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

Some Like It Hot… Nucleons + mesons Quark-gluon plasma Genre: Comedy / Crime / Romance / Thriller Nucleons + mesons Quark-gluon plasma Melting nuclear matter (at RHIC / LHC / FAIR)

Elements of matter and force Matter Particles Quarks Leptons Force Particles Photon (γ), gluon (g), weak bosons (W/Z) Higgs boson (H), graviton (G)

Transitions Normal (atomic) matter: Nuclear 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1012 K) quarks and gluons are liberated; nuclear matter becomes a quark-gluon plasma.

When the Universe was hot… Atoms form and Universe becomes transparent Quarks acquire QCD mass and become confined

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)

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 = 310-24 s  time for light to traverse a proton

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,m near Tc,mc ?) Solid, color superconducting plasma (m  mc)

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

QCD equation of state RHIC quarks gluons Indication of weak coupling? color spin flavor 170 340 510 MeV RHIC Indication of weak coupling?

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

Color screening fa Induced color density Static color charge (heavy quark) generates screened potential

Quark masses change Higgs field quark Quark condensate quark Quark consendate “melts” above Tc and QCD mass disappears: chiral symmetry restoration

The practical path to the QGP… STAR …is hexagonal and 3.8 km long Relativistic Heavy Ion Collider

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

Collision Geometry: Elliptic Flow 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: e(x,ti), P(e), (h,etc.). 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

Elliptic flow: early creation momentum anisotropy spatial eccentricity Time evolution of the energy density: initial energy density distribution: Anisotropic observables are of special interest as they reflect the dynamics of the earliest stages of the reaction, and thus the dynamics of the hottest phases, eventually the plasma phase that we hope to achieve in heavy ion collisions at RHIC. The overlap region of two nuclei at finite impact parameter is strongly deformed, which you can see here characterized by contours of constant wounded nucleon density in the plane orthogonal to the beam axis. If the system is driven apart by the pressure in the system, then you see that it will expand faster into the direction of the strongest pressure gradients, and that is in the direction of the reaction plane. Upon building up an anisotropic flow field, the system will therefore get rounder with time, as you can see in those subsequent shots of the transverse plane at different times. This reduction of the spatial eccentricity can be quantified by averaging the difference of the width in x direction and the width in y direction over this transverse distribution function. You see how this leads to a rapid decrease of the initial large geometric anisotropy over timescales relevant for heavy ion dynamics, once displayed here for a system with a very hard equation of state of a ideal gas, where the transition is very rapid, and once for an equation of state that involves a phase transition from hadronic to partonic degrees of freedom. While the system becomes isotropic in coordinate space, it builds up anisotropies in momentum space, which you can characterize by the difference of the diagonal components of the energy momentum tensor. And here you see nicely how, as the system gets round in coordinate space, no further momentum anisotropy is built up. Note that for a system with a large mixed phase, the generation of further anisotropies is stalled significantly earlier. The momentum anisotropy you observe is really built up in the plasma stage! The timescale suggested from all model calculations, no matter if macroscopic or microscopic is generally below 5 fm/c. Anisotropies thus probe the earliest stages of the collision. Flow anisotropy must generated at the earliest stages of the expansion, and matter needs to thermalize very rapidly, before 1 fm/c.

v2(pT) vs. hydrodynamics Failure of ideal hydrodynamics tells us how hadrons form Mass splitting characteristic property of hydrodynamics

Quark number scaling of v2 In the recombination regime, meson and baryon v2 can be obtained from the quark v2 : Chiho Nonaka T,m,v  Emitting medium is composed of unconfined, flowing quarks.

Phenomenology provides the connection Investigative tools Detectors Computers BG-J Phenomenology provides the connection

Purpose of dynamic modeling initial state pre-equilibrium QGP and hydrodynamic expansion hadronization hadronic phase and 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

Transport theory for RHIC hadronization initial state pre-equilibrium QGP and hydrodynamic expansion hadronic phase and freeze-out

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

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

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 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:

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(e,ρi) Initial conditions are input for calculation RFD assumes: local thermal equilibrium vanishing mean free path

Hybrid transport models Rel. Hydro Q-G-Plasma Micro time Hadron Gas Monte Carlo Hadronization Hydrodynamics + microscopic transport Ideally suited for dense systems model early QGP reaction stage Well defined Equation of State Parameters: initial conditions equation of state 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

Analysis challenge Models Analysis Parameters: Observables: 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

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:  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.

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)

RTI structure

Optimization strategy Use Bayesian statistical approach. Vector of observables {yO(x,q)} with known system parameters x and model parameters q. Compare with vector of modeled values {yM(x,q)} as yO(x,q) = yM(x,q) + b(x) + e , with bias b(x) and mean-zero random e describing experimental errors and fluctuations. Create Gaussian random field surrogate zM(x,q) of yM(x,q) for efficient MCMC simulation of posterior probability distribution P(q|yM).

Visualization framework

IT Infrastructure

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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