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
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Elements of matter and force
Matter Particles
Force Particles
Photon (?), gluon (g), weak bosons (W/Z) Higgs
boson (H), graviton (G)
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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 ( 2?1012 K) quarks and
  gluons are liberated nuclear matter becomes a
  quark-gluon plasma.

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When the Universe was hot
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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 3?10-24 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 gt 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)

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QCD phase diagram
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QCD equation of state
170 340
510 MeV
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 (? its 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
Static color charge (heavy quark) generates
screened potential
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Quark masses change
Quark consendate melts above Tc and QCD mass
disappears chiral symmetry restoration
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The practical path to the QGP
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

• 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.).

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Elliptic flow early creation
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
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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.
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Investigative tools
BG-J
Phenomenology provides the connection
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Purpose of dynamic modeling
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
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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
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
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Relativistic fluid dynamics

• Transport of macroscopic degrees of freedom based
  on conservation laws ?µTµ?0, ?µ jµ0
• For ideal fluid Tµ? (ep) uµ u? - p gµ? and
  jiµ ?i uµ
• Equation of state closes system of PDEs
  pp(e,?i)
• Initial conditions are input for calculation
• RFD assumes
• local thermal equilibrium
• vanishing mean free path

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Hybrid transport models
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

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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,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 ops per simulation.
• Total numerical task O(1020) floating point ops.
• 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 PIs 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,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(qyM).

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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