Short-distance production of three particles with large scattering length

TL;DR

This paper calculates the production amplitude of three particles with large scattering length in pionless EFT, revealing insights into low-energy resonances and correlations in multi-neutron and boson systems.

Contribution

It provides the first leading-order calculation of three-particle production amplitudes with large scattering length, including next-to-next-to-leading order corrections for neutrons.

Findings

Identifies signatures of low-energy resonances in energy distributions.

Shows the impact of conformal symmetry near the unitary limit.

Provides range correction estimates up to NNLO.

Abstract

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.