1 / 45

A Nearly Perfect Ink !? Theoretical Challenges from RHIC

A Nearly Perfect Ink !? Theoretical Challenges from RHIC. Dublin - 29 July 2005 LATTICE 2005. Berndt Mueller (Duke University). Hint:. A perfect ink…. Is brilliantly dark and opaque Yet flows smoothly and easily A painful challenge to fountain pen designers

gili
Download Presentation

A Nearly Perfect Ink !? Theoretical Challenges from RHIC

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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.

More Related