Universal Dimer-Dimer and Atom-Trimer Scattering for Identical Bosons

Identical bosons with a large positive scattering length $a$ form universal bound states, including a shallow dimer, Efimov trimers, and universal tetramers. We present analytic approximations to the universal low-energy dimer-dimer and atom-trimer scattering amplitudes. The numerical parameters in the amplitude are determined using accurate 4-body results calculated by Deltuva. The coupled-channel scattering amplitudes are exactly unitary if the Efimov 3-body parameter is real. The analytic expressions for the scattering amplitudes allow the effects of deeply-bound diatomic molecules to be taken into account through the analytic continuation of the Efimov parameter.