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Universal Correlations in Pion-less EFT with the Resonating Group Model: 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 3H and 4He, and for the singlet S-wave 3He-neutron scattering length a_0(3He-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(3He-n) and the 3H binding energy is found. Furthermore, we confirm at next-to-leading order the correlations, already found at leading-order, between the 3H binding energy and the 3H charge radius, and the Tjon line. With the 3H 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 3H of (1.6\pm 0.2) fm, for the 4He binding energy of (28\pm 2.5) MeV, and for Re(a_0(3He-n)) of (7.5\pm 0.6)fm. Including the Coulomb interaction, the splitting in binding energy between 3H and 3He is found to be (0.66\pm 0.03) MeV. The discrepancy to data of (0.10\mp 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 negligible. Our results demonstrate the convergence and usefulness of the pion-less theory at next-to-leading order in the 4He channel. We conclude that no 4-nucleon interaction is needed to renormalize the theory at next-to-leading order in the 4-nucleon sector.