Exploring Hot Dense Matter at RHIC and LHC

Exploring Hot Dense Matter at RHIC and LHC Peter Jacobs Lawrence Berkeley National Laboratory Lecture 3: Collective Flow and Hydrodynamics 6/22/11 Hot Matter at RHIC and LHC - Lecture 3 1

“Hydrodynamic” flow in unusual systems 1. Cornstarch+water (“oobleck”, Non-Newtonian fluid) on an audio speaker: http: //youtu. be/3 zo. TKXXNQIU 2. Stream of sand particles striking a target in symmetric geometry: http: //nagelgroup. uchicago. edu/Nagel-Group/Granular. html 6/22/11 Hot Matter at RHIC and LHC - Lecture 3 2

Elliptic flow of a degenerate Fermi fluid J. Thomas et al. , Duke time Optically trapped atoms degenerate Fermi gas nanokelvin temperature (!) Interactions magnetically tuned to Feshbach resonance infinite 2 -body scattering cross-section prototypical“strongly-coupled” system Prepare the system with spatial anisotropy and let it evolve develops momentum anisotropy “elliptic flow” (!) 6/22/11 Hot Matter at RHIC and LHC - Lecture 3 3

What is fluid dynamics? Fluid dynamics = Conservation of Energy+Momentum for long wavelength modes of excitation breaks down for small or dilute systems Degrees of freedom for a relativistic fluid • fluid velocity um (4 -vector) • pressure p (scalar) • energy density e (scalar) • General relativity: metric tensor gmn Quantum field theory: • Energy-Momentum Tensor: Tmn • Conservation of Energy+Momentum: 6/22/11 Hot Matter at RHIC and LHC - Lecture 3 4

Shear viscosity in fluids Shear viscosity characterizes the efficiency of momentum transport quasi-particle interaction cross section Comparing relativistic fluids: h/s • s = entropy density • scaling param. h/s emerges from relativistic hydro eqns. • generalization for non-rel. fluids: h/w (w=enthalpy) (Liao and Koch, Phys. Rev. C 81 (2010) 014902) 6/22/11 Large s small h/s Strongly-coupled matter ”perfect liquid” Hot Matter at RHIC and LHC - Lecture 3 5

Gauge/string duality and the QGP Ad. S/CFT correspondence (Maldacena ’ 97): conjecture of deep connection in String Theory between strongly coupled non-abelian gauge theories and weak gravity near a (higher-dimensional) black hole Ad. S/CFT correspondence = holography 6/22/11 Hot Matter at RHIC and LHC - Lecture 3 6

Shear viscosity and entropy in String Theory (Ad. S/CFT) h/s of a black hole (M. Natsuume, hep-ph/0700120) Shear visc. ~ cross section: Beckenstein entropy: Universal result: gauge theory plasmas with gravity duals have a universal low value h/s=1/4 p at strong (‘t Hooft) coupling Kovtun, Son and Starinets (KSS), PRL 94, 111601 7 6/22/11 (More precisely: h/s=1/4 p is only Leading Order result for infinite coupling) Hot Matter at RHIC and LHC - Lecture 3

Back to nuclear collisions… STAR 6/22/11 Hot Matter at RHIC and LHC - Lecture 3 8

Collective Flow of QCD Matter Initial spatial anisotropy Final momentum anisotropy py px z y x Interaction of constituents Elliptic flow 6/22/11 Hot Matter at RHIC and LHC - Lecture 3 9

A teaser: v 2 at RHIC v 2 is sizable: ~10% anisotropy Light particles Heavy particles Mass hierarchy vs momentum is characteristic of common velocity distribution Ideal hydro: qualitative agreement but missing the details 10 6/22/11 Hot Matter at RHIC and LHC - Lecture 3

How do we actually measure v 2? STAR Heavy Ion event: Find momentum-weighted plane of azimuthal view in symmetry of the event momentum space (“reaction plane” ΨR ) py px y z x Calculate the momentum-weighted azimuthal asymmetry relative to that plane: 6/22/11 Hot Matter at RHIC and LHC - Lecture 3 11

Wait: can it really be that simple? Actually, no. Initial state is (highly) non-uniform: nucleon correlations, local hot spots of energy density, … Theory calculation: Schenke, Jeon, Gale, PRL 106, 042301 This will bias the measurement of the reaction plane orientation: y 6/22/11 Hot Matter at RHIC and LHC - Lecture 3 z x 12

Another complication: “non-flow” from jets RHIC/Star Large anisotropic contribution to momentum flow in the event But complex and unknown correlation with reaction plane orientation LHC/CMS y 6/22/11 z x Hot Matter at RHIC and LHC - Lecture 3 13

Controlling “non-flow” Want to remove all correlations that are not due to collective flow of many particles: • Measure reaction plane orientation and flow signal in widely separated regions of phase space (large Dh separation) • Compare cumulants of various order: 2, 4, 6, …particle • cumulants are well-known in statistics: isolate true n-particle correlations by removing lower order correlations (e. g. n particles can be mutually correlated due to 2 -particle correlations) Methods are under good control small systematic uncertainties due to “non-flow” correlations 6/22/11 Hot Matter at RHIC and LHC - Lecture 3 14

Elliptic flow v 2: LHC vs RHIC ALICE, PRL 105, 252302 (2010) Striking similarity of p. T-differential v 2 at RHIC and LHC 6/22/11 Hot Matter at RHIC and LHC - Lecture 3 15

Hydrodynamic modeling of a heavy ion collision P. Romatschke, QM 11 Shear viscosity 6/22/11 Bulk viscosity Hot Matter at RHIC and LHC - Lecture 3 16

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v 2: data vs. viscous hydrodynamic modeling Song, Bass, and Heinz, ar. Xiv: 1103. 2380 p. T-differential p. T-integrated central peripheral Preferred values: h/s(RHIC)=0. 16, h/s(LHC)=0. 20 …. . ? ? 6/22/11 Hot Matter at RHIC and LHC - Lecture 3 19

Higher harmonics ALICE ar. Xiv: 1105. 3865 ALICE: v 2 and v 3 have contradictory preferences for h/s not understood 6/22/11 Hot Matter at RHIC and LHC - Lecture 3 20

CMS: similar ambiguities Qualitatively: h/s is within ~2 -3 times 1/4 p Quantitatively: need better theoretical and experimental control for definite measurement 6/22/11 Hot Matter at RHIC and LHC - Lecture 3 21

Shear viscosity: expectations from QCD Analytic: Csernai, Kapusta and Mc. Clerran PRL 97, 152303 (2006) Lattice: H. Meyer, PR D 76, 101701 R (2007) Chiral limit, resonance gas p. QCD w/ running coupling 1/4 p Lattice QCD Temperature (Me. V) 6/22/11 If TLHC > TRHICHot , expect h/s(LHC) > h/s(RHIC) Matter at RHIC and LHC - Lecture 3 22

Remember this plot: QCD calculated on the lattice (m. B=0) Energy density S. Borsanyi et al. , JHEP 1011, 077 (2010) Slow convergence to non-interacting Steffan-Boltzmann limit What carries energy - complex bound states of q+g? “strongly-coupled” plasma? Both flow measurements and Lattice QCD calculations suggest that the Quark-Gluon Plasma at high temperature is very different than a simple gas of non-interacting quarks and gluons Why? What are the dominant degrees of freedom (“quasiparticles”)? We don’t know yet… Cross-over, not sharp phase transition (like ionization of atomic plasma) 6/22/11 Temperature [Me. V] Hot Matter at RHIC and LHC - Lecture 3 23