Ground State Energy of Dilute Bose Gases with Two-Body and Three-Body Interactions

Abstract We study dilute Bose gases in the thermodynamic limit interacting via two-body and three-body interaction potentials. We prove that the leading order of the thermodynamic ground state energy is entirely characterized by both the scattering length of the two-body potential and the scattering energy of the three-body potential. The corresponding result for two-body interactions was proven in seminal papers of Dyson (1957) [1] and Lieb–Yngvason (1998) [2], and the result for three-body interactions was proven much more recently by Nam–Ricaud–Triay (2022) [3]. The present result resolves a conjecture of Nam–Ricaud–Triay (2022) [4].