The R.H.I.C. Transport Challenge

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

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

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

4. 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1012K) quarks and gluons are liberated; nuclear matter becomes a quark-gluon plasma.

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

6. 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)

7. 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

8. 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)

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

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

11. 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

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

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

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

15. 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

16. z Reaction plane y x • 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 Collision Geometry: Elliptic Flow • 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.).

17. Elliptic flow: early creation spatial eccentricity momentum anisotropy Time evolution of the energy density: initial energy density distribution: Flow anisotropy must generated at the earliest stages of the expansion, and matter needs to thermalize very rapidly, before 1 fm/c.

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

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

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

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

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

23. 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

24. 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

25. 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:

26. 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

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

28. 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. Analysis challenge Models Analysis

29. 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.

30. 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)

31. RTI structure

32. 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).

33. Visualization framework

34. IT Infrastructure

35. 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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