RHIC-LHC 高エネルギー原子核反応の物理研究会 2013 年 6 月 日 平野哲文（上智大理工） 共同研究者 : 村瀬功一, 橘保貴 1

1. はじめに 2.Initial fluctuation 3.Relativistic fluctuating hydrodynamics 4.Jet propagation in expanding medium 5.Summary and outlook 2

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

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PHOBOS, Phys. Rev. Lett. 98, (2007) 5

B.Alver et al., Phys. Rev. C 77, (2008) 6

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

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) coarse graining size initial profile 8

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 ? 9

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

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

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

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

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

 Colored noise!  (Indirect) consequence of causality  Note: white noise in differential form K.Murase and TH, arXiv: [nucl-th] 17

Phenomenological constitutive eqs. 1 st order: 2 nd order: 18 RFH:,

Rayleigh-Taylor instability Non-linearity, instability, dynamic critical phenomena,… Kelvin-Helmhortz instability Figures from J.B.Bell et al., ESAIM 44-5 (2010) Seeds for instabilities

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

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

Lost energy goes to low p T particles at large angle Figure adapted from talk by C.Roland (CMS) at QM Horizontal: Jet asymmetry Vertical: Transverse momenta (anti-)parallel to jet axis

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 25 in the case that jet propagates parallel to x-axis

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

4/12/ mount-etna-blows-smoke-ring- during-volcanic-eruptions 27

First fully non-linear and fully 3D hydro simulation of Mach cone Y.Tachibana and TH, Nucl.Phys.A (2013)1023c 28

Jet pair created at off central position Enhancement of low momentum particles at large angle from jet axis out-of-cone  Y.Tachibana and TH, Nucl.Phys.A (2013)1023c 29

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

Alternative constraint for shear viscosity through propagation of jets? Heat-up from mini-jets propagation similar to neutrino reheating in SNE? Jet propagation momentum transfer 31

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

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Hadronic cascade 3D ideal hydro Monte Carlo I.C. (MC-KLN or MC-Glauber) 0 collision axis time 35

conventional hydro event-by-event hydro 36

40-50% Almost boost invariant 37

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

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) 39

ATLAS, arXiv: Even Harmonics Odd Harmonics # of events: (Remember full 3D hydro+cascade!) Subevent “N”: charged, -4.8<  < -3.2 (FCal in ATLAS) Subevent “P”: charged, 3.2<  < 4.8 (FCal in ATLAS) 40

Even HarmonicsOdd Harmonics Not boost inv.  almost boost inv. for epsilon 40-50% 41

Even HarmonicsOdd Harmonics 40-50% v odd {RP}~0 v even {EP}>v even {RP} due to fluctuation v n {RP}: v n w.r.t. reaction plane known in theory 42