1. Koichi Murase A, Tetsufumi Hirano B The University of Tokyo A, Sophia University B Hydrodynamic fluctuations and dissipation in an integrated dynamical model 2015/9/29, QM2015 2015/9/291

2. PartX (1/1) Final observables – flow harmonics v n, etc. Initial-state fluctuations –nucleon distribution –quantum fluctuations Fluctuations in heavy-ion collisions 2015/9/292 Response of Matter EoS, η, ζ, τ R, λ, … 0 collision axis time

3. PartX (1/1) Final observables – flow harmonics v n, etc. Initial state fluctuation –nucleon distribution –quantum fluctuations Fluctuations in heavy-ion collisions 2015/9/293 Other fluctuations + hydro fluctuations + jets/mini-jets + critical phenomena + … 0 collision axis time Relativistic hydrodynamics ( ～ QGP)

4. PartX (1/1) Hydrodynamic Fluctuations HF ＝ Thermal fluctuations of dissipative currents 2015/9/294 ensemble/event averaged thermal fluctuations at each spacetime x e.g. V: 3+1 dim. volume decrease anisotropy HF is important in e-by-e description of HIC Balance Fluctuation-Dissipation Relation FDR HF increase anisotropy

5. Integrated dynamical model 2015/9/295

6. PartX (1/1) Integrated Dynamical Model 2015/9/296 0 collision axis time 2. (3+1)-dim. Relativistic Fluctuating Hydrodynamics EoS: lattice QCD&HRG, η/s = 1/4π 1. Initial condition MC-KLN 5. Analysis of hadron distribution 3. Particlization at T sw = 155 MeV Cooper-Frye formula: f + δf 4. Hadronic cascades (JAM) Updated version of T. Hirano, P. Huovinen, KM, Y. Nara, PPNP 70, 108 (2012) [arXiv:1204.5814]

7. PartX (1/1) Setup: Target Collision system Au+Au, √s NN = 200 GeV Fluctuations Initial-state fluctuations from nucleon positions Hydrodynamic fluctuations  Comparison between the effects of both fluctuations 2015/9/297 Au

8. PartX (1/1) Setup: IS Fluctuations and HF Initial condition Centrality: Minimum bias Model: MC-KLN (CGC) (3+1)-dim Relativistic Fluctuating Hydrodynamics: 2015/9/298 x-y planeη s -x plane Typeη/sη/sHFHydroCascades Viscous1/4πnone100 k events 10 M (100k ☓ 100) Fluctuating1/4πλ = 1.0 (fm)100 k events 10 M (100k ☓ 100) λ : HF cutoff length scale (Gaussian width)

9. PartX (1/1) Numerical Simulation: Evolution 2015/9/299 Hydrodynamic evolution ηsηs x [fm] ηsηs y [fm] x [fm] without HF with HF conventional 2 nd -order viscous hydro 2 nd -order fluctuating hydro τT ττ

10. PartX (1/1) v n {EP} vs p T 2015/9/2910 EP: η-sub, |η| = 1.0-2.8 0-5% HF increase anisotropies larger effects in a higher order  HF ∝ V -1/2

11. PartX (1/1) v n {EP} vs p T 2015/9/2911 EP: η-sub, |η| = 1.0-2.8 Central: (IS Fluct.) + (HF) Non-central: (IS Fluct.) + (HF) + (Collision geometry) 20-30%

12. PartX (1/1) v n {2m} vs p T 2015/9/2912 v{4} 2 ＝ v{6} 2 ＞ v{2} 2 flow fluctuations σ: larger with HF ～ flow fluct. v{2} 2 ＝ v 2 ＋ σ 2, v{4} 2, v{6} 2 ～ v 2 － σ 2, 20-30%

13. PartX (1/1) E-by-E distribution of v 2 2015/9/2913 v{2} 2 ＝ v 2 ＋ σ 2, v{4} 2, v{6} 2 ～ v 2 － σ 2, Broader distribution of v2 20-30%

14. PartX (1/1) Event-plane fluctuations by HF 2015/9/2914 Event-plane decorrelation by HF 20-30% CMS, arXiv:1503.01692 J. Jia, and P. Huo, Phys. Rev. C 90, 034905 (2014),

15. Summary 2015/9/2915

16. PartX (1/1) Summary Hydrodynamic fluctuations ＝ thermal fluctuations of hydrodynamics Relativistic fluctuating hydrodynamics in an integrated dynamical model – increase of anisotropies – larger effects in higher order v n s – larger flow fluctuations HF: Important in extracting the transport properties Outlook – Scan viscosity η & cutoff λ, and compare them to data – Modifications of f(p, λ), η(λ), etc. by cutoff λ. 2015/9/2916

17. Backup 2014/08/0617

18. Setup A: HF only 2015/7/2718

19. PartX (1/1) Setup A: HF only Initial condition b = 6.45 fm ( ～ Centrality 20%) Averaged MC-KLN (CGC) (3+1)-dim Relativistic Fluctuating Hydrodynamics: 2015/7/2719 x-y planeη s -x plane Typeη/sη/sHFHydroCascades Ideal0none1 event10 4 events Viscous1/4πnone1 event10 4 events Fluctuating1/4πσ=0.8, 1.0, 1.2 (fm) ＊ 10 4 events ☓ 3 σ: HF cutoff length scale

20. PartX (1/1) Numerical Simulation: Evolution 2015/7/2220 A: Hydrodynamic evolution ηsηs x [fm] ηsηs y [fm] x [fm] without HF with HF conventional 2 nd -order viscous hydro 2 nd -order fluctuating hydro τT ττ

21. PartX (1/1) A: dN ch /dη Increase  entropy production by HF Larger effect with a shorter cutoff length σ 2015/7/2221

22. PartX (1/1) A: p T -spectra (pions) High-pt particles increase with HF  accelerated by local flows 2015/7/2222 local flows by HF

23. PartX (1/1) A: Elliptic flow v 2 {2} decreased by viscosity, unchanged by HF  local flows do not change the global flow profile 2015/7/2223 local flows by HF

24. PartX (1/1) A: Elliptic flow v 2 {2}(η) Decrease with viscosity, increase with HF  increase of high-p T particles 2015/7/2224 v2(p T ) in the last slide High-p T particles v2v2 η

25. PartX (1/1) B: p T -spectra (pions) 2015/7/2225 Points: PHENIX PRC69 (2004) 034909 Black lines: ideal hydrodynamics Blue lines: viscous hydrodynamics Red lines: fluctuating hydrodynamics 0-4%, 5-10%, 10-15%, 15-20%, 20-30%, 30-40%, 40-50%, 50-60%, 60-70%, 70-80% from top to bottom (multiplied by 10 4 -10 -5 ) Increase of high-p T pions: larger in peripheral collisions  larger thermal fluctuations in smaller systems Correction of distribution in Cooper-Frye formula by HF?

26. Setup B: IS fluctuations + HF 2015/7/2726

27. PartX (1/1) Elliptic flow v 2 (η) v2(fluctuating) > v2(ideal) in central collisions Central: (IS Fluct.) + (HF) Non-central: (IS Fluct.) + (HF) + (Collision geometry) Same order with IS fluctuations 2015/9/2927 ηpηp ηpηp 10-15% 0-5%

28. PartX (1/1) v 2 {2}(p T ), v 3 {2}(p T ) v 2 increase with HF in central collisions Similar behavior for v 3 2015/9/2928 v2v2 v3v3

29. PartX (1/1) v 2 {2} vs p T Calculations: η/s = 1/4pi 2015/9/2929