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

Sep 1, 2007Saturday Show: S. Gupta2 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!

Sep 1, 2007Saturday Show: S. Gupta3 The first 3 digits

Sep 1, 2007Saturday Show: S. Gupta4 Particles in the Standard Model (1990s)

Sep 1, 2007Saturday Show: S. Gupta5 The Eightfold Way (variables)

Sep 1, 2007Saturday Show: S. Gupta6 The Eightfold Way (variables)

Sep 1, 2007Saturday Show: S. Gupta7 The Eightfold Way (variables)

Sep 1, 2007Saturday Show: S. Gupta8 The Eightfold Way (variables)

Sep 1, 2007Saturday Show: S. Gupta9

Sep 1, 2007Saturday Show: S. Gupta10 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, 2007Saturday Show: S. Gupta11 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

Sep 1, 2007Saturday Show: S. Gupta12 The RHIC at Brookhaven

Sep 1, 2007Saturday Show: S. Gupta13 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

Sep 1, 2007Saturday Show: S. Gupta14 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

Sep 1, 2007Saturday Show: S. Gupta15 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?

Sep 1, 2007Saturday Show: S. Gupta16 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

Sep 1, 2007Saturday Show: S. Gupta17 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

Sep 1, 2007Saturday Show: S. Gupta18 Charge renormalization: screening in QED

Sep 1, 2007Saturday Show: S. Gupta19 Anti-screening in QCD Asymptotic freedom is anti-screening: the opposite of electrodynamics

Sep 1, 2007Saturday Show: S. Gupta20 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

Sep 1, 2007Saturday Show: S. Gupta21 The phase diagram Several phases Several 1st order transitions More than one critical point More variables not shown: tri-critical points… Rajarshi Ray

Sep 1, 2007Saturday Show: S. Gupta22 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

Sep 1, 2007Saturday Show: S. Gupta23 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, 2007Saturday Show: S. Gupta24 It’s totally rewarding