Lattice Gauge Theory for the QuarkGluon Plasma

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Lattice Gauge Theory for the Quark-Gluon Plasma

• Sourendu Gupta
• TIFR

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Can particle physics predict the mass of this
system?

• Protein folding and other entropic terms about 1
  eV
• Binding energy of electrons 1 keV
• Electron rest mass 1 MeV
• Proton mass 1 GeV
• 3-6 digit accuracy!

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The first 3 digits
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Particles in the Standard Model (1990s)
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The Eightfold Way (variables)
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The Eightfold Way (variables)
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The Eightfold Way (variables)
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The Eightfold Way (variables)
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The basics of extreme matter

• Normal matter made of baryons
• Baryons contain 3 quarks and interact by
  exchanging mesons
• Mesons contain 2 quarks
• When you squeeze this matter by applying pressure
  (or heating it up) you get matter with large
  numbers of quarks
• This is the quark gluon plasma

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Quark matter factories

• Create an universe through a big bang and let it
  cool
• Create a supernova and let its core collapse into
  a really compressed star
• Bang some (relatively) large chunks of matter
  together very hard
• Think hard you may get a patent

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The RHIC at Brookhaven
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Chronology of heavy-ion collisions

• Initial 1 fm or so nuclei collide and many
  particles are created
• Next 7 fm or so secondary collisions and flow?
• Later particles free stream to detector

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On quark matter

• Quark matter needs QCD or its effective theories
• There are many phases of quark matter
• Quark matter may be neutral or a plasma
• Quark matter is fluid either gas or liquid

• Normal matter needs QED or its effective theories
• There are many phases of normal matter
• Normal matter may be neutral or a plasma
• Normal matter may be a solid, liquid or a gas

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How to pro(b/v)e a liquid

• Show that there is some matter
• count the number of particles coming out of the
  collision and compute density
• Show that this generates pressure
• elliptic flow also used in the BEC
• Does the pressure drive flow?
• detailed analysis of velocities
• Is there transport energy, baryon etc?

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How to predict its properties

• Need to use quantum field theory
• Equation for fields due to Maxwell
• Equation for matter due to Dirac
• 8 first found by Lorentz (self interaction of
  point particle)
• 8 in the quantum theory Heisenberg, Bethe
• Removed by Feynman, Schwinger, Tomonaga
• Modern formulation by Wilson unifying field
  theory and statistical mechanics

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The bubbling vacuum

• Quantum fluctuations ????t ? h/2?
• Particles can be produced from vacuum for a short
  time and disappear again (if no one is
  looking)
• Mobile charges ? the vacuum screens
• No one measures the charge of an electron without
  the screening cloud it is actually 8
• and cancels Lorentzs 8
• This affects the mass gauge symmetry

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Charge renormalization screening in QED
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Anti-screening in QCD

• Asymptotic freedom is anti-screening the
  opposite of electrodynamics

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Numerical renormalization

• Solve coupled differential equations Maxwell
  Dirac
• Do it many times quantum theory is a sum over
  possibilities (Feynman)
• Do it on a lattice (spacing d) no infinities in
  solid state physics
• e changes with d

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The phase diagram

• Several phases
• Several 1st order transitions
• More than one critical point
• More variables not shown tri-critical points

Rajarshi Ray
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Flow parameters

• P(T) or P(T,?) relativistic gas
• Equation of state is either E(P) or E(P,N)
• Speed of sound
• Specific heat
• Compressibility
• Viscosity

Swagato Mukherjee
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Lots more to do

• Analogues of Debye screening for pions, strange
  and charmed particles, causing them to dissolve
• Photon emission rates is the plasma a black
  body? Are there plasmons?
• Supersonic shock waves jets of particles travel
  with speed of light through the plasma
• Quantum coherence created as particles freeze out
  of the liquid
• Anything else that you can think of

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Its totally rewarding