Nonanalytic dependence of the transition temperature of the homogeneous dilute Bose gas on scattering length.

We show that the shift in the transition temperature of the dilute homogeneous Bose gas is nonanalytic in the scattering amplitude a. The first correction beyond the positive linear shift in a is negative and of order a(2)lna. This nonuniversal nonanalytic structure indicates how the discrepancies between numerical calculations at finite a can be reconciled with calculations of the limit a-->0, since the linearity is apparent only for anomalously small a.