues: Consistent treatment of virtuality of parton created by hard scattering; Nature of scattering centers

37. RAA vs. reaction plane Closing in on q-hat More differential measurements of jet quenching with very high statistics are needed, as well as consistent theories of jet quenching for these observables. Bass et al. Zhang et al. (using higher twist energy loss theory + back-to-back coincidences)

38. collisons radiation coll+rad collisons radiation coll+rad Collisions + radiation Qin, Ruppert, Gale, Jeon, Moore & Mustafa, PRL 100,072301 (2007) Inclusion of collisional energy loss leads to reduction of s from 0.33 to 0.27, corresponding to a reduction of extracted value of q-hat by 33%. Contributions from collisional and radiative energy loss may be separated due to their different fluctuations (Poisson vs. intermittent) by comparing singles quenching (RAA) with coincident back-to-back quenching (IAA), and by their different quark mass dependence by comparing with charm RAA.

39. With p ~ 3T and s  3.6(for gluons) one finds: A. Majumder, BM, X-N. Wang, PRL 99 (2007) 192301 From RHIC data: Connecting jets with the medium Hard partons probe the medium via the density of colored scattering centers: If kinetic theory applies, thermal gluons are quasi-particles that experience the same medium. Then the shear viscosity is: In QCD, small angle scattering dominates:

40. What happens here ?!? An interesting question • How does a fast parton interact with the quark- gluon plasma ? • What happens to the energy and momentum lost by a fast parton on its passage through the hot medium ? • How does the energy and momentum perturbation of the medium propagate ? Trigger jet Back jet Hard scattering Thanks to: E. Wenger (PHOBOS)

41. Color field of moving parton interacts with the quanta of the medium Parton-medium coupling Space-time distribution of collisional eneregy loss

42. Unscreened source For an unscreened color charge, an analytical result is obtained in u1 limit: R.B. Neufeld Spatial integral over deposited energy and momentum distribution equalscollisional energy loss; radiated gluons increase effective color charge.

43. Linearized hydro Linearize hydro eqs. for a weak source: T00  + , T0i  gi . Solvein Fourier space for longitudinal sound: … and dissipative transverse perturbation: See: J. Casalderrey-Solana, E.V. Shuryak and D. Teaney, arXiv:hep-ph/0602183

44. pQCD vs. N=4 SYM u = 0.99955 c  (z - ut) Neufeld et al. arXiv:0802.2254  Chesler & Yaffe arXiv:0712.0050 u = 0.75 c

45. Plasma behind jet: Correlated flow, not just thermal ! [Xu & Greiner] [Arnold, Moore & Yaffe (AMY)] Mach cone: cs and η

46. Away side shape modification Central Au+Au 0-12% (STAR) 2.5 < pTtrig< 4 GeV/c 1< pTassoc < 2.5 GeV/c (1-2)/2 RHIC data Technique: Measure 2- and 3- particle correlations on the away-side triggered by “high” pT hadron in central coll’s. Cone-shaped emission should show up in 3-particle correlations as signal on both sides of backward direction.

47. Summary 1 • The RHIC program has shown that • equilibrated matter is rapidly formed in heavy ion collisions; • new, powerful probes become available at collider energies; • systematic study of matter properties is possible. • QGP appears to be a strongly coupled, maybe turbulent color liquid with novel and unanticipated transport properties. • Experimental and theoretical surprises have opened a gold mine for theorists: • extreme opaqueness of matter to colored probes; • collective flow phenomena; • collective medium response to jets; • large enhancement of baryon production; • connection to string theory and AdS/CFT duality.

48. Summary 2 • Ultimate success of the RHIC program requires: • precision data for key (often rare) observables; • continued progress of our understanding of thermal QCD; • sustained collaboration between theorists and experimentalists on precision data interpretation. • Superficially different observables (flow, jet quenching, two-particle correlations) are connected at a deep level. • Their exploration in a comprehensive framework will lead to deep insights into how bulk QCD matter behaves and, ultimately, to the fulfillment of the scientific promise of RHIC. • The LHC heavy ion program will help resolve ambiguities, due to its extended kinematic range for critical observables.

49. Summary 3 Experimental and theoretical surprises have opened a gold mine for theorists, but to extract the gold, painstaking work will be required in collaboration between theorists and experimentalists. The first steps have been taken: For report and details see: https://wiki.bnl.gov/TECHQM/index.php/Main_Page

50. THE END