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重イオン衝突における 散逸と 揺らぎ

RHIC-LHC 高エネルギー原子 核反応の 物理 研究会 2013 年 6 月 22-23 日. 重イオン衝突における 散逸と 揺らぎ. 平野哲文（上智大理工）. 共同研究者 : 村瀬功一 , 橘保貴. Outline. はじめに Initial fluctuation Relativistic fluctuating hydrodynamics Jet propagation in expanding medium Summary and outlook. はじめに. 重イオン衝突 における QGP の物理　. 発見のステージ  精密科学に向けて

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重イオン衝突における 散逸と 揺らぎ

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  1. RHIC-LHC 高エネルギー原子核反応の物理研究会 2013年6月22-23日 重イオン衝突における散逸と揺らぎ 平野哲文（上智大理工） 共同研究者: 村瀬功一, 橘保貴

  2. Outline はじめに Initial fluctuation Relativistic fluctuating hydrodynamics Jet propagation in expanding medium Summary and outlook

  3. はじめに 重イオン衝突におけるQGPの物理　 発見のステージ 精密科学に向けて  新奇な現象の発見 より詳細なQGPダイナミクスの 記述に向けた試み

  4. Initial Fluctuation

  5. Eccentricity Fluctuation in Small System PHOBOS, Phys. Rev. Lett. 98, 242302 (2007)

  6. Fluctuation in Initial Conditions B.Alveret al., Phys. Rev. C 77, 014906 (2008)

  7. Higher Harmonics is Finite! Two particle correlation function is composed solely of higher harmonics Figures adapted from talk by J.Jia (ATLAS) at QM2011

  8. Impact of Finite Higher Harmonics coarse graining size • Most of the people did not believe hydro description of the QGP (~ 1995) • Hydro at work to describe elliptic flow (~ 2001) • Hydro at work (?) to describe higher harmonics (~ 2010) initial profile

  9. Open Questions • Can system respond hydrodynamically to such a fine structure? • Why is local thermalization achieved at such a short length/time scale (~1 fm)? • Concept of hydrodynamics? Is ensemble average taken? • Thermal fluctuation on an event-by-event basis ?

  10. Relativistic Fluctuating Hydrodynamics

  11. Fluctuation Appears Everywhere Finite number of hadrons Propagation of jets Hydrodynamic fluctuation Initial fluctuation and particle production time collision axis 0

  12. Green-Kubo Formula • Slow dynamics  How slow? • Macroscopic time scale ~  • Microscopic time scale ~ • cf.) Long tail problem (liquid in 2D, glassy system, super-cooling, etc. )

  13. Relaxation and Causality Constitutive equations at Navier-Stokes level • Instantaneous response violates causality • Critical issue in relativistic theory • Relaxation plays an essential role … thermodynamics force Realistic response

  14. Causal Hydrodynamics Linear response to thermodynamic force Retarded Green function Differential form Maxwell-Cattaneo Eq. (simplified Israel-Stewart Eq.)

  15. K.Murase and TH, arXiv:1304.3243[nucl-th] Relativistic Fluctuating Hydrodynamics (RFH) Generalized Langevin Eq. hydrodynamic fluctuation thermodynamic force dissipative current ) Fluctuation-Dissipation Relation (FDR) : Symmetrized correlation function For non-relativistic case, see Landau-Lifshitz, Fluid Mechanics

  16. Coarse-Graining in Time Non-Markovian Markovian coarse graining ??? Navier Stokes  causality Maxwell-Cattaneo Existence of upper bound in coarse-graining time (or lower bound of frequency) in relativistic theory???

  17. K.Murase and TH, arXiv:1304.3243[nucl-th] Colored Noise in Relativistic System : Extention to t<t’ Correlation in Fourier space • Colored noise! • (Indirect) consequence of causality • Note: white noise in differential form

  18. A Comment on Heat Conductivity Phenomenological constitutive eqs. 1st order: , 2ndorder:  for Gluonic system () ??? RFH: , Getting meaningful solely in RFH  Fluctuation of ?

  19. Figures from J.B.Bellet al., ESAIM 44-5 (2010)1085 Need Fluctuation? Seeds for instabilities Rayleigh-Taylor instability Kelvin-Helmhortz instability Non-linearity, instability, dynamic critical phenomena,…

  20. Outlook for RFH • Numerical implementation and its consequences in observables • Langevin simulation in constrained system? • Dynamic critical phenomenaSeparation of systematic motion from noise? • RFH from quantum Langevin eq.? • Heat conductivity in gluonic system • from Hosoya-Kajantie •  lattice QCD? AdS/CFT?

  21. Jet PROPAGATION inEXPANDING MEDIUM

  22. Fluctuation Appears Everywhere Finite number of hadrons Propagation of jets Hydrodynamic fluctuation Initial fluctuation and particle production time collision axis 0

  23. Figures adapted from talk by C.Roland (CMS) at QM2011 Jet Quenching as Missing pT in-cone out-of- cone Jet momentum balanced by low pT hadrons out of jet cone!

  24. Figure adapted from talk by C.Roland (CMS) at QM2011 Momentum Balance Restored Horizontal: Jet asymmetry Vertical: Transverse momenta (anti-)parallel to jet axis Lost energy goes to low pT particles at large angle

  25. Energy-Momentum Flow from Jets • Jet quenching could affect QGP expansion at LHC (and even at RHIC) • Many jets could disturb fluid evolution (or even heat them up?) • Beyond linearized hydro in the case that jet propagates parallel to x-axis

  26. Y.Tachibana and TH, Nucl.Phys.A904-905(2013)1023c QGP Wake by Jet A 50 GeV jet traverses a background with T=0.5 GeV  Mach-cone like structure Vortex ring behind a jet

  27. April 13, 2013 at Mt. Etna http://photoblog.nbcnews.com/_news/2013/04/12/17720274-mount-etna-blows-smoke-ring-during-volcanic-eruptions

  28. Y.Tachibana and TH, Nucl.Phys.A904-905(2013)1023c QGP Mach Cone Induced by a Jet First fully non-linear and fully 3D hydro simulation of Mach cone

  29. Y.Tachibana and TH, Nucl.Phys.A904-905 (2013)1023c Large Angle Emission from Expanding Medium q out-of-cone Jet pair created at off central position Enhancement of low momentum particles at large angle from jet axis

  30. Momentum Balance out of cone in cone preliminary Pb+Pb central collisions at sqrt(s_NN) = 2.76 TeV

  31. Outlook for Interplay between Soft and Hard • Alternative constraint for shear viscosity • through propagation of jets? • Heat-up from mini-jets propagation similar to neutrino reheating in SNE? momentum transfer Jet propagation

  32. Summary and Outlook • Fluctuation appears everywhere • Hydrodynamic fluctuation • Fluctuation induced by jet propagation • Development of a more sophisticated dynamical model towards precision/new heavy-ion physics

  33. BACKUPS

  34. Hydro-based event generator

  35. Current Status: E-by-E H2C time Hadronic cascade 3D ideal hydro Monte Carlo I.C. (MC-KLN or MC-Glauber) collision axis 0

  36. Initial Density Fluctuation conventional hydro event-by-event hydro

  37. Eccentricity, Triangularity, … 40-50% Almost boost invariant

  38. v2{***} v2{EP}, v2{2}, v2{4}, v2{6}, v2{LYZ}, … Hydro-based event generator  Analysis of the outputs almost in the same way as experimental people do. Demonstration of vn analysis according to event plane method by ATLAS setup. E.g.) Centrality cut using ET in FCal region ATLAS, arXiv:1108.6018

  39. Resolution of Event Plane Reaction (Event) plane is not known experimentally nor in outputs from E-by-E H2C. Event plane method Event plane resolution using two subevents c.f.) A.M.Poskanzer and S.Voloshin, Phys. Rev. C 58, 1671 (1998)

  40. Resolution of Event Plane from E-by-E H2C Odd Harmonics Even Harmonics # of events: 80000 (Remember full 3D hydro+cascade!) Subevent “N”: charged, -4.8< h < -3.2 (FCal in ATLAS) Subevent“P”: charged, 3.2< h < 4.8 (FCal in ATLAS) ATLAS, arXiv:1108.6018

  41. Vn{EP}(h) Even Harmonics Odd Harmonics 40-50% 40-50% Not boost inv.almost boost inv. for epsilon

  42. vn{EP} vs. vn{RP} vn{RP}: vn w.r.t. reaction plane known in theory Even Harmonics Odd Harmonics 40-50% 40-50% veven{EP}>veven{RP} due to fluctuation vodd{RP}~0

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