Four-loop screened perturbation theory

Abstract

We study the thermodynamics of massless {phi}{sup 4}-theory using screened perturbation theory. In this method, the perturbative expansion is reorganized by adding and subtracting a thermal mass term in the Lagrangian. We calculate the free energy through four loops expanding in a double power expansion in m/T and g{sup 2}, where m is the thermal mass and g is the coupling constant. The expansion is truncated at order g{sup 7} and the loop expansion is shown to have better convergence properties than the weak-coupling expansion. The free energy at order g{sup 6} involves the four-loop triangle sum-integral evaluated by Gynther, Laine, Schroeder, Torrero, and Vuorinen using the methods developed by Arnold and Zhai. The evaluation of the free energy at order g{sup 7} requires the evaluation of a nontrivial three-loop sum-integral, which we calculate by the same methods.