Universal Correlations in ``Pion-less'' Effective Field Theory: 3, 4 and 6 Nucleons

In a feasibility study for chiral EFT and heavier systems, we analyse bound and scattering properties of 3-, 4- and 6-nucleon systems in the Effective Field Theory ``without pions'' at next-to-leading order using the Refined Renormalisation Group Method with full Coulomb treatment, with 3N-interactions, phase-equivalent potentials and a range of cut-offs for convergence checks. For correlations between the triton binding energy $B_{3H}$, its charge radius and the binding energy of ${}^4$He, convergence is consistent with an expansion parameter $\approx\frac{1}{3}$. No 4N-interaction is needed for renormalisation. With the correlation between $B_{3H}$ and the $^3$He binding energy iso-spin symmetric at NLO, the model-independent difference at the physical $B_{3H}$, $[0.10\mp 0.03]$MeV, is the same both in magnitude and uncertainty as estimates from charge-symmetry breaking. In the first scattering calculation for $A\ge4$, we found a correlation between $B_{3H}$ and the real part of the singlet scattering length of ${}^3$He--n scattering similar to the Tjon line. Finally, we address convergence of ``pion-less'' EFT in the halo nucleus ${}^6$He.