BEC transition temperature of a dilute homogeneous imperfect bose gas

The leading-order effect of interactions on a homogeneous Bose gas is theoretically predicted to shift the critical temperature by an amount DeltaT(c) similar or equal to ca(sc) n(1/3)T(o) from the ideal gas result T-o, where a(sc) is the scattering length, n is the density, and c is a pure number. There have been several different theoretical estimates for c. We claim to settle the issue by measuring the numerical coefficient in a lattice simulation of O(2) phi (4) field theory in three dimensions-an effective theory which, as observed previously in the literature, can be systematically matched to the dilute Bose gas problem to reproduce nonuniversal quantities such as the critical temperature. We find c = 1.32 +/- 0.02.