重イオン衝突における 散逸と 揺らぎ

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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 - PowerPoint PPT Presentation

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Page 1: 重イオン衝突における 散逸と 揺らぎ

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

平野哲文(上智大理工)共同研究者 : 村瀬功一 , 橘保貴

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Page 2: 重イオン衝突における 散逸と 揺らぎ

Outline1. はじめに2. Initial fluctuation3. Relativistic fluctuating

hydrodynamics4. Jet propagation in expanding

medium5. Summary and outlook

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はじめに発見のステージ 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

Page 4: 重イオン衝突における 散逸と 揺らぎ

INITIAL FLUCTUATION

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Page 5: 重イオン衝突における 散逸と 揺らぎ

Eccentricity Fluctuation in Small System

𝜀 part>𝜀stdPHOBOS, Phys. Rev. Lett. 98, 242302 (2007) 5

Page 6: 重イオン衝突における 散逸と 揺らぎ

Fluctuation in Initial Conditions

B.Alver et al., Phys. Rev. C 77, 014906 (2008)

𝜀𝑛=⟨𝑟2𝑒𝑖𝑛 𝜙 ⟩

⟨𝑟 2 ⟩

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Page 7: 重イオン衝突における 散逸と 揺らぎ

Higher Harmonics is Finite!

Figures adapted from talkby J.Jia (ATLAS) at QM2011

Two particle correlation function is composed solely of higher harmonics

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Page 8: 重イオン衝突における 散逸と 揺らぎ

Impact of Finite Higher Harmonics• 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)

𝑑≲5 fm

coarsegraining

sizeinitialprofile

𝑑≲1 fm8

Page 9: 重イオン衝突における 散逸と 揺らぎ

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 ? 9

Page 10: 重イオン衝突における 散逸と 揺らぎ

RELATIVISTIC FLUCTUATING HYDRODYNAMICS

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Page 11: 重イオン衝突における 散逸と 揺らぎ

Fluctuation Appears Everywhere

0collision axis

time Finite number of

hadrons

Propagation of jets

Hydrodynamic fluctuation

Initial fluctuation andparticle production

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Page 12: 重イオン衝突における 散逸と 揺らぎ

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. )

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Page 13: 重イオン衝突における 散逸と 揺らぎ

Relaxation and CausalityConstitutive equations at Navier-Stokes level

𝑡

thermodynamics force

𝑡 0

𝐹∨𝑅

/𝜅

Realistic response

Instantaneous response violates causality Critical issue in

relativistic theory Relaxation plays an

essential role

𝜏 13

Page 14: 重イオン衝突における 散逸と 揺らぎ

Causal Hydrodynamics

Π (𝑡 )=∫𝑑𝑡′𝐺𝑅 (𝑡 , 𝑡′ ) 𝐹 (𝑡 ′ )Linear response to thermodynamic force

Retarded Green function𝐺𝑅 (𝑡 ,𝑡 ′ )= 𝜅

𝜏 exp(− 𝑡− 𝑡′𝜏 )𝜃 (𝑡−𝑡 ′)

Differential formΠ̇ (𝑡 )=− Π (𝑡 )−𝜅 𝐹 (𝑡 )

𝜏 ,

Maxwell-Cattaneo Eq. (simplified Israel-Stewart Eq.)

𝑣 signal=√ 𝜅𝜏 <𝑐

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Page 15: 重イオン衝突における 散逸と 揺らぎ

Relativistic Fluctuating Hydrodynamics (RFH)

)

⟨ 𝛿Π (𝑥 )𝛿Π (𝑥′ )⟩=𝑇𝐺∗(𝑥 , 𝑥′ )

Generalized Langevin Eq.dissipative current

hydrodynamicfluctuationthermodynamic force

For non-relativistic case, see Landau-Lifshitz, Fluid Mechanics

Fluctuation-Dissipation Relation (FDR)

K.Murase and TH, arXiv:1304.3243[nucl-th]

𝐺∗: Symmetrized correlation function15

Page 16: 重イオン衝突における 散逸と 揺らぎ

Coarse-Graining in Time

𝑡

𝐺𝑅

𝑡 ′

𝐺𝑅

𝐺𝑅=𝜅𝜏 𝑒

− 𝑡𝜏 𝐺𝑅≈ 𝜅𝛿 (𝑡 ′ )coarse

graining???

Existence of upper bound in coarse-graining time (or lower bound of frequency) in relativistic theory???

Navier Stokes causality

Non-Markovian Markovian

Maxwell-Cattaneo

𝑡→ 𝑡 ′

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Colored Noise in Relativistic System

⟨𝛿Π 𝜔 ,𝒌∗ 𝛿Π 𝜔 ′ ,𝒌 ′ ⟩=2𝜅 (2𝜋 )4 𝛿(𝜔−𝜔 ′)𝛿(3 )(𝒌−𝒌 ′)

1+𝜔2𝜏2

𝐺𝑅 (𝑡 ,𝑡 ′ )= 𝜅𝜏 exp(− 𝑡− 𝑡′

𝜏 )𝜃 (𝑡−𝑡 ′)

: Extention to t<t’Correlation in Fourier space

Colored noise! (Indirect) consequence of causalityNote: white noise in differential form

K.Murase and TH, arXiv:1304.3243[nucl-th]

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A Comment on Heat Conductivity

Phenomenological constitutive eqs.,

for Gluonic system () ???𝜏 𝐷𝑞𝜇

𝐷𝑡 +𝑞𝜇=𝜅𝑇𝑋 𝜇

1st order:

2nd order:

𝜏 𝐷𝑞𝜇

𝐷𝑡 +𝑞𝜇=𝜅𝑇𝑋 𝜇+𝜉𝜇

Getting meaningful solely in RFH Fluctuation of ? 18

RFH: ,

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Need Fluctuation?

Rayleigh-Taylor instabilityNon-linearity, instability, dynamic critical phenomena,…

Kelvin-Helmhortz instability

Figures from J.B.Bell et al., ESAIM 44-5 (2010)1085

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Seeds for instabilities

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Outlook for RFH

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• Numerical implementation and its consequences in observables• Langevin simulation in constrained

system?• Dynamic critical

phenomenaSeparation of systematic motion from noise?• RFH from quantum Langevin eq.?• Heat conductivity in gluonic system

from Hosoya-Kajantie lattice QCD? AdS/CFT?

Page 21: 重イオン衝突における 散逸と 揺らぎ

JET PROPAGATION INEXPANDING MEDIUM

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Page 22: 重イオン衝突における 散逸と 揺らぎ

Fluctuation Appears Everywhere

0collision axis

time Finite number of

hadrons

Propagation of jets

Hydrodynamic fluctuation

Initial fluctuation andparticle production

22

Page 23: 重イオン衝突における 散逸と 揺らぎ

Jet Quenching as Missing pT

Figures adapted from talk

by C.Roland (CMS) at QM2011

Jet momentum balanced by low pT hadrons out of jet cone!

in-coneout-of-cone

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Page 24: 重イオン衝突における 散逸と 揺らぎ

Momentum Balance Restored

Lost energy goes to low pT particles at large angle

Figure adapted from talk by C.Roland (CMS) at QM2011

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Horizontal: Jet asymmetryVertical: Transverse momenta (anti-)parallel to jet axis

Page 25: 重イオン衝突における 散逸と 揺らぎ

𝜕𝜇𝑇 𝜇𝜈= 𝐽𝜈

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

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𝐽 0 (𝑥 )= 𝐽 1 (𝑥 )=−𝑑𝑝0𝑑𝑡 𝛿(3 )(𝒙− 𝒙 (𝑡 ))

𝐽 2 (𝑥 )= 𝐽 3 (𝑥 )=0in the case that jet propagates parallel to x-axis

Page 26: 重イオン衝突における 散逸と 揺らぎ

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

Y.Tachibana and TH, Nucl.Phys.A904-905(2013)1023c

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Page 27: 重イオン衝突における 散逸と 揺らぎ

April 13, 2013 at Mt. Etna

http://photoblog.nbcnews.com/_news/2013/04/12/17720274-mount-etna-blows-smoke-ring-during-volcanic-eruptions

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QGP Mach Cone Induced by a Jet

First fully non-linear and fully 3D hydro simulation of Mach cone

Y.Tachibana and TH, Nucl.Phys.A904-905(2013)1023c

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Page 29: 重イオン衝突における 散逸と 揺らぎ

Large Angle Emission from Expanding Medium

Jet pair created atoff central position Enhancement of low

momentum particles at large angle from jet axis

Δ ( 𝑑𝑝∥

𝑑cos𝜃  )= 𝑑𝑝∥w . jet

𝑑 cos𝜃 −𝑑𝑝∥

w .o . jet

𝑑cos𝜃

out-of-coneqcos𝜃=−1cos𝜃=1

Y.Tachibana and TH, Nucl.Phys.A904-905 (2013)1023c

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Page 30: 重イオン衝突における 散逸と 揺らぎ

Momentum Balance

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preliminaryin cone out of cone

Pb+Pb central collisions at sqrt(s_NN) = 2.76 TeV

Page 31: 重イオン衝突における 散逸と 揺らぎ

Outlook for Interplay between Soft and Hard• Alternative constraint for shear

viscositythrough propagation of jets?

• Heat-up from mini-jets propagation similar to neutrino reheating in SNE?

Jet propagationmomentumtransfer

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Page 32: 重イオン衝突における 散逸と 揺らぎ

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

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Page 33: 重イオン衝突における 散逸と 揺らぎ

BACKUPS

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HYDRO-BASED EVENT GENERATOR

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Current Status: E-by-E H2C

Hadronic cascade

3D ideal hydro

Monte Carlo I.C.(MC-KLN or MC-Glauber)0

collision axis

time

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Page 36: 重イオン衝突における 散逸と 揺らぎ

Initial Density Fluctuation

1𝑁 ∑ initial condition single initial condition

conventionalhydro

event-by-eventhydro 36

Page 37: 重イオン衝突における 散逸と 揺らぎ

Eccentricity, Triangularity, …𝜀𝑛 , part=

|⟨𝑟 2𝑒𝑖𝑛 𝜙 ⟩|⟨𝑟2 ⟩ 𝑛𝜓𝑛=arg ⟨𝑟2𝑒𝑖𝑛 𝜙 ⟩

40-50%

Almost boost invariant37

Page 38: 重イオン衝突における 散逸と 揺らぎ

v2{***}v2{EP}, v2{2}, v2{4}, v2{6}, v2{LYZ}, …

Hydro-based event generator Analysis of the outputs almost in the sameway as experimental people do.

Demonstration of vn analysis according toevent plane method by ATLAS setup.E.g.) Centrality cut using ET in FCal region

ATLAS, arXiv:1108.601838

Page 39: 重イオン衝突における 散逸と 揺らぎ

Resolution of Event Plane

𝑅𝑛=√ ⟨cos [𝑛 (𝛹 𝑛❑1−𝛹 𝑛

2 ) ]⟩

Reaction (Event) plane is not known experimentally nor in outputs from E-by-E H2C. Event plane method

Event plane resolution using two subevents

𝑛𝛹𝑛=tan−1(∑ 𝐸𝑇 ,𝑖 sin𝑛𝜙𝑖

∑ 𝐸𝑇 ,𝑖cos𝑛𝜙𝑖)

c.f.) A.M.Poskanzer and S.Voloshin, Phys. Rev. C 58, 1671 (1998)39

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Resolution of Event Plane from E-by-E H2C

ATLAS, arXiv:1108.6018

Even Harmonics Odd 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)

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Vn{EP}(h)

Even Harmonics Odd Harmonics

Not boost inv. almost boost inv. for epsilon

40-50%40-50%

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Page 42: 重イオン衝突における 散逸と 揺らぎ

vn{EP} vs. vn{RP}

Even Harmonics Odd Harmonics40-50% 40-50%

vodd{RP}~0veven{EP}>veven{RP}due to fluctuation

vn{RP}: vn w.r.t. reaction plane known in theory

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