Two-body and Three-body Contacts for Identical Bosons near Unitarity

In a recent experiment with ultracold trapped Rb-85 atoms, Makotyn et al. have studied a quantum-degenerate Bose gas in the unitary limit where its scattering length is infinitely large. We show that the observed momentum distributions are compatible with a universal relation that expresses the high-momentum tail in terms of the 2-body and the 3-body contacts. We determine the 2- and 3-body contact densities for the unitary Bose gas with number density n to be approximately 20n^{4/3} and 2n^{5/3}, respectively. We also show that the observed atom loss rate is compatible with that from 3-atom inelastic collisions, which gives a contribution proportional to the 3-body contact, but the loss rate is not compatible with that from 2-atom inelastic collisions, which gives a contribution proportional to the 2-body contact. We point out that the contacts could be measured independently by using the virial theorem near and at unitarity.