The R.H.I.C. Transport Challenge

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1 The R.H.I.C. Transport Challenge Berndt Mueller (with Steffen A. Bass) Modeling Methodology Working Group SAMSI, November 23, 2006

description

The R.H.I.C. Transport Challenge. Berndt Mueller (with Steffen A. Bass) Modeling Methodology Working Group SAMSI, November 23, 2006. Nucleons + mesons. Nucleons + mesons. Quark-gluon plasma. Genre: Comedy / Crime / Romance / Thriller. Melting nuclear matter (at RHIC / LHC / FAIR). - PowerPoint PPT Presentation

Transcript of The R.H.I.C. Transport Challenge

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The R.H.I.C. Transport Challenge

Berndt Mueller (with Steffen A. Bass)

Modeling Methodology Working Group SAMSI, November 23, 2006

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Some Like It Hot…

Genre: Comedy / Crime /

Romance / Thriller

Nucleons +

mesons

Quark-gluon

plasma

Nucleons +

mesons

Melting nuclear matter (at RHIC / LHC

/ FAIR)

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Elements of matter and force

Matter Particles

Force Particles

Photon (γ), gluon (g), weak bosons (W/Z)

Higgs boson (H), graviton (G)

e

u e

d

c

s

t

b

Quarks

Leptons

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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 (~ 21012 K) quarks and gluons are

liberated; nuclear matter becomes a quark-gluon plasma.

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When the Universe was hot…

Quarks acquire QCD mass and become confined

Atoms form and Universe becomes transparent

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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)

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Interlude about units

Energy (temperature) is usually measured in units

1 MeV 105 binding energy of H-atom 10-3 rest energy of proton

Time is usually measured in units

1 fm/c = 310-24 s time for light to traverse a proton

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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 7 MeV) Plasma - the QGP (T > Tc 150 – 200 MeV)

The QGP itself may exist in different phases: Gaseous plasma (T Tc) Liquid plasma (T, near Tc,c ?) Solid, color superconducting plasma ( c)

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QCD phase diagram

B

Hadronicmatter

Critical end point

Plasma

Nuclei

Chiral symmetrybroken

Chiral symmetryrestored

Color superconductor

Neutron stars

T

1st order line

Quark-Gluon

RHIC

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QCD equation of state

RHIC

2

30

170 340 510 MeV

27f4(2 8)Degrees of fr (2 3 ) 1 ( )eedom : N O g

quarksgluons

colorcolorspin spin flavor

Indication of weak coupling?

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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

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Color screening

a

2 ( ) ( )a a b a bG Qg g

2a a Induced color density

2 2 2 2( ) ,wit (6

h )FG Q

NgT gT

Static color charge (heavy quark) generates screened potential

a a rst er

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Quark masses change

Higgs

field

quark

Quark

condensate

quarkqq

qq

Quark consendate “melts” above Tc and QCD mass

disappears: chiral symmetry restoration

1

10

100

1000

10000

100000

1000000

u d s c b t

QCD mass

Higgs mass

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The practical path to the QGP…

STAR

…is hexagonal and 3.8 km long

Relativistic Heavy Ion Collider

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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

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Collision Geometry: Elliptic Flow

Elliptic flow (v2):

• Gradients of almond-shape surface will lead to preferential expansion in the reaction plane• Anisotropy of emission is quantified by 2nd Fourier coefficient of angular distribution: v2

prediction of fluid dynamics

Reaction plane

x

z

y

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: (x,i), P(), (,etc.).

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spatial eccentricity

momentumanisotropy

initial energy density distribution:

Elliptic flow: early creation

Time evolution of the energy density:

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

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v2(pT) vs. hydrodynamics

Mass splitting characteristic property of hydrodynamics

Failure of ideal hydrodynamics tells us how hadrons form

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Quark number scaling of v2

In the recombination regime, meson and baryon v2 can be obtained from the quark v2 :

2 2 2 2v22

v3

v3v Btt

q tM q tp ppp

qqq

qqT,,v

Emitting medium is composed of unconfined,

flowing quarks.

Chiho Nonaka

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Investigative tools

Phenomenology provides the connection

Detectors Computers

BG-J

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Purpose of dynamic modeling

initial state

pre-equilibrium

QGP andhydrodynamic expansion

hadronization

hadronic phaseand freeze-out

Lattice-Gauge Theory: rigorous calculation of QCD quantities works in the infinite size / equilibrium limit

Experiments: only observe the final state rely on QGP signatures predicted by Theory

Transport-Theory: full description of collision dynamics connects intermediate state to observables provides link between LGT and data

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Transport theory for RHIC

PCM & clust. hadronization

NFD

NFD & hadronic TM

PCM & hadronic TM

CYM & LGT

string & hadronic TM

hadronization

initial state

pre-equilibrium

QGP andhydrodynamic expansion

hadronic phaseand freeze-out

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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

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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

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Microscopic transport

The state of the system is defined by the N-body distribution function fN

In the low-density limit, neglecting pair correlations and assuming that f1 only changes via two-body scattering, the time-evolution of f1 can be described by a Boltzmann equation:

1processes

, , , ,p

f p r t C p r tt E r

Microscopic transport models describe the temporal evolution of a system of individual particles by solving a transport equation derived from kinetic theory

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Relativistic fluid dynamics

Transport of macroscopic degrees of freedom based on conservation laws: μTμν=0, μ jμ=0

For ideal fluid: Tμν= (ε+p) uμ uν - p gμν and jiμ = ρi uμ

Equation of state closes system of PDE’s: p=p(,ρi)

Initial conditions are input for calculation

RFD assumes: local thermal equilibriumvanishing mean free path

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Rel. Hydro

Q-G-Plasma

Micro

time

Hadron GasMonte Carlo

Hadronization

Hybrid transport models

Ideally suited for dense systems model early QGP reaction stage

Well defined Equation of State Parameters:

initial conditions equation of state

Hydrodynamics + 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

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Analysis challenge

Parameters:

Initial conditions Equation of state Transport coefficients Reaction rates Scattering cross

sections Emission source Etc.

Observables:

Hadron spectra Angular distributions Chemical composition Pair correlations Photons / di-leptons Jets Heavy quarks Etc.

Models

Analysis

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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,) is highly nonlinear. Output of MC simulations is noisy.

Estimate of required resources: 104 simulations for each point in parameter space. MC sampling of O(105) points in parameter space. O(1011) floating point op’s per simulation.

Total numerical task O(1020) floating point op’s. Efficient strategy is critical.

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RHIC Transport Initiative

Modeling Relativistic Heavy Ion Collisions

Proposal to DOE Office of Science

Scientific Discovery through Advanced Computing 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)

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RTI structure

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Optimization strategy

Use Bayesian statistical approach. Vector of observables {yO(x,)} with known system

parameters x and model parameters . Compare with vector of modeled values {yM(x,)} as

yO(x,) = yM(x,) + b(x) + ,with bias b(x) and mean-zero random describing experimental errors and fluctuations.

Create Gaussian random field surrogate zM(x,) of yM(x,) for efficient MCMC simulation of posterior probability distribution P(|yM).

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Visualization framework

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IT Infrastructure

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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!

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THE END