Experimental investigations of relativistic hydrodynamics and the ideal fluid scenario at RHIC

Transkript

1 Experimental investigations of relativistic hydrodynamics and the ideal fluid scenario at RHIC Juan F. Castillo Hernandez Relativistische Schwerionenphysik Seminar Juan Castillo RHI seminar 1

2 Outline Introduction Relativistics Hydrodynamics and the Equation Of State (EOS) Heavy Ion Collisions (HIC) Initial Conditions: the Bjorken picture and the Landau picture Hidrodynamic evolution, freeze-out conditions and flow Hadron spectra and flow: low viscosity (agree with the ideal fluid) Radii (HB puzzle) Mixed approaches (parton cascade, hadron cascade) Connections with Cold Atoms Summary Juan Castillo RHI seminar

3 Introduction : Relativistic Hydro A non-relativistic ideal fluid: Continuity ρ + t A relativistic ideal fluid Current conservation μ ( ρv) = 0 Navier-Stokes Energy-momentum conservation Assumptions to have it ideal: We can define local 4-velocity Small variations in space-time Local thermal equilibrium Equation Of State (EOS) t x ( ρv ) + Π = 0 = 0 μ J μ = 0 i μν i ij See "K. Heckmann - Relativistic hydrodynamics and the Bjorken model ()" Juan Castillo RHI seminar 3

4 Juan Castillo RHI seminar 4 Introduction : the EOS General relation: p(x) = p(є(x),n(x)) p(x) pressure Є(x): local energy density n(x): baryon density x = (t,x) (spacetime) EOS I: "hot"ideal gas of massles partons EOS H: "cold" Hagedorn hadron resonance gas EOS Q: Connection of EOS I and EOS H via a firstorder phase transition Stefan-Boltzmann approach: ) ( 90 ) ( 4 1 Δ = = = = = g B g P P B g P P c c H C H c c I C I c π π π

5 HIC: Bjorken vs Landau Spacetime picture(s) Landau Hydrodynamics Expanding Fireball Bjorken Hydrodynamics Longitudinal flow "pancakes" Juan Castillo RHI seminar 5

6 HIC: Bjorken vs Landau Landau assuptions: Full thermalization in the whole volume Ideal EOS (p= Є/3) All chemical potentials (baryon, meson) zero Bjorken assuptions: space-time evolution: the same in all center-of-mass frames symmetry "leading baryon" effect (baryon number found in the pancakes) one dimensional flow Initial conditions: gaussian entropy density (ds/dη) in the whole rapidity Resulting in: Gaussian dn/dη Resulting in: dn/dη constant entropy is constant of the motion ( τ ) τ = ( τ ) 0 τ s s EOS not ideal Є =3p Є >3p Juan Castillo RHI seminar 6

7 HIC: the hydro evolution Hydrodynamic range "Crossing" Expansion and cooling Hadronization Inelastic dispersions Elastic dispersions τ 0 ~1 fm/c Initial conditions: - Є 0 ~ 10 GeV/fm 3 (SAR 30-60) - 0 ~ MeV - ρ 0 ~ -0 fm -3 (see PHENIX white paper)? QGP hadrons: - C ~ MeV τ ch ~10 fm/c τ fo ~1 fm/c Chemical Freeze-out: - ch ~ 160 MeV - ρ ch ~ 0.1 fm -3 Kinetic Freeze-out: FO ~ MeV Juan Castillo RHI seminar 7

8 HIC: freeze-out conditions freeze-out interactions cease inelastic interactions chemical freeze-out particle rates elastic interactions kinetic freeze-out particle spectra n V j = (J + 1) j 3 ( ) π μ = μ Q + μ B + μ S j p + m j + μ j exp Q j if abundances determined by thermodynamical equilibrium particle ratios described by two parameters:, µ B B d 3 j p S ± 1 j What about data? first approach: Boltzmann fit m : transverse mass, m: mass 1 m dn dm m exp( FO freeze-out temperature particle-independent? What is transverse flow? + apparent temperature kinetic freeze-out temperature ) 1 m < v > transv. flow velocity Juan Castillo RHI seminar 8

9 HIC: Chemical freeze-out chemical freeze-out particle rates SAR: central 00 GeV Au+Au ch = 163 ± 4 MeV μ B = 4 ± 4 MeV γ s = 0.99 ± 0.07 MeV Where: γ s strangeness undersaturation factor: for each particle, a factor γ s N(s+s) e.g.: [Becattini et al.: hep-ph/ ] Juan Castillo RHI seminar 9

10 HIC: Chemical freeze-out ch = 165 MeV ( μ B = 0) Juan Castillo RHI seminar 10

11 HIC: kinetic freeze-out dn/dydm (particle spectra) SAR: mid-rapidity, 00 GeV Au+Au After fit: Ω and φ give higher..but thermal spectra, by themselves, do not imply thermalization or collectivity! let's have a more detailed look!! m mass = p c + mass mass Juan Castillo RHI seminar 11

12 HIC: Kinetic freeze-out kinetic freeze-out particle spectra data from NA35 S+S 00 A GeV Wrong approach! he inverse slope, or apparent temperature increases with the particle mass Juan Castillo RHI seminar 1

13 HIC: Blast wave model & flow A more detailed model is needed. Let's describe m distribution as combined result of thermal motion () collective transverse expansion (β) Blast wave model d N m dydm j RG mt cosh ρ pt sinh ρ = Ajm K1 I0 rdr 0 1 ρ( r) = tanh β ( r) β ( r) = β S r R G n r R G β r (r) : transverse velocity distribution β s : surface velocity ρ(r) : boost angle no flow β s = 0 ρ = 0 d N m dydm m exp( ) there is flow [Schnedermann et al.: Phys. Rev. C48 (1993) 46] NA GeV, 10% cent y (0% for W); constant velocity profile (n=0) Juan Castillo RHI seminar 13

14 HIC: transverse and elliptic flow transverse flow: β elliptic flow: v y Au Au x coordinate space elipticity p y ε = y y + x x p x SAR, 00 GeV Au +Au, showing centrality bins Higher strangeness as a probe of early stages momentum space dn/dφ = 1 + V cos (φ - ψ) Juan Castillo RHI seminar 14

15 HIC: elliptic flow elliptic flow: v SAR, 00 GeV Au +Au dashed: hydro calculations, assuming: - early thermalization - ideal fluid expansion - phase transition ( c = 165 MeV) -EOS Q - Kinetic FO = 130 MeV Juan Castillo RHI seminar 15

16 HIC: elliptic flow dn/dφ elliptic flow (v ) SAR, 00 GeV Au +Au, dashed: analytical fit dotted: hydro calculations Low p : ideal fluid with low viscosity (null) High p : hydro doesn't work? Juan Castillo RHI seminar 16

17 HIC: elliptic flow dn/dφ elliptic flow (v ) CGC Glauber CGC: reats the nucleus as a saturated gluon field From Hallman, QM' Juan Castillo RHI seminar 17

18 HIC: elliptic flow dn/dφ elliptic flow (v ) mid-rapidity, mid-central A ~ 00 AGS, SPS, RHIC Hydro limits: assuming no phase transition! Juan Castillo RHI seminar 18

19 RHIC data: Radii (HB puzzle) Hydro should be coherent with -particle correlation measurements (HB) SAR measurements from pion HB correlations, central Au+Au (using Bertsch- Partt parameters R long,r side, R out )... C [ ] q ( q K ) = 1+ exp R ( K ) q R ( K ) q R ( K ), out out side side long long correlation function, with q = p 1 +p, K= (p 1 +p )/ Juan Castillo RHI seminar 19

20 RHIC data: Radii (HB puzzle) Possible solutions to HB puzzle: 1) the collective flow does not last in reality as long as considered in hydro ) hydrodynamics is NO responsible of the observed v 3) freeze-out in hydro ton realistic (hyperspace moving inwards) 4) short-lived resonances 5) Gauss initial distribution instead of Glauber 6) Measure the viscosity, use an hybrid model... Can we measure the viscosity of this "ideal" fluid? Not up to now! Solution 1) heory shear viscosity of a classical massless gas with constant σ Solution ) Comparison with other systems cold quantum gases? η = 1.64 / σ Juan Castillo RHI seminar 0

21 HIC: hybrid approaches Parton Cascade Model (PCM): to explore the mechanisms for the formation of QGP and to determine the initial condition of the equilibrated state. AKA string fragmentation. Related BAMPS perturbative QCD approach Hadronic cascade: color strings are formed and they decay into hadrons according to Lund string model PYHIA. URQMD approach Hadrons hydro range q q partons Space-ime Parton Cascade in High-Energy Collisions :(K. Geiger, B. Müller: 199) initial conditions String final conditions Juan Castillo RHI seminar 1

22 Connection with cold atoms Similar Elliptic Flow Strongly Interacting Degenerate 6 Li gas = 10-7 K Duke, Science (00) O Hara et al. Is a Strongly-interacting atomic Fermi gas a fluid with the minimum shear viscosity? Can we directly compare them with HIC data? Juan Castillo RHI seminar

23 Connection with cold atoms Viscosity/entropy density (units of h / k B ) He near λ point QGP simulations String theory limit Juan Castillo RHI seminar 3

24 Summary Hydro model is working relatively fine for low p HB puzzle (discrepancy with hydro) needs to be solved We need still to prove without ANY doubt the EOS (is there a phase transition?) Promising common points with cold atoms Juan Castillo RHI seminar 4

25 Literature RHIC white papers (SAR, PHENIX, PHOBOS, BRAHMS) Results from the first 3 years at RHIC (April 18, 005) J.Letessier-J.Rafelski. Hadrons and Quark-Gluon Plasma. Cambridge monographs on particle physics, nuclear physics and cosmology. Cambridge University Press 005. High relativistic nucleus-nucleus collision: he central rapidity region. J.D.Bjorken. Phys.Rev.D (1 January 1983) From AGS-SPS and onwards to the LHC. L.McLerran. doi: / /35/10/ Landau Hydrodynamics and RHIC Phenomena Peter Steinberg. arxiv:nucl-ex/04050v1 (4 May 004) he formation of QGP in ultra-relativistic nucleus-nucleus collisions. K. Heckmann (previous RHI seminar, ) J/Ψ Suppression and Enhancement. he Statistical Hadronization Model. Jun Nian (previous RHIC seminar, ) QCD Phasendiagramm Katja Grossmann, Katharina Lohnert. QGP meets Cold Atoms. EMMI workshop. September 008 QM008 talks: L. McLerran : SPS to RHIC and Onwards to LHC. P. Seyboth : Recent Results from the Study of the Nucleus-Nucleus Collisions at the CERN SPS Juan Castillo RHI seminar 5

26 Shear viscosity/entropy ratio in Cold Atoms Addendum to: "Experimental investigations of relativistic hydrodynamics and the ideal fluid scenario at RHIC" Juan F. Castillo Hernandez alk based on the one given by J. the EMMI workshop Quark-Gluon Plasma meets Cold Atoms "Measuring Entropy and Quantum Viscosity in a Strongly Interacting Atomic Fermi Gas" Juan Castillo RHI seminar 6

27 Connection with cold atoms Viscosity/entropy density (units of h / k B ) He near λ point String theory limit QGP simulations how to measure these points? We need η, s, E, E F Juan Castillo RHI seminar 7

28 Short outline Experimental settings hermodynamics of strongly-interacting Fermi gases: Model-independent measurements of entropy and energy Calibrating the endpoint temperature for adiabatic sweeps Quantum viscosity in strongly-interacting Fermi gases: Expansion dynamics of rotating Fermi gases Comparison to the minimum viscosity conjecture Juan Castillo RHI seminar 8

29 Optically rapped Fermi Gas Our atom: Fermionic Μagnet coils 1 1 =,1 =, 0 electron spin, nuclear spin Juan Castillo RHI seminar 9

30 Universal Regime Ideal Fermi Gas = 0 Parameters: R 0 = range of the interatomic potential L = Interparticle spacing a = scattering length Strongly Interacting Fermi Gas B = 58 G Scattering lenght Fermi Energy E ideal a = 0 h ml Universal Regime when: Interparticle spacing L is the only length scale. he gas is: diluted R 0 << L strongly interacting a >> L E gnd = (1 + β ) B = 840G a >> L E ideal Baker 1999, Heiselberg, 001 heory: Carlson (003) β = Strinati (004) β = ground state Juan Castillo RHI seminar 30

31 Quantum Viscosity in the Universal Regime d v F A =η d v η Viscosity Viscosity natural unit: p η = σ h / L L η hn Entropy density natural unit: s nk B Ratio natural unit: η / s h / k B Juan Castillo RHI seminar 31

32 Energy E Measurement Universal hermodynamics Ho, PRL (004) Harmonic Potential: ε = ( n + n + n hν x y z) Virial heorem in HO potential E = U Energy per particle E = 3 mω z z Measure energy E from the cloud size Juan Castillo RHI seminar 3

33 Entropy S Measurement by Adiabatic Sweep of Magnetic Field B Start 840 G B Weakly interacting: Entropy at 100 G known from cloud size Ideal Fermi gas End 100 G classical thermodynamics (adiabatic process) ΔS = 0 = ΔQ = ΔU + ΔW Juan Castillo RHI seminar 33

34 Expansion Dynamics: Comparison to theory E = 0.56 E F, Ω 0 = 178 rad/s y I I rig0 x Moment of inertia I = L/Ω I I = δ x rig x + y y deformation parameter δ Juan Castillo RHI seminar 34

35 Comparison to the minimum viscosity conjecture Red normal fluid Blue superfluid Cold Atoms: Normal fluid rotates like a Superfluid! very low η!! η =αh n Superfluid: Irrotational Flow v = Juan Castillo RHI seminar 35

36 Comparison to the minimum viscosity conjecture y α α = =1 x θ is the angle of the principal axes with respect to the laboratory axes θ Juan Castillo RHI seminar 36

37 Literature Measuring Entropy and Quantum Viscosity in a Strongly Interacting Atomic Fermi Gas. J. homas EMMI Quark-Gluon Plasma meets Cold Atoms Introductory workshop Virial heorem and Universality in a Unitary Fermi Gas J. E. homas, J. Kinast, and A. urlapov. Phys. Rev. Lett. 95, 1040 (005) Virial theorems for trapped cold atoms. Félix Werner. Phys. Rev. A 78, (008) Ratio of shear viscosity to entropy for trapped fermions in the unitary limit.. Schäfer. Phys. Rev. A 76, (007) heory of ultracold atomic Fermi Gases. Stefano Giorgini, Lev P. Pitaevskii and Sandro Stringari arxiv: (June 007) Juan Castillo RHI seminar 37