Heavy Ion Meeting 2013-10, Inha Univ., Korea, Nov.2, 2013 Tetsufumi Hirano Sophia Univ. K.Murase,...
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Transcript of Heavy Ion Meeting 2013-10, Inha Univ., Korea, Nov.2, 2013 Tetsufumi Hirano Sophia Univ. K.Murase,...
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REVIEW OF RECENT DEVELOPMENT IN HYDRO
Heavy Ion Meeting 2013-10,Inha Univ., Korea, Nov.2, 2013
Tetsufumi HiranoSophia Univ.
K.Murase, TH, arXiv:1304.3243Y.Tachibana, TH, Nucl.Phys.A904-905(2013)1023c
Y.Tachibana, talk at Hard Probes 2013M.Hongo, Y.Hirono, TH, arXiv:1309.2823
2
Outline Introduction Relativistic fluctuating hydrodynamics Medium response to jet propagation Anomalous hydrodynamics and chiral
magnetic effect Summary
3
Introduction
0collision axis
time
3. QGP fluid
4. Hadron gas
1. QCD aspects of nuclear structure
2. Non-equilibriumstatistical physics
3. Relativistichydrodynamics
4. Relativistic kinetic theory
1. Color glass condensate
2. Glasma
โFormโ of matterApproach
Hydrodynamics as a central framework of heavy ion collisions
Higher Harmonics is Finite!
Figures adapted from talkby J.Jia (ATLAS) at QM2011
Two particle correlation function is composed solely of higher harmonics
5See talks by Y.-S.Kim and M.-J. Kweon
Impact of Finite Higher Harmonicsโข Most of the people did not
believe hydro description of the QGP (~ 1995)
โข Hydro at work to describe elliptic flow (~ 2001)
โข E-by-e hydro at work to describe higher harmonics (~ 2010)
๐โฒ5 fm
coarsegraining
size
initialprofile
๐โฒ1 fm
6
Is fluctuation important in such a small system?
7
Thermal Fluctuation โข Conventional hydro describes space-time
evolution of (coarse-gained) thermodynamic quantities.
โข Some of microscopic information must be lost through coarse-graining process.
โข Does the lost information play an important role in dynamics on an e-by-e basis? Thermal (Hydrodynamic) fluctuation!
J.Kapusta, B.Muller, M.Stephanov, PRC85(2012)054906.J.Kapusta, J.M.Torres-Rincon, PRC86(2012)054911.P.Kovtun, G.D.Moore, P.Romatschke, PRD84(2011)025006.J.Peralta-Ramos, E.Calzetta, JHEP1202(2012)085.
Causal Hydrodynamics
ฮ (๐ก )=โซ๐๐กโฒ๐บ๐ (๐ก , ๐กโฒ )๐น (๐ก โฒ )Linear response to thermodynamic force
8
Dissipative current Themodynamic force Shear Shear stress tensor Gradient of flowBulk Bulk pressure Divergence of flow
Diffusion Diffusion current Gradient of chemical potential
9
Causal Hydrodynamics (contd.)
Differential form
ฮ ฬ (๐ก )=โ ฮ (๐ก )โ๐ ๐น (๐ก )๐
,
Maxwell-Cattaneo Eq. (simplified Israel-Stewart Eq.)
๐ฃ signal=โ ๐ ๐ <๐
2. Retarded Green function (causal, 2nd order hydro)
๐บ๐ (๐ก ,๐ก โฒ )= ๐ ๐exp(โ ๐กโ ๐ก
โฒ
๐ )๐ (๐กโ๐ก โฒ)
1. Delta function (acausal, 1st order hydro)
๐บ๐ (๐ก ,๐ก โฒ )=๐ ๐ฟ (๐กโ ๐ก โฒ )โฮ (๐ก )=๐ ๐น (๐ก )
Relativistic Fluctuating Hydrodynamics (RFH)
ฮ (๐ฅ )=โซ๐4 ๐ฅ โฒ๐บ๐ (๐ฅ ,๐ฅ โฒ )๐น (๐ฅโฒ )+๐ฟฮ (๐ฅ)โจ๐ฟฮ (๐ฅ )๐ฟฮ (๐ฅโฒ )โฉ=๐๐บโ(๐ฅ , ๐ฅโฒ )
Generalized Langevin Eq. for fields
For non-relativistic case, see Landau-Lifshitz, Fluid Mechanics
Fluctuation-Dissipation Relation (FDR)
K.Murase and TH, arXiv:1304.3243[nucl-th]
๐บโ : Symmetrized correlation function
10
๐ฟฮ : Hydrodynamic fluctuation
Colored Noise in Relativistic System
โจ๐ฟฮ ๐ ,๐โ ๐ฟฮ ๐ โฒ ,๐ โฒ โฉ=2๐ (2๐ )4 ๐ฟ(๐โ๐ โฒ)๐ฟ(3 )(๐โ๐ โฒ)
1+๐2๐2
๐บ๐ (๐ก ,๐ก โฒ )= ๐ ๐exp(โ ๐กโ ๐ก
โฒ
๐ )๐ (๐กโ๐ก โฒ)
: Extention to Correlation in Fourier space
Colored noise! As a consequence of causalityNote: white noise in differential form
K.Murase and TH, arXiv:1304.3243[nucl-th]
11cf.) C. Young, arXiv:1306.0472
Fluctuation in Non-Linear Equation
Rayleigh-Taylor instability
Need numerical implementation of fluctuating hydro
Kelvin-Helmhortz instability
Figures from J.B.Bell et al., ESAIM 44-5 (2010)1085
12
Ex.) Seeds for instabilities
Jet Quenching as Missing pT
Figures adapted from talkby C.Roland (CMS) at QM2011
Jet momentum balanced by low pT hadrons outside the jet cone! Medium response?
in-cone
out-of-cone
14See talk by Y.-S. Kim
Momentum Balance Restored
Lost energy low pT particles at large angle
Figure adapted from talk by C.Roland (CMS) at QM2011
15
Horizontal: Jet asymmetryVertical: Transverse momenta (anti-)parallel to jet axis
๐๐๐ fluid๐๐ = ๐ฝ jet
๐
Energy and Momentum Flowing into QGPโข Jet quenching could affect QGP expansion
at LHC (and even at RHIC?)โข Relativistic hydrodynamics with a source
term due to propagation of jets
16
๐ฝ jet0 (๐ฅ )=โ
๐๐0๐๐ก
๐ฟ(3 )(๐โ ๐ (๐ก ))
๐ฝ jet๐ (๐ฅ )=โ
๐๐0๐๐ก
๐๐
๐0๐ฟ(3 )(๐โ ๐ (๐ก ))
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
17
QGP Mach Cone Induced by a Jet
Fully non-linear and fully 3D hydro simulation of Mach cone
Y.Tachibana and TH, Nucl.Phys.A904-905(2013)1023c
18
Central collisionat LHCJet momentum:
19
Energy Balance in and out-ofJet Cone in Hydro + Jet Model
Energy balance Leading jet Soft particle
Qualitatively consistent with CMS results
Another Channel to Constrain Shear Viscosity?โข Jet propagation induces large flow velocity
along jet axis.โข How much momentum diffuses perp. to
jet axis?
20
Y.Tachibana and TH, Nucl.Phys.A904-905 (2013)1023c
Momentum diffusion
22
Strong EM fields in Heavy Ion Collisions
Figure taken from http://physics.aps.org/articles/v2/104
!!!
Electr
ic cu
rrent
Electr
ic cu
rrent
Positively charged heavy ion as a source ofelectro magnetic field Ampereโs law
Magnetic field
23
Charge Asymmetry of Pion
๐ดยฑ=๐+ยฟโ๐โ
๐+ยฟ+๐โยฟยฟ
G.Wang (STAR), arXiv:1210.5498
Charge asymmetic results indicate existenceof electromagnetic effects of transport?
24
Chiral Magnetic Wave
Slide taken from a seminar talk by M.Hongo at BNL (2013)
D.Kharzeev and H.U.Yee(2011);Y.Burnier et al.(2011)
For introduction of CME and CSE, see K.Fukushima, arXiv:1209.5064
chiralseparation
effect
chiralmagnetic
effect
Anomalous HydroHydrodynamic eqs. under EM fields + anomaly
Constitutive eqs. incl. CME and CSE
D.T.Son and P.Surowka,PRL103(2009)19160125
27
Charge density and axial charge density in thetransverse plane at
Charge and Axial Charge in Expanding Case
๐ก=6 fm/c
M.Hongo, Y.Hirono, TH, arXiv:1309.2823
28
Difference of btw. Positive and Negative pions
STAR data without anomalyIntercept is finite with anomaly
Need more quantitative analysis of anomalous hydro
M.Hongo, Y.Hirono, TH, arXiv:1309.2823
29
SummaryHydrodynamic framework/simulation extended in three directionsโข Relativistic fluctuating hydrodynamics
โข Source term from jet propagation
โข Quantum anomalous effects
Eccentricity Fluctuation in Small System
๐ part>๐stdPHOBOS, Phys. Rev. Lett. 98, 242302 (2007) 30
Fluctuation in Initial Conditions
B.Alver et al., Phys. Rev. C 77, 014906 (2008)
๐๐=โจ๐2๐๐๐ ๐ โฉ
โจ๐ 2 โฉ
31
Fluctuation Appears Everywhere
0collision axis
tim
e Finite number of hadrons
Propagation of jets
Hydrodynamic fluctuation
Initial fluctuation andparticle production 32
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. )
33
Relaxation and CausalityConstitutive equations at Navier-Stokes level
โฆ
๐ก
thermodynamics force
๐ก 0
๐นโจ๐
/๐
Realistic response
Instantaneous response violates causality Critical issue in
relativistic theory Relaxation plays an
essential role
๐ 34
Coarse-Graining in Time
๐ก
๐บ๐
๐ก โฒ
๐บ๐
๐บ๐ =๐ ๐๐โ ๐ก๐ ๐บ๐ โ ๐ ๐ฟ (๐ก โฒ )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
๐กโ ๐ก โฒ
35
Outlook for RFH
36
โข Numerical implementation in full hydro equation (not linearized one) and its consequences in observablesโข Langevin simulation in constrained system?โข Dynamic critical phenomena
Need further formulation of RFH
Large Angle Emission from Expanding Medium
Jet pair created atoff central position Enhancement of low
momentum particles at large angle from jet axis
ฮ ( ๐๐โฅ
๐cos๐ )= ๐๐โฅ
w . jet
๐ cos๐โ๐๐โฅ
w .o . jet
๐cos๐
out-of-coneqcos๐=โ1cos๐=1
Y.Tachibana and TH, Nucl.Phys.A904-905 (2013)1023c
37
Outlook for Interplay between Soft and Hardโข Alternative constraint for shear viscositythrough propagation of jets?
โข Heat-up due to mini-jets propagation similar to neutrino reheating in Super Nova Explosion?
Jet propagationmomentum
transfer perp. tojet propagation
38
41
Full 3D Anomalous Hydro Simulation
๏ฟฝโ๏ฟฝ
๐๐ ๐๐ฟ
๐=๐๐ +๐๐ฟ
M.Hongo, Y.Hirono and TH, arXiv:1309.2823
๐๐ต๐ฆ=1.0GeV2
โGroup velocityโ of chiral magnetic wave CME under expanding background? Source of charge asymmetric ?
๐=0.5GeV
Backgroundtemperature