Lattice Gauge Theory for the Quark-Gluon Plasma
Sourendu GuptaTIFR
Sep 1, 2007 Saturday Show: S. Gupta 2
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
Sep 1, 2007 Saturday Show: S. Gupta 11
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• 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
• 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
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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• ∞ first found by Lorentz (self interaction of point
particle)• ∞ 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/2Particles can be produced from vacuum for a
short time … and disappear again (if no one is looking)
Mobile charges the vacuum screensNo one measures the charge of an electron
without the screening cloud: it is actually ∞ and cancels Lorentz’s ∞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…
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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
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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
Sep 1, 2007 Saturday Show: S. Gupta 24
It’s totally rewarding