The

R.H.I.C.

Transport Challenge

Berndt Mueller (with Steffen A. Bass)

Modeling Methodology Working Group

SAMSI, November 23, 2006

1

Some Like It Hot…

Genre:

Comedy / Crime / Romance Thriller / Quark gluon plasma Melting nuclear matter (at RHIC / LHC / FAIR)

2

Elements of matter and force Matter Particles

Quarks Leptons

u



e e c

  

t

  

Force Particles

Photon (γ), gluon (g), weak bosons (W/Z) Higgs boson (H), graviton (G)

3

Transitions

 Normal (atomic) matter:  Electrons and atomic nuclei are bound into atoms  With sufficient heat (~ 3000 K) electrons can be set free; atomic matter becomes a electron-ion plasma.

 Nuclear matter:   Quarks and gluons are bound into protons and neutrons With sufficient heat (~ 2  10 12 K) quarks and gluons are liberated; nuclear matter becomes a quark-gluon plasma.

4

When the Universe was hot…

Atoms form and Universe becomes transparent Quarks acquire QCD mass and become confined 5

Why Heat Stuff Up?

 What heat does to matter:  Increases disorder (entropy)  Speeds up reactions  Overcomes potential barriers  States / phases of matter:  Solid [long-range correlations, shear elasticity]  Liquid [short-range correlations]  Gas [few correlations]  Plasma [charged constituents] (solid / liquid / gaseous)

6

Interlude about units

 Energy (temperature) is usually measured in units 1 MeV   10 5 10 -3   binding energy of H-atom rest energy of proton  Time is usually measured in units 1 fm/c = 3  10 -24 s  time for light to traverse a proton

7

QCD (Nuclear) Matter

 Matter governed by the laws of QCD can also take on different states:  Solid, e.g. crust of neutron stars    Liquid, e.g. all large nuclei Gas, e.g. nucleonic or hadronic gas (T  Plasma - the QGP (T > T c  150 7 MeV) – 200 MeV)  The QGP itself may exist in different phases:    Gaseous plasma (T  Tc) Liquid plasma (T,  near T c ,  c ?) Solid, color superconducting plasma (    c )

8

QCD phase diagram

RHIC T Quark Gluon Critical end point Plasma Hadronic matter Chiral symmetry broken 1 st order line Nuclei Chiral symmetry restored Color superconductor Neutron stars  B

9

QCD equation of state

Degrees of fr eedom :  gluons   (2 8) spin color 4 quarks (2 3

N

f ) spin color flavor  30 

170 340 510 MeV

RHIC

Indication of weak coupling?

2 ) 

10

QGP properties

 The

Quark-Gluon Plasma

is characterized by two properties not normally found in our world:  Screening of color fields (  it’s a plasma!):  Quarks and gluons are liberated  Disappearance of 98% of (

u,d

) quark masses:  Chemical equilibrium among quarks is easily attained

11

Color screening

 2 f

a



g a G b

) 

g a Q

Induced color density 

a

 

b

)

a

wit h 

G

2  (

gT



Q

2 

N F

6 (

gT

) 2 f

a

Static color charge (heavy quark) generates screened potential f

a



t a



s r e

 

r

12

Quark masses change

1000000

Higgs

100000 QCD mass Higgs mass

quark

10000

field

1000 100 10

quark Quark

qq qq

1 u d s c b t

condensate Quark consendate “melts” above

T

c and QCD mass disappears: chiral symmetry restoration

13

The practical path to the QGP…

…is hexagonal and 3.8 km long

R

elativistic

H

eavy

I

on

C

ollider

STAR

14

RHIC results

Some important results from RHIC:       Chemical and thermal equilibration (incl.

s

-quarks!) 

u, d, s

-quarks become light and unconfined Elliptic flow  rapid thermalization, extremely low viscosity Collective flow pattern related to valence quarks Jet quenching  parton energy loss, high color opacity Strong energy loss of

c

and

b

quarks (why?) Charmonium suppression is not increased compared with lower (CERN-SPS) energies

15

Collision Geometry: Elliptic Flow

Reaction plane

z y x

Elliptic flow (v 2 ):

• Gradients of almond-shape surface will lead to preferential expansion in the reaction plane • Anisotropy of emission is quantified by 2 nd Fourier coefficient of angular distribution: v 2  prediction of fluid dynamics     Bulk evolution described by relativistic fluid dynamics , assumes that the medium is in local thermal equilibrium, but no details of how equilibrium was reached.

Input:

e

(x,



i ), P(

e

), (

h

,etc.).

16

Elliptic flow: early creation

spatial eccentricity momentum anisotropy Flow anisotropy must generated at the earliest stages of the expansion, and matter needs to thermalize very rapidly, before 1 fm/c.

17

v

2

(

p

T

) vs. hydrodynamics

Failure of ideal hydrodynamics tells us how hadrons form Mass splitting characteristic property of hydrodynamics

18

Quark number scaling of v

2 In the recombination regime, meson from the quark v 2 : v 2  

t

 2 v 2

q

 

p

2

t

  and baryon v 2 can be obtained v 2

B

 

t

 3 v

q

2  

p t

3  

qqq

T,



,v

qq



Emitting medium is composed of unconfined, flowing quarks.

19

Investigative tools Detectors Computers

BG-J

Phenomenology

provides the connection

20

Purpose of dynamic modeling

QGP and hydrodynamic expansion hadronic phase and freeze-out initial state Lattice-Gauge Theory: Experiments: pre-equilibrium Transport-Theory: hadronization

 rigorous calculation of QCD quantities  works in the infinite size / equilibrium limit  only observe the final state  rely on QGP signatures predicted by Theory  full description of collision dynamics  connects intermediate state to observables  provides link between LGT and data

21

Transport theory for RHIC

initial state QGP and hydrodynamic expansion hadronic phase and freeze-out pre-equilibrium CYM & LGT hadronization PCM & clust. hadronization PCM & hadronic TM NFD NFD & hadronic TM string & hadronic TM 22

Observables / Probes

 Two categories of observables probing the QGP:  Fragments of the bulk matter emitted during break-up  Baryon and meson spectra  Directional anisotropies  Two- particle correlations  Rare probes emitted during evolution of bulk  Photons and lepton pairs  Very energetic particles (jets)  Very massive particles (heavy quarks)  Both types of probes require detailed transport modeling

23

RHIC transport: Challenges

• Collisions at RHIC cover a sequence of vastly different dynamical regimes • Standard transport approaches (hydro, Boltzmann, etc.) are only applicable to a subset of the reaction phases or are restricted to a particular regime   Hybrid models can extend the range of applicability of conventional approaches The dynamical modeling of the early reaction stage and thermalization process remain special challenges

24

Microscopic transport

Microscopic transport models describe the temporal evolution of a system of individual particles by solving a transport equation derived from kinetic theory The state of the system is defined by the function In the low-density limit, neglecting pair correlations and assuming that f 1 f 1 f N N -body distribution only changes via two-body scattering, the time-evolution of can be described by a Boltzmann equation :     

t E

 

r

  

f

1     processes  

25

Relativistic fluid dynamics

 Transport of macroscopic degrees of freedom based on conservation laws:  μ T μν =0,  μ j μ =0   For ideal fluid: T μν = (ε+p) u μ u ν - p g μν and j i μ = ρ i u μ Equation of state closes system of PDE’s: p=p( e ,ρ i )  Initial conditions are input for calculation  RFD assumes:  local thermal equilibrium  vanishing mean free path

26

Hybrid transport models

Rel. Hydro Q-G-Plasma Hydrodynamics

  

Ideally suited for dense systems

 model early QGP reaction stage

Well defined Equation of State Parameters:

  initial conditions equation of state

Hadronization + Micro Hadron Gas

Monte Carlo time

microscopic transport

 

Ideally suited for dilute systems

  model break-up/ freeze-out stage describe transport properties microscopically

Parameters:

 scattering cross sections matching condition: • same equation of state • generate hadrons in each cell using local conditions

27

Analysis challenge

 Parameters:  Initial conditions  Equation of state  Transport coefficients  Reaction rates  Scattering cross sections  Emission source  Etc.

Models Analysis  Observables:  Hadron spectra  Angular distributions  Chemical composition  Pair correlations  Photons / di-leptons  Jets  Heavy quarks  Etc.

28

Estimate of challenge

Optimization of parameters (with errors) involves:     20 – 30 parameters.

Large set of independent observables (10s – 100s).

Calculation for each parameter set: 1 – 10 h CPU time.

y

(

x

, q ) is highly nonlinear.

 Output of MC simulations is noisy.

Estimate of required resources:   10 4 simulations for each point in parameter space.

   MC sampling of O(10 5 ) points in parameter space.

O(10 11 ) floating point op’s per simulation.

Total numerical task

O

(10 20 ) floating point op’s.

 Efficient strategy is critical.

29

RHIC Transport Initiative

Modeling Relativistic Heavy Ion Collisions

Proposal to DOE Office of Science

Sci

entific

D

iscovery through

A

dvanced

C

omputing Program 10 PI’s from 5 institutions led by Duke, including 4 Duke faculty members (S.A. Bass, R. Brady, B.Mueller, R. Wolpert) Proposed budget ($4.5M over 5 years)

30

RTI structure

31

Optimization strategy

    Use Bayesian statistical approach.

Vector of observables {

y

O (

x

, q )} parameters

x

with known system and model parameters q .

Compare with vector of modeled values {

y

M (

x

, q )} as with bias

b

(

x y

O (

x

, q ) =

y

M (

x

, q ) +

b

(

x

) + e ) and mean-zero random e , describing experimental errors and fluctuations.

Create Gaussian random field surrogate

z

M (

x

, q )

y

M (

x

, q ) probability distribution P( q |

y

M ).

of for efficient MCMC simulation of posterior

32

Visualization framework

33

IT Infrastructure

34

Outlook

The first phase

of the

RHIC science program has shown that:

•

equilibrated matter is rapidly formed in heavy ion collisions;

•

wide variety of probes of matter properties available;

•

systematic study of matter properties is possible.

The Quark-Gluon Plasma appears to be a novel type of liquid with unanticipated transport properties.

The successful execution of the next phase of the RHIC science program will require:

•

sophisticated, realistic modeling of transport processes;

•

state-of-the-art statistical analysis of experimental data in terms of model parameters.

Exciting opportunities for collaborations between physicists and applied mathematicians!

35

THE END

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