Recent Development in RELATIVISTIC HYDRODYNAMIC MODEL

1. Recent Development in RELATIVISTIC HYDRODYNAMIC MODEL Tetsufumi Hirano Sophia Univ.

2. DISCLAIMER From organizers: “Your recent work on hydrodynamics” Highlights from hadron physics group in Sophia My charge: Invitation to parallel talks by students from our group

3. SPACE-TIME EVOLUTION in heavy ion collisions • TOPICS • Hadronicrescattering effects • Causal hydrodynamic fluctuation • Energy/Momentum transport away from jet • Chiral magnetic effect and anomalous hydrodynamics time collision axis 0

4. TH, P.Huovinen, K.Muraseand Y.Nara, Prog. Part. Nucl. Phys. 70, 108 (2013). S.Takeuchi, TH, P.Huovinen, K.Murase and Y.Nara, in preparation. H.Hinoharaand TH, work in progress. HADRONIC Rescattering effects Members: Shiori Takeuchi, Hiromi Hinohara, Koichi Murase Collaborators: PasiHuovinen, Yasushi Nara

5. HADRONIC RESCATTERING EFFECTS • Final hadronic observables • History of the whole space-time evolution • Direct information about the QGP? • Contaminated by hadronicrescatterings • Need penetrating probes? time collision axis 0

6. INTEGRATED DYNAMICAL APPROACH • Hadronic cascade • JAM • On/off rescatterings time • Particlization • Cooper-Frye • Tsw = 155 MeV • Ideal hydrodynamics • Full 3D • Lattice EOS • Event-by-event collision axis 0 • Monte-Carlo initialization • Glauber • Karzeev-Levin-Nardi TH, P.Huovinen, K.Murase and Y.Nara, Prog. Part. Nucl. Phys. 70, 108 (2013).

7. 1D Pion source function Two-pion correlation function from Koonin-Pratt eq. in PCMS Non-Gaussian tail Significant hadronicrescattering effects on pion source function Pions, WITHOUTrescatterings Pions, WITHrescatterings Calculations by H. Hinohara S.E. Koonin, Phys. Lett. B70, 43(1977); S.Prattet al., Phys. Rev. C42,2646 (1990). S.S.Adler et al. [PHENIX Collaboration], Phys. Rev. Lett. 98, 132301 (2007).

8. VIOLATION OF MASS ORDERING for Phi mesons Typical example of hadronicrescattering effect Phi mesons  less rescattering with other hadrons TH et al., Phys. Rev. C 77, 044909 (2008). See also, A. Shor, Phys. Rev. Lett. 54, 1122 (1985); H. Van Heckeet al., Phys. Rev. Lett. 81, 5764 (1985).

9. VIOLATION OF MASS ORDERING for PHI mesons (contd.) M.Nasim[STAR Collaboration], Nucl. Phys. A 904-905, 413c (2013) Violation of mass ordering discovered by STAR

10. Freeze-out time distribution Minimum bias Minimum bias W-baryons f-mesons Mesons Baryons Early freezeout for multi-strange hadrons “Multi-strange hadrons as penetrating probes” S.Takeuchi, 8/6(wed), 16:20-, hadron production session

11. K.Murase and TH, arXiv:1304.3243 TH, R.Kurita, K.Muraseand K.Nagai, arXiv:1407.8357 CAUSAL hydrodynamic fluctuation Members: Koichi Murase, Ryuichi Kurita, Kenichi Nagai

12. FLUCTUATION DISSIPATION RELATION Thermal equilibrium state = Maximum entropy state dissipation Entropy Balance between fluctuation and dissipation  Stability of the thermal equilibrium state fluctuation

13. Relativistic Fluctuating hydrodynamics Stochastic constitutive equation Fluctuation-Dissipation relation : Symmetrized correlation function : Thermal fluctuation K.Murase and TH, arXiv:1304.3243

14. QGP Fluids in a box Ideal hydro Dissipative hydro Fluctuating hydro Almost ready to calculate observables within fluctuating hydro + cascade “Higher harmonics from causal hydrodynamic fluctuation” K.Murase, 8/6(wed), 14:40-,collective dynamics session

15. Hydrodynamic fluctuation in BJOrken expansion : Energy density Equation of motion : Pressure : Entropy density : Shear stress Stochastic constitutive equations : Bulk pressure : Shear viscosity Shear: : Bulkviscosity : Relaxation time Bulk: Hydrodynamic noise Numerical simulations by K. Nagai (work in progress)

16. ENTROPY FLUCTUATION IN HEAVY ION COLLISIONS Centrality dependence of multiplicity fluctuation THEOREM: Upper bound of entropy fluctuation in Bjorken expansion : Transverse overlapping area “Entropy fluctuation from hydrodynamic noise” R.Kurita, 8/6(wed), 14:20-,collective dynamics session TH, R.Kurita, K.Murase and K.Nagai, arXiv:1407.8357

17. Y.Tachibana and TH, arXiv:1402.6469, to appear in Phys. Rev. C (Rapid Communication) Energy/momentum transport away from jet Member: Yasuki Tachibana

18. Hydrodynamic response to jet quenching QGP wake induced by jet energy and momentum loss

19. Distorted mach cone

20. EOS DEPENDENCE Ideal gas (Conformal matter) Lattice EoS (Wuppertal Budapest) S. Borsanyiet al., JHEP 1011, 077 (2010) The larger emission angle, the softer EoS

21. Momentum transport out of JET cone Momentum transport away from jet axis “Momentum flow in dijet+QGP fluid system” Y.Tachibana, 8/6(wed), 15:00-, jets session

22. Chiral Magnetic Effect and Anomalous Hydrodynamics Member: Masaru Hongo Collaborator: Yuji Hirono

23. CHIRAL MAGNETIC WAVE chiral magnetic effect chiral separation effect D.Kharzeev and H.U.Yee(2011);Y.Burnier et al.(2011) Adapted from a seminar talk by M.Hongo at BNL (2013) For introduction of CME and CSE, see K.Fukushima, arXiv:1209.5064

24. SIMULATION OF CHIRAL MAGNETIC WAVE Quadrupole deformation of charge density in transverse plane “Anomaly-induced transport in heavy-ion collisions” M.Hongo, 8/7(thu), 15:00-, Initial state physics session

25. (INSTEAD OF) SUMMARY • Collective dynamics (8/6, wed., pm) • Ryuichi Kurita • “Entropy fluctuation from hydrodynamic noise” • Koichi Murase • “Higher harmonics from causal hydrodynamic fluctuation” • Jets (8/6, wed., pm) • Yasuki Tachibana • “Momentum flow in dijet + QGP-fluid system” • Hadron production (8/6, wed., pm) • Shiori Takeuchi • “Multi-strange hadrons as penetrating probes” • Initial state physics (8/7, thu., pm) • Masaru Hongo • “Anomaly-induced transport in heavy-ion collisions” • Stay-tuned • Hiromi Hinohara, “Femtoscopic analysis from hybrid model” • Kenichi Nagai, “Simulation of fluctuating hydro in Bjorken expansion”