  We develop the perturbation theory for bosons interacting via a two-body
potential $V$ of vanishing mean value. We find that the leading nonpairwise
contribution to the energy emerges in the third order in $V$ and represents an
effective three-body interaction, the sign of which in most cases (although not
in general) is anticorrelated with the sign of the long-range tail of $V$.
Explicit results are obtained for a few particular two-body interaction
potentials and we perform a detailed perturbative analysis of tilted dipoles in
quasi-low-dimensional geometries.
