Probing the existence of η3He mesic nucleus with a few-body approach

Abstract

Motivated by recent observations in the WASA-at-COSY detector, we investigate the η3He nucleus using the ηNNN few body method. We construct an effective s-wave energy dependent ηN potential that reproduces the ηN subthreshold scattering amplitude as per the 2005 Green-Wycech model, yielding the η separation energy and decay width of 0.19 MeV and 1.71 MeV, respectively. Additionally, we construct various sets of effective s-wave energy independent ηN potentials, where the corresponding complex scattering lengths (aηN) are fallen within the range provided in most theoretical models. Our investigation aims to explore the potential existence of a bound η3He nucleus under these scattering lengths, and to calculate the resulting binding energies and decay widths. Our findings indicate that the η3He nucleus is bound by 1.65 MeV with a decay width of about 5 MeV when aηN is (1.0+0.3i) fm, and by 1.46 MeV with a decay width of about 10 MeV when aηN is (1.0+0.5i) fm.