Ground state energy of the low density Bose gas with two-body and three-body interactions

In the present paper we study the low density Bose gas in the thermodynamic limit interacting via two-body and three-body interaction potentials. We prove that the leading order of the ground state energy is entirely characterised 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) and of Lieb-Yngvason (1998), and the result for three-body interactions was proven by Nam-Ricaud-Triay (2022). The present result resolves a conjecture of Nam-Ricaud-Triay (2022).