Short-distance production of three particles with large scattering length

The short-distance production of multi-particle states in high-energy nuclear reactions provides a unique way to study the low-energy properties of few-body systems. In particular, the production amplitude of multi-neutron systems is strongly constrained by an approximate conformal symmetry of the underlying theory. We calculate the full amplitude for the short-distance production of three particles with large scattering length in leading order pionless EFT, focusing on the cases of three neutrons and three spinless bosons. We investigate the signature of low-energy resonances and other correlations in the relative energy distributions. For the case of neutrons, we compare to the predictions from approximate conformal symmetry close to the unitary limit and calculate the range corrections up to next-to-next-to leading order.