Course Outline for Physics 880.05

III. A. Thermodynamics and Phase Transitions (Chs. 9,13) Part 4

Thermal Model (cont.)

Last time we introduced a model for the hadronic phase consisting of all noninteracting hadrons. The energy density and pressure are found from the expressions given last time, adding the contributions from each hadron included in the model. This simple construction is possible because we neglect interactions.

We can use this model to test the possibility that thermal and chemical equilibrium are reached in a high-energy heavy-ion collision by measuring the relative abundances of different hadrons detected. If equilibrium was reached, these abundances should be consistent with a single temperature and constant baryon and strangeness chemical potentials at "freeze-out". Freeze-out is the point in the evolution of the plasma when hadrons have been formed and then have stopped interacting with each other. So energy and momentum are no longer exchanged (as when in thermal equilibrium) but are "frozen". Comparison of predicted (given a fit to T and the \mu's) and measured abundances are given in the other figures from the Braun-Munzinger and Stachel paper.

Hydrodynamics (Section 13.3)

Now we want to step back and fill in the gap between the estimate of Bjorken of the initial conditions (energy density and time) for the QGP and the hadronization of the plasma. We assume the QGP has formed and is in local equilibrium at proper time \tau_0, with initial e_0 following Bjorken.

Energy-Momentum Tensor

Collision Scenario and Lorentz Invariance

Specialize to 2-D Space-time


So what have we got?

Interactions in the Hadron Phase

The problem set project for PS #3 is to study the phase coexistence curve with a model for the hadronic side including a free gas of pions and a model for interacting nucleons. On the QGP side we use the same bag model used before, although now you must solve it for general T and \mu_B, not just the limiting cases.

Corrections to Free QGP

So far we have calculated the pressure and energy density of the QGP phase in the limit of noninteracting (massless) quarks and gluons. Of course, there are interactions. If the effective coupling is relatively small, we might hope to use perturbation theory (Feynman diagrams) as in QED.

One can work to higher order in perturbation theory, but there are complications from infrared divergences. The only reliable calculations when nonperturbative physics is still important are numerical simulations on a lattice. We consider these next.

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Copyright © 1997,1998 Richard Furnstahl and James Steele.