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 becomes weaker as the temperature increases. One might therefore expect the behavior of hadronic matter at sufficiently high temperature to be calculable using perturbative methods. Unfortunately, a straightforward perturbative expansion in powers of the coupling constant does not seem to be of any quantitative use even at temperatures orders of magnitudes higher than those achievable in heavy-ion collisions. In a recently completed next-to-leading order calculation of the free energy of a pure gluon plasma using a reorganization technique called Hard Thermal Loop perturbation theory the region of convergence has been improved by three to four orders of magnitude in the temperature in a systematically improvable way which yields completely analytic expressions for the free energy. The aim is to continue this work on improving the convergence of finite temperature perturbation theory by exploring methods similar to the so-called Phi-Derivable approach or by finding ways to improve upon the work on Hard Thermal Loop perturbation theory. Additionally, these methods should be applied to phenomenological heavy-ion physics. With the Relativistic Heavy-Ion Collider coming online in the US and the Large Hadron Collider on the not-to-distant horizon at CERN finding reliable phenomenological techniques for including many- body effects in strongly interacting systems has become very important.