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Lattice Gauge Theory for the Quark-Gluon Plasma

Lattice Gauge Theory for the Quark-Gluon Plasma. Sourendu Gupta TIFR. 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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Lattice Gauge Theory for the Quark-Gluon Plasma

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  1. Lattice Gauge Theory for the Quark-Gluon Plasma Sourendu Gupta TIFR

  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! Saturday Show: S. Gupta

  3. The first 3 digits Saturday Show: S. Gupta

  4. Particles in the Standard Model (1990s) Saturday Show: S. Gupta

  5. The Eightfold Way (variables) Saturday Show: S. Gupta

  6. The Eightfold Way (variables) Saturday Show: S. Gupta

  7. The Eightfold Way (variables) Saturday Show: S. Gupta

  8. The Eightfold Way (variables) Saturday Show: S. Gupta

  9. Saturday Show: S. Gupta

  10. 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 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 Saturday Show: S. Gupta

  12. The RHIC at Brookhaven Saturday Show: S. Gupta

  13. 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 Saturday Show: S. Gupta

  14. 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 On quark matter Saturday Show: S. Gupta

  15. 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? Saturday Show: S. Gupta

  16. 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 Saturday Show: S. Gupta

  17. 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 ∞ and cancels Lorentz’s ∞ This affects the mass: gauge symmetry Saturday Show: S. Gupta

  18. Charge renormalization: screening in QED Saturday Show: S. Gupta

  19. Anti-screening in QCD Asymptotic freedom is anti-screening: the opposite of electrodynamics Saturday Show: S. Gupta

  20. 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 Saturday Show: S. Gupta

  21. The phase diagram • Several phases • Several 1st order transitions • More than one critical point • More variables not shown: tri-critical points… Saturday Show: S. Gupta Rajarshi Ray

  22. 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 Saturday Show: S. Gupta Swagato Mukherjee

  23. 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 Saturday Show: S. Gupta

  24. It’s totally rewarding Saturday Show: S. Gupta

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