Dynamics of Relativistic Heavy Ion Collisions and THE Quark - PowerPoint Presentation

Slide1

Dynamics of Relativistic Heavy Ion Collisions and THE Quark Gluon PlasMA

Nonequilibrium Dynamicsin Astrophysics and Material ScienceYITP, Kyoto, Japan, Oct. 31-Nov. 3, 2011

Tetsufumi

Hirano

Sophia Univ./

the Univ. of TokyoSlide2

Outline

IntroductionPhysics of the quark gluon plasmaRelativistic heavy ion collisionsElliptic flow“perfect fluidity”Higher harmonicsSome topics in relativistic hydrodynamicsSlide3

Introduction

“Condensed” matter physics for elementary particlesHeavy ion collisions as a playground of non-equilibrium physics in relativistic systemRecent findings of the quark gluon plasma and related topics Slide4

Physics of the quark gluon plasmaSlide5

Two Aspects of Quantum ChromoDynamics

Confinement of

color charges

Asymptotic free

of QCD

coupling vs. energy scale

QCD: Theory of strong interactionSlide6

What is the Quark Gluon Plasma?

Hadron Gas

Quark Gluon Plasma (QGP)

Degree of freedom: Quarks (matter) and gluons (gauge)

Mechanics: Quantum

ChromoDynamics

(QCD)

Low



Temperature

 High

Novel matter under extreme conditionsSlide7

How High?

Suppose “transition” happens whena pion (the lightest hadron) gas is close-packed,

Note 1:

T

inside the Sun ~ 10

7

K

Note 2:

T

c

from the 1

st

principle calculation ~2x10

12

K

Slide8

Where/When was the QGP?

History of the Universe~ History of form of matterMicro seconds after Big Bang

Our Universe is filled

with the QGP!Slide9

relativistic heavy ion collisionsSlide10

The QGP on the Earth

Front View

Side

View

Relativistic heavy ion collisions

Turn kinetic energy (

v

> 0.99

c

) into thermal energySlide11

Big Bang vs. Little Bang

Figure

adapted

from

http://www-utap.phys.s.u-tokyo.ac.jp/~sato/index-j.htmSlide12

Big Bang vs. Little Bang (contd.)

Big Bang

Little Bang

Time scale

10

-5

sec >>

m.f.p

./c

10

-23

sec ~ m.f.p./c

Expansion rate

10

5-6

/sec

10

22-23

/sec

Spectrum

Red shift (CMB)

Blue shift (hadrons)

m.f.p

. = Mean Free Path

Non-trivial issue on thermal equilibrationSlide13

Non-Equilibrium Aspects of Relativistic Heavy Ion Collisions

0

collision axis

time

Au

Au

3. QGP

fluid

4. hadron

gas

1. Entropy production

2. Local equilibration

3. Dissipative relativistic

fluids

4. Kinetic approach

for relativistic gases

1.

2.Slide14

Hydrodynamic Simulation of a

Au+Au Collision

quark gluon plasma

Time scale ~ 10

-22

sec

http://youtu.be/p8_2TczsxjMSlide15

Elliptic Flow

dN

/

d

f

f

0

2

p

2

v

2

~10

35

Pa

Elliptic flow (

Ollitrault

, ’92)

Momentum anisotropy as a response to spatial anisotropy

Known to be sensitive to properties of the system

(Shear) viscosity

Equation of state

2

nd

harmonics (elliptic flow)



Indicator of hydrodynamic

behaviorSlide16

Relativistic Boltzmann Simulations

Zhang-

Gyulassy

-

Ko

(’99)

v

2

is

generated through secondary collisions

saturated in the early stage

sensitive to cross section (~1/m.f.p.~1/viscosity)

l

: mean free path

h

: shear viscositySlide17

“Hydrodynamic Limit”

Eccentricity

x

y

Response of the system

reaches “hydrodynamic limit”

vs. transverse particle density

 Slide18

Ideal Hydrodynamics at Work

Au+Au

Cu+Cu

T.Hirano

et al. (in preparation)

vs. centrality

 Slide19

Viscous Fluid Simulations

Ratio of shear viscosity to entropy density

vs. transverse particle density

H.Song

et al., PRL106, 192301 (2011)Slide20

Strong Coupling Nature of the QGP

L

arge expansion rate of the QGP in relativistic heavy ion collisions

 Tiny

v

iscosity when hydrodynamic description of the QGP works in any ways

Manifestation of the strong coupling nature of the QGP

Note: Underlying theory  Quantum

ChromoDynamics

(theory of strong interaction)Slide21

Event-by-event Fluctuation

Figure adapted from talk

by

J.Jia

(ATLAS) at QM2011

Ideal, but unrealistic?

OK on average(?)

Actual collision?

Higher order deformationSlide22

Deformation at Higher OrderSlide23

Dynamical Modeling of Relativistic Heavy Ion Collisions*

0

collision axis

time

Au

Au

QGP fluid

hadron gas

Relativistic Boltzmann

Relativistic Ideal Hydro

Monte Carlo I.C.

*

K.Murase

et al.

(in preparation)Slide24

Deformation in Model Calculations

Sample of entropy

density profile in a

plane

perpendicular

to

collision axisSlide25

Higher Harmonics from Ideal QGP Fluids

vs. centrality (input)

vs. centrality (output)

Response of the QGP to initial deformation

roughly scales with

 Slide26

Comparison of vn with Data

Tendency similar to experimental data

Absolute value

 Viscosity

Theory

ExperimentSlide27

Impact of Finite Higher Harmonics

Most of 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

i

nitial

profile

 Slide28

Thermal Radiation from the QGP

Photon spectra in relativisticheavy ion collisions

Blue shifted spectra with T~200-300 MeV~(2-3)x10

12

KSlide29

Relativistic HydrodynamicsSlide30

Several Non-Trivial Aspects of Relativistic Hydrodynamics

Non conservation of particle number nor massChoice of local rest frameRelaxation beyond Fourier, Fick and Newton lawsSlide31

Hydrodynamic Equations (Ideal Hydro Case)

,

Energy conservation

Momentum conservation

,

Charge conservation (net baryon number in QCD)

,

 Slide32

Several Non-Trivial Aspects of Relativistic Hydrodynamics

Non conservation of particle number nor massChoice of local rest frameRelaxation beyond Fourier, Fick and Newton lawsSlide33

Choice of Local Rest Frame in Dissipative Fluids

1. Charge flow

2. Energy flow

(Eigenvector of energy-momentum tensor)

Charge diffusion vanishes on average

No heat flow!

heat flow

charge

diffusion

See also talk by

Kunihiro

*Energy flow is relevant

in heavy ion collisionsSlide34

Several Non-Trivial Aspects of Relativistic Hydrodynamics

Non conservation of particle number nor massChoice of local rest frameRelaxation beyond Fourier, Fick and Newton lawsSlide35

Relaxation and Causality

Constitutive equations at Navier-Stokes level

thermodynamics force

Realistic response

Instantaneous response violates causality

Critical issue in relativistic theory

Relaxation plays an essential role

See also talk by

Kunihiro

 Slide36

Causal Hydrodynamics

Within linear response

Suppose

one obtains differential form

Maxwell-

Cattaneo

Eq.

 Slide37

Relativistic Fluctuating Hydrodynamics (RFH)

)

Thermal fluctuation in event-by-event simulations

d

issipative current

thermal noise

thermodynamic force

*

In

non-relativistic cases, see Landau-

Lifshtiz

, Fluid Mechanics

** Similar to glassy system, polymers,

etc

?

Fluctuation

 DissipationSlide38

Coarse-Graining in Time

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

 Slide39

Finite Size Effect

F

luctuation



Local volume.

Information about coarse-grained size?

Fluctuation term ~ average value?

Non-equilibrium small system?

Fluctuation would play a crucial role.

Need to consider (?) finite size effects in

equation of state and t

ransport coefficientsSlide40

Conclusion

Physics of the quark gluon plasmaStrong coupling natureSmall viscosityPhysics of relativistic heavy ion collisionsPlayground of relativistic non-equilibrium systemRelativistic dissipative hydrodynamicsRelativistic kinetic theory

Non-equilibrium field theory