Onset of η-nuclear binding in a pionless EFT approach

ηNNN and ηNNNN bound states are explored in stochastic variational method (SVM) calculations within a pionless effective field theory (EFT) approach at leading order. The theoretical input consists of regulated NN and NNN contact terms, and a regulated energy dependent ηN contact term derived from coupled-channel models of the N^⁎(1535) nucleon resonance. A self consistency procedure is applied to deal with the energy dependence of the ηN subthreshold input, resulting in a weak dependence of the calculated η-nuclear binding energies on the EFT regulator. It is found, in terms of the ηN scattering length a_ηN, that the onset of binding η ³He requires a minimal value of Rea_ηN close to 1 fm, yielding then a few MeV η binding in η ⁴He. The onset of binding η ⁴He requires a lower value of Rea_ηN, but exceeding 0.7 fm.