The R.H.I.C. Transport Challenge
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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
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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
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