Probing the existence of η^3He mesic nucleus with a few-body approach

Motivated by the two recent observations in the WASA-at-COSY detector, we investigate the $η^3$He nucleus with the $ηNNN$ few body method. We construct the effective $s$-wave energy dependent $ηN$ potential which reproduce the $ηN$ subthreshold scattering amplitude in the 2005 Green-Wycech model. It gives the $η$ separation energy and decay width of 0.19 MeV and 1.71 MeV, respectively. We also construct various sets of effective $s$-wave energy independent $ηN$ potentials where the corresponding complex scattering lengths (a) are within the range given in most theoretical models. We obtain the bound $η^3$He nucleus with decay width of about 5 MeV when a is (1.0 fm, 0.3 fm), and of about 10 MeV when a is (1.0 fm, 0.5 fm).