Neutron-neutron distribution of the triton from pionless effective field theory

We compute the neutron-neutron relative-energy distribution of the triton following the hard knockout of the proton in pionless effective field theory (EFT). This distribution can be used to study universality as well as to obtain information on the neutron-neutron interaction. In particular, 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 Møller operator to the ground state. We present leading-order 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.