HTL-quasiparticle approach to the entropy and density
Perturbative results for the pressure in hot QCD have shown disappointingly poor convergence properties. On the other hand, simple massive-quasiparticle models with masses equal to the asymptotic hard-thermal-loop (HTL) thermal masses and certain "bag functions" have been found to give good fits to lattice data, suggesting that the thermodynamics of the quark-gluon plasma may be approximated by weakly interacting quasiparticles. The failure of conventional perturbation theory would then be more a reflection of a poor fit of polynomials in the coupling to the actual result rather than an indication of a complete inadequacy of the perturbative HTL picture.
One should therefore aim at a more faithful treatment, nonperturbative in the coupling, of the (perturbative) hard-thermal-loop physics. One such approach has been proposed in simple scalar models by Karsch et al. in what they called screened perturbation theory. This amounts to adding and subtracting a thermal mass term to the free Lagrangian and subtracting it again as a counterterm. This indeed greatly improves the convergence properties of a perturbation theory which does not expand out again the powers of the coupling buried in the thermal mass. On the other hand, it introduces artificial UV divergences and renormalization scale dependencies which are suppressed by powers of the coupling as the order of the calculation is increased, though this might still remain a problem when this coupling is large. Screened perturbation theory has been adapted to QCD by Andersen, Braaten, and Strickland. This requires to add and subtract the full HTL effective action (in the imaginary-time formalism). Besides the above UV difficulties, this also has the problem that HTL's are resummed at hard momenta where (in contrast to the scalar toy models) they are no longer accurate. Moreover, the leading-order interaction pressure is overincluded at HTL-resummed one-loop order, while a fully resummed 2-loop order evaluation might turn out to be just too difficult.
In work done in collaboration with J.-P. Blaizot and E. Iancu, we are adopting a conceptionally quite different approach. The main idea is to take the entropy and the quark density as primary objects, since this should be more directly describable in terms of the spectrum of quasiparticles rather than their interactions. Indeed when considering self-consistent approximations, this leads to important simplifications when keeping only two-loop skeletons. The requirement of self-consistency takes care of overcounting issues automatically without the need of thermal counterterms. We preserve this self-consistency in a perturbative sense using HTL perturbation theory, which also guarantees the gauge independence of our approximations. As a result, the latter turn out to be manifestly UV-finite; moreover, at high momenta they are sensitive only to that part of the HTL self-energies which are accurate there, the asymptotic thermal masses. Numerically, our results agree remarkably well with lattice data where available. They are also found to change only moderately by going from the leading HTL contributions to ones including NLO corrections, if the latter are resummed such as to preserve a monotonous behaviour of the asymptotic thermal mass as a function of the strong coupling. The same holds true for the pressure which can be obtained by integration after fixing a genuinely nonperturbative integration constant.
Last modified: Oct. 28 1999