Constraining the neutron-neutron scattering length using the effective field theory without explicit pions

We compute a model-independent correlation between the difference of neutron-neutron and proton-proton scattering lengths, vertical bar a(nn) - a(pp)(C)vertical bar, 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(pp)(C), yields a(nn) = -22.9 +/- 4.1fm.