Universal correlations in pion-less EFT with the resonating group method: Three and four nucleons

The Effective Field Theory "without pions" at next-to-leading order is used to analyze universal bound-state and scattering properties of the 3- and 4-nucleon system. Results of a variety of phase shift equivalent nuclear potentials are presented for bound-state properties of 3 H and 4 He, and for the singlet S-wave (3)He- neutron scattering length a(0)((3)He-n). The calculations are performed with the Refined Resonating Group Method and include a full treatment of the Coulomb interaction and the leading-order 3-nucleon interaction. The results compare favorably with data and values from AV18(+UIX) model calculations. A new correlation between a(0)((3)He-n) and the (3)H binding energy is found. Furthermore, we confirm at next-to-leading order the correlations, already found at leading order, between the (3)H binding energy and the (3)H charge radius, and the Tjon line. With the (3)H binding energy as input, we get predictions of the effective field theory "without pions" at next-to-leading order for the root mean square charge radius of (3)H of (1.6 +/- 0.2) fm, for the (4)He binding energy of (28 +/- 2.5) MeV, and for Re{a(0)((3)He-n)} of (7.5 +/- 0.6) fm. Including the Coulomb interaction, the splitting in binding energy between (3)H and (3)He is found to be (0.66 +/- 0.03) MeV. The discrepancy to data of (0.10 +/- 0.03) MeV is model independently attributed to higher-order charge independence breaking interactions. We also demonstrate that different results for the same observable stem from higher-order effects, and carefully assess that numerical uncertainties are neg-ligible. Our results demonstrate the convergence and usefulness of the pion-less theory at next-to-leading order in the 4 He channel. We conclude that no 4-nucleon interaction is needed to renormalize the theory at next-to-leading order in the 4-nucleon sector.