Neutron-neutron distribution of the triton from pionless EFT

TL;DR

This paper calculates the neutron-neutron energy distribution in the triton using pionless EFT, demonstrating its effectiveness and sensitivity to the neutron-neutron scattering length, with implications for universality and interaction studies.

Contribution

It provides the first detailed calculation of the neutron-neutron distribution in the triton within pionless EFT, including LO and NLO results with uncertainty quantification.

Findings

Pionless EFT reliably describes the neutron-neutron distribution.

The distribution is highly sensitive to the neutron-neutron scattering length.

NLO results include effective range effects semi-perturbatively.

Abstract

We compute the neutron-neutron relative-energy distribution of the triton following the hard knockout of the proton in pionless effective field theory. This distribution can be used to study universality as well as to obtain information on the neutron-neutron interaction. Especially, one can infer the scattering length from fitting theory predictions for the shape of the distribution to experimental data. To obtain the distribution for the triton, we first solve the ground-state three-body problem using momentum-space Faddeev equations. Next, we include the neutron-neutron final-state interaction by applying the corresponding M{\o}ller operator to the ground state. We present leading-order (LO) and next-to-leading order (NLO) pionless effective field theory results with quantified uncertainties. At NLO, we include the effective ranges semi-perturbatively. We conclude, that pionless EFT works reliably as expected and that the neutron-neutron distribution of the triton shows a significant sensitivity to the scattering length.