Lattice Gauge Theory for the Quark-Gluon Plasma

Sourendu Gupta

TIFR

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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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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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Droplets from Colliders

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Gas or Liquid?

Difference is in flow

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QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

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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: Bhalerao’s talk• Does the pressure cause coherent velocities?• …detailed analysis of spectra and flow• Is the flow turbulent?

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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 Can d

o larg

e

e !

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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

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 plasma

• Anything else you can think of…