Phenomenological and Theoretical Applications of Finite Temperature Resummation Techniques

Relativistic heavy-ion collisions allow the experimental study of hadronic matter at energy densities exceeding that required to create a quark-gluon plasma. A quantitative understanding of the properties of a quark-gluon plasma is essential in order to determine whether it has been created. Because QCD is asymptotically free, its running coupling constant a becomes weaker as the temperature increases. One might therefore expect the behavior of hadronic matter at sufficiently high temperature to be calculabe using perturbative methods. Unfortunately, a straightforward perturbative expansion in powers of a does not ssem to be of any quantitative use even a temperatures orders of magnitude higher than those achieveable in heavy-ion collisions. The problem is evident in the free energy of a quark-gluon plasma, whose weak-coupling expansion has been calculated through fifth order. An analysis of the perturbative series shows that the perturbative series is convergent only for temperatures greater than about T~10^4 GeV. For the past several years my collaborators and I have been working on a method of reorganizing finite temperature perturbation theory in order to improve its convergence. The hope is to be able to find an analytic technique which allows for precise determination of thermodynamic and dynamical quantities at experimentally relevant temperatures, T~1 GeV. We have recently completed a next-to-leading-order calculation of the free energy of a pure gluon plasma using a reorganization technque we have called Hard Thermal Loop perturbation theory. An analysis of the convergence of the successive approximations obtained using this method show that we can extend the region of convergence down to T~1-10 GeV, however, we have found that accessing extremely low temperatures, 0.25 GeV