Higher-order effective interactions for bosons near a two-body zero crossing

We develop the perturbation theory for bosons interacting via a weak two-body potential $V$, attractive and repulsive parts of which cancel each other. find that leading nonpairwise contribution to energy emerges in third order $V$ represents an effective three-body interaction, sign most cases (although not general) is anticorrelated with long-range tail $V$. apply our few particular interaction potentials calculate corrections tilted dipoles quasi-low-dimensional geometries. show approach consistent many-body Bogoliubov treatment.