Gluon propagator at high temperature: Screening, improvement and nonzero momenta

We study the gluon propagator and the singlet potential in Landau gauge in the deconfined phase of SU(2) lattice gauge theory, using both the standard Wilson action and a tree-level Symanzik improved action. From the long-distance behavior of correlation functions of temporal and spatial components of the gauge fields we extract electric (m(e)) and magnetic (m(m)) screening masses. For the magnetic mass we find m(m)(T) = 0.456(6)g(2)(T)T. The electric mass can be described by a next-to leading order ansatz. obtained from one loop resummed perturbation theory. However, the best description is given by m(e)(T)=root 1.70(2)g(T)T. The electric screening mass thus is different from its lowest order perturbative prediction even for temperatures as high as T similar to 10(4)T(c).