Lattice QCD calculations of Tc and Equation of State

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Lattice QCD calculations of Tc and Equation of
State
Rajan Gupta T-8 Los Alamos National Laboratory
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Heavy quarks flow in a medium defined by gluons
and light quarks. Quantities needed to model the
hydrodynamic flow of QGP are

• Tc
• Order of the transition
• EOS (pressure and energy density)

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What we know

• The underlying microscopic theory of hadronic
  interactions is Quantum Chromodynamics (QCD)
• Matter consists of a plasma of quarks and gluons
  in the central collision region
• QCD is strongly interacting at T 200-500 MeV
  (T lt gT lt g2T)
• Phase diagram Qualitative. Need
  non-perturbative calculations for Tc, EOS and
  transport coefficients

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The QCD phase diagram
Quark- Gluon Plasma
T
Critical endpoint ?
QGP
Tc
Hadronic matter
1st order line ?
?B
Nuclei
Neutron stars
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Gauge action on a lattice
a
S action for the gluons Uxy the 3
space-space plaquettes Uxt the 3 space-time
plaquettes ? 6/g2 (gauge coupling on the
lattice) as,t lattice spacing in space, time
direction
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Lattice QCD at Finite Temperature
Nt of points in time direction Ns of
points in space direction at lattice spacing in
time direction as lattice spacing in space
direction
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Parameters we tune

• Lattice action (to reduce discretization errors
  and improve chiral symmetry)
• Values of light (up and down) quark masses
• N? (continuum limit N???, a?0, aN? fixed)
• Lattice asymmetry as/a?
• Number of ? (T) values for each N? and mq
• Monte Carlo Update algorithm

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Order of the transitions and Tc

• Look for discontinuities, singularities, peaks in
  thermodynamics quantities
• Polyakov line and its susceptibility
• Chiral condensate and its
  susceptibility
• Quark number susceptibility
• Finite size scaling analysis

For 21 light quark flavors the transition is a
seen to be a crossover
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A 20MeV uncertainty in Tc
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Hydro dynamical analysis gives Tfreeze-out
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Fodor etal different observables give different
Tc
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EOS from Lattice QCD
Z Partition function V spatial volume (Ns
a)3 ? energy density p pressure density
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Equation of State (NT4, 2000)
One can test many kinds of EoS in hydrodynamics.
Typical EoS in hydro model
Lattice QCD simulations
H resonance gas(RG)
Q QGPRG
P.Kolb and U.Heinz(03)
F.Karsch et al. (00)
pe/3
Latent heat
Lattice QCD predicted a cross over in the
vicinity of Tc 170 MeV with rapid increase in
energy density
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Issues with previous calculations

• Calculations with NT4 are on very coarse
  lattices (a 0.2 fermi).
• Simulate NT4,6,8, and do a?0 extrapolation
• Tc with different actions differ by 20 MeV
• Reduce uncertainty to 5 MeV
• Need simulations with 21 flavors with realistic
  light (up, down) and strange quark masses
• Mlight / ms 0.1

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Goal Reliable continuum limit results

• Reduce discretization errors (compare 3 different
  improved actions)
• Asqtad Staggered (MILC collaboration)
• p4 staggered (RBC-Bielefeld collaboration)
• Domain wall fermions
• New simulations at NT8 with 21 flavors (mlight
  ? 0.1 ms)
• Combine with ongoing/previous NT 4,6
  simulations to perform a?0 extrapolation

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Timeline

• Develop collaboration with Ron Soltz and
  formulate project for Blue Gene L at LLNL
  (Nov-Dec 2005)
• Organized US wide meeting to explore doing RHIC
  phenomenology and Lattice QCD at LLNL (Feb 06)
• Develop white paper for calculation of Tc and
  EOS on the Blue Gene L (Feb May 06)
• Get NNSA approval to run on Blue Gene L ( July
  06)
• Port Asqtad and p4fat codes to Blue Gene L
  (Aug-Sept 06)
• Start NT8 lattice QCD simulations Oct 06
• Optimized code and started production runs (30
  done)

Blue Gene L at LLNL represents a 4-6 Teraflop
sustained resource
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P4 action N??8 simulations Status

• Lattice Size 8?32?32?32
• Quark mass ml/ms 0.1
• (real world 0.04)

• Line of constant physics (LCP)
• Mss r0 1.58
• M? r0 ? 0.52 ? M? ? 220 MeV

Calculate Action, Polyakov loop, condensate
their susceptibilities
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Susceptibilities N? 4, 6, 8
Susceptibility for light (l u,d) and strange
(s) quarks
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Asqtad action data set as of 4/20/07
About 33 of target 15000 trajectories
(statistics) achieved
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Future Timeline

• Present results on Tc and EOS at Lattice 2007
  (July 31-Aug 4)
• First Publication of Tc August 2007
• Simulate T0 as needed for EOS
• Publish EOS results Jan 2008
• Plan for the calculation of spectral functions
• Develop non-perturbative methods for calculating
  renormalization constants for transport
  coefficients

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Extras
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Space-time picture of a R.H.I.C.
Thermal freeze-out
Hadronization
Equilibration