We consider the low density Bose gas in the thermodynamic limit with a three-body interaction potential. We prove that the leading order of the ground state energy of the system is determined completely in terms of the scattering energy of the interaction potential. The corresponding result for two-body interactions was proved in seminal papers of Dyson [Phys. Rev. 106, 20–26 (1957)] and of Lieb and Yngvason [Phys. Rev. Lett. 80, 2504–2507 (1998)].
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