Lattice Gauge Theory for the Quark-Gluon Plasma Sourendu Gupta TIFR.
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Transcript of Lattice Gauge Theory for the Quark-Gluon Plasma Sourendu Gupta TIFR.
Lattice Gauge Theory for the Quark-Gluon Plasma
Sourendu Gupta
TIFR
17 May, 2005 Tuesday Talk: S. Gupta 2
Particles in the Standard Model (1990s)
17 May, 2005 Tuesday Talk: S. Gupta 3
The Eightfold Way (variables)
17 May, 2005 Tuesday Talk: S. Gupta 4
The Eightfold Way (variables)
17 May, 2005 Tuesday Talk: S. Gupta 5
The Eightfold Way (variables)
17 May, 2005 Tuesday Talk: S. Gupta 6
The Eightfold Way (variables)
17 May, 2005 Tuesday Talk: S. Gupta 7
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
17 May, 2005 Tuesday Talk: S. Gupta 8
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
17 May, 2005 Tuesday Talk: S. Gupta 9
The RHIC at Brookhaven
17 May, 2005 Tuesday Talk: S. Gupta 10
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
17 May, 2005 Tuesday Talk: S. Gupta 11
Droplets from Colliders
17 May, 2005 Tuesday Talk: S. Gupta 12
Gas or Liquid?
Difference is in flow
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are needed to see this picture.
17 May, 2005 Tuesday Talk: S. Gupta 13
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?
17 May, 2005 Tuesday Talk: S. Gupta 14
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
17 May, 2005 Tuesday Talk: S. Gupta 15
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
17 May, 2005 Tuesday Talk: S. Gupta 16
Charge renormalization: screening in QED
17 May, 2005 Tuesday Talk: S. Gupta 17
Anti-screening in QCD
Asymptotic freedom is anti-screening: the opposite of electrodynamics
17 May, 2005 Tuesday Talk: S. Gupta 18
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 !
17 May, 2005 Tuesday Talk: S. Gupta 19
The phase diagram
• Several phases• Several 1st order
transitions• More than one
critical point• More variables not
shown: tri-critical points…
17 May, 2005 Tuesday Talk: S. Gupta 20
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
17 May, 2005 Tuesday Talk: S. Gupta 21
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…