Bose-Einstein condensation temperature of a homogeneous weakly interacting Bose gas in variational perturbation theory through six loops

We compute the shift of the transition temperature for a homogeneous weakly interacting Bose gas in leading order in the scattering length a for given particle density n. Using variational perturbation theory through six loops in a classical three-dimensional scalar field theory, we obtain DeltaT(c)/T-c=1.25+/-0.13an(1/3), in agreement with recent Monte Carlo results.