Lattice Gauge Theory for the Quark-Gluon Plasma

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!


The first 3 digits


Particles in the Standard Model (1990s)


The Eightfold Way (variables)


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


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


The RHIC at Brookhaven


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


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


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?


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


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


Charge renormalization: screening in QED


Anti-screening in QCD

Asymptotic freedom is anti-screening: the opposite of electrodynamics


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


The phase diagram

• Several phases• Several 1st order

transitions• More than one

critical point• More variables not

shown: tri-critical points…


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


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


It’s totally rewarding

Lattice Gauge Theory for the Quark-Gluon Plasma

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