Tc for homogeneous dilute Bose gases:: A second-order result -: art. no. 013606

The transition temperature for a dilute, homogeneous, three-dimensional Bose gas has the expansion T-c = T-0{1 + c(1)an(1/3) + [c(2)' 1n(an(1/3)) + c(2)"]a(2)n(2/3) + O(a(3)n)}, where a is the scattering length, n the number density, and T-0 the ideal gas result. The first-order coefficient c(1) depends on nonperturbative physics. In this paper, we show that the coefficient c(2)' may be computed perturbatively. We also show that the remaining second-order coefficient c(2)" depends on non-perturbative physics but may be related, by a perturbative calculation, to quantities that have previously been measured using lattice simulations of three-dimensional O(2) scalar field theory. Making use of those simulation results, we find T(c)similar or equal toT(0){1 + (1.32+/-0.02) an(1/3) + [19.7518 1n(an(1/3)) + (75.7+/-0.4)]a(2)n(2/3) + O(a(3)n)}.