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Thermal Statistics, Hydrodynamics and Thermalization

Thermal Statistics, Hydrodynamics and Thermalization. Zhangbu Xu ( 科大 / BNL). Therm al statistics ( 热统 ) Hydrodynamics ( 流体力学 ) F low ( 流 ). STAR whitepaper. Temperature from Chemistry among hadrons. Statistical Mechanics describes the relative particle abundances

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Thermal Statistics, Hydrodynamics and Thermalization

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  1. Thermal Statistics, Hydrodynamics and Thermalization Zhangbu Xu (科大/BNL) • Thermal statistics (热统) • Hydrodynamics (流体力学) • Flow (流)

  2. STAR whitepaper Temperature from Chemistry among hadrons • Statistical Mechanics describes the relative particle abundances • This happens at the phase boundary (T=165+-10MeV) STAR whitepaper, NPA757(2005) 强子的热统分布: 温度和化学势

  3. Thermal Statistical Model热统计模型 Particle Density粒子密度分布 Modified Bessel Function Must Include all particles including resonances !! http://arxiv.org/abs/nucl-th/0304013

  4. SU(3) Representation of Particles

  5. Strangeness Conservation奇异数守恒 In Strong Interaction: 奇异夸克只能成对产生, 因为不是价夸克 Associated Production联合产生: p + N  NLK+ Pair Production对产生: p + N pNK+K- Threshold in fixed target: s = (E+mN)2 – p2 作业题：Associated Production More Effective (lower Threshold)@ low beam energies

  6. Strong force generates mass Proton: up+up+down quarks Neutron: up+down+down quarks p,n mass: ~ 1 GeV/c2/3=0.3 GeV/c2 Proton: up+up+down quarks Neutron: up+down+down quarks p,n mass: ~ 1 GeV/c2/3=0.3 GeV/c2 • Quark has two kind of masses: • Constituent quark mass 组分夸克质量(“dressed” with sticky gluons, m=E/c2), • Current quark mass流夸克质量

  7. Strange quark yields Sensitive to Bulk Partonic Matter 奇异夸克(s) 组分夸克质量:0.45GeV 流夸克质量: 0.1 GeV In QGP, Tc>ms 热力学的对产生占主要 而且流夸克质量只有0.1 GeV J. Rafelski and B. Muller, Phys.Rev.Lett.48:1066,1982

  8. STAR whitepaper Chemistry among hadrons • Statistical Mechanics describes the relative particle abundancesThis is not trivial • Strange particles are suppressed in e+e- or p+p but fully equilibrated in central Au+Au collisions • This happens at the phase boundary (T~=165 MeV)

  9. QCD Phase Diagram强相互作用的相图 A thermodynamic state (热力学态)is specified by a set of values of all the thermodynamic parameters necessary for the description of the system. --- statistical mechanics by K. Huang Temperature (T), chemical potential (m), pressure(P) … • Chemical/thermal Equilibrium at certain stage of the evolution在某个时候达到化学和热平衡 • At the predicted QCD phase boundary和理论预言吻合 • persistent from SPS to RHIC • Below the phase boundary atAGS and SIS

  10. 什么是温度? • 我们上述测量的是不是热力学所定义的温度? • 什么是热力学所定义的温度? • 粒子的无规则运动程度? • 物质的冷热? • 能量均分和能量守恒的Lagrangian插值量 • 这跟我们学科有什么关系? • 相图(三相点) • QGP态 • 能否用到天体物理和宇宙学上(中子星,宇宙早期) 作业题 作业题

  11. 重核子碰撞的时空演化 p, K, N, … t p, K, N, … • Stages in the collision 1. Pre-equilibrium Hard parton scattering processes 2. Equilibration After t≤ 1 fm/c partons materialise and either hadronise or rescatter. 3. Thermal quark-gluon plasma Hydrodynamic expansion 4. Hadronization (phase transition) Quark coalescence + gluon fragmentation … or … String fragmentation 5. Hadron gas Hadrons continue to interact 6. Particle freeze-out • Chemical freeze-out 化学冻结 粒子数不再变化 • Thermal freeze-out热冻结不再有强相互作用 tf tf 6. t(eH) Hadron gas t(eQ) 5. t0 = th 6. Mixed phase Hadron gas t0 = tq 4. QGP 5. 3. 4. 2. 1. 1. Hadron formation. Parton formation and thermalisation. z A A a) Without QGP b) With QGP

  12. QCD Phase Diagram强相互作用的相图 A thermodynamic state (热力学态)is specified by a set of values of all the thermodynamic parameters necessary for the description of the system. --- statistical mechanics by K. Huang Temperature (T), chemical potential (m), pressure(P) … • Chemical/thermal Equilibrium at certain stage of the evolution在某个时候达到化学和热平衡 • At the predicted QCD phase boundary和理论预言吻合 • persistent from SPS to RHIC • Below the phase boundary atAGS and SIS

  13. Blast Wave 爆炸波模型 where: E.Schnedermann et al, PRC48 (1993) 2462 F. Retiere, M. Lisa, http://arxiv.org/abs/nucl-th/0312024 r =s(r/R)n STAR Preliminary

  14. Blast Wave Fit爆炸波模型拟合 Parameters: Freeze-out T; Transverse Flow Velocity bT

  15. pT: mass dependence • STAR Preliminary • p+p collisions (m.b.) • All fit to thermal (T,bT) = (0.17,0)  Except f, L(1520) Au+Au collisions (5%) • All fit to thermal (T,bT) = (0.1,0.6c) • Except W • (T,bT) = (0.17,0.3c) Partonic collectivity? ===================== • Note: • (1) W- + W+ (10%) • (2) d+anti-d (top 18%) (Phenix)

  16. Blast wave fits: Tfo vs. bT 1) p, K, and p change smoothly from peripheral to central collisions. 2) At the most central collisions, <T> reaches 0.6c. 3) Multi-strange particles ,  are found at higher T and lower <T> •  Sensitive to early partonic stage! • STAR: NPA715, 458c(03); PRL 92, 112301(04); 92, 182301(04). 200GeV Au + Au collisions

  17. F.D. O’Hara et al. Science 298(2002) STAR Visual v2 0.2<pT<0.6 Taking pictures in different ways • Strongly interacting Li6 cold atoms (superfluid fermion) • Take pictures at different time • Strongly interacting QGP • “Take” pictures for different particles, beam, rapidityHigher harmonics • ±0,K±0,p,,,,,K*,D20, 62,130,200 GeV v1,v2, v4 Time: 10-23s – 400ms Size: 10fm – 100mm

  18. Equation of State状态方程 ideal hydrodynamics Tmn : energy-momentum tensor f(x,p): phase space - dynamics um: 4-velocity g: Lorentz factor K.J. Eskola, et al., nucl-th/9705015 --------------------------------- - Initial conditions (?) - EOS (?) - Freeze-out conditions (?) With given degrees of freedom, the EOS - the system response to the changes of the thermal condition - is fixed by its p and T or.

  19. Equation of State Energy Density/T4 Pressure pGeV/fm3 Energy Density (GeV/fm3) • Equation of state: • EOS I : relativistic ideal gas • p = /3 • EOS H: resonance gas • p ~ /6 • - EOS Q: Maxwell construction: • Tcrit= 165 MeV • B1/4 = 0.23 GeV • lat=1.15 GeV/fm3 • P. Kolb et al., Phys. Rev. C62, 054909 (00).

  20. Hydrodynamics and anisotropic flow • Ideal hydrodynamics describes the anisotropic flow • Even the mass splitting • Liquid-like matter • Strong couplingFast thermalization low viscosity  important theoretical implication

  21. Transverse Flow Observables Particle mass dependent. 1) Radial flow – integrated over whole evolution 2) Directed flow (v1) – relatively early 3) Elliptic flow (v2) – relatively early

  22. directed flow py elliptic flow px Flow Vector Sum of vectors of all the particles S. Voloshin and Y. Zhang, Z. Phys. C 70, 665 (1996)

  23. bounce-off all v2{EP} In-plane elliptic flow squeeze-out six decades Elliptic Flow vs. Beam Energy 25% most central mid-rapidity powerful, widely-used tool, to study EOS of nuclear matter A. Wetzler (2005)

  24. flow scaled by eccentricity Au+Au 200 GeV particle density Approach to Hydro Sergei Voloshin, QM06, S883 (2007)

  25. LHC, U+U at RHIC? Is hydrodynamic limit a limit? What is the viscosity? Value+-error

  26. 200 GeV Au+Au STAR Preliminary Coalescence of Quarks Non-equilibrium process • Number of Constituent Quark (NCQ) • transition regime 2<pT<5 GeV/c • Multi-strangeness baryons • Heavy Mesons (K*, f) Surprising Discoveries at RHIC: Coalescence of quarks? New hadronization mechanism?

  27. Models prior to RHIC CGC: high density gluons Dilute gas Physics Today, Ludlam/McLerran momentum Thermalization Simple Counting Initial condition: high density gluons DIS: ep, eA (eRHIC)

  28. Vacuum Engineering Big Bang It is just the beginning Hydrodynamics Theory of color Heavy Ion new state Perfect (QCD) Non-Abelian Experiments of matter Liquid Renaissance-simon F. Wilczek Chern-simon Hall Effect Quantum Hall FQHE 5/2 Quantum Quantum Mechanics Effect Anyon Non-Abelian Computing

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