Constraining the neutron-neutron scattering length with \eftnopi

TL;DR

This paper uses an effective field theory approach to relate neutron-neutron and proton-proton scattering lengths to nuclear binding energy differences, providing a new estimate for the neutron-neutron scattering length.

Contribution

It introduces a model-independent correlation between scattering length differences and nuclear binding energy splittings using EFT without explicit pions.

Findings

Estimated neutron-neutron scattering length: -22.9 ± 4.1 fm.

Established a correlation relying only on large NN scattering lengths.

Demonstrated the effectiveness of EFT in nuclear scattering length predictions.

Abstract

We compute a model-independent correlation between the difference of neutron-neutron and proton-proton scattering lengths |a(nn)-a^C(pp)| and the splitting in binding energies between Helium-3 and tritium nuclei. We use the effective field theory without explicit pions to show that this correlation relies only on the existence of large scattering lengths in the NN system. Our leading-order calculation, taken together with experimental values for binding energies and a^C(pp), yields a(nn)=-22.9 \pm 4.1 fm.