Effects of \(\phi\) and \(\sigma ^{*}\)-meson on properties of hyperon stars including \(\Delta\) resonance

In this work, we research the properties of neutron stars using the nonlinear relativistic mean-field theory and consider multiple degrees of freedom inside neutron stars, including hyperons and \(\Delta\) resonances. We investigate different coupling parameters \(x_{\sigma \Delta }\) between \(\Delta\) resonances and nucleons and compare the differences between neutron stars with and without strange mesons \(\sigma ^*\) and \(\phi\) These effects include particle number distributions, equations of state (EOS), mass–radius relations, and tidal deformabilities. To overcome the “hyperon puzzle,” we employ the \(\sigma -cut\) scheme to obtain neutron stars with masses up to \(2M_{\odot }\). We find that strange mesons appear at around 3\(\rho _0\) and reduce the critical density of baryons in the high-density region. With increasing coupling parameter \(x_{\sigma \Delta }\), the \(\Delta\) resonances suppress hyperons, leading to a shift of the critical density toward lower values. The early occurrence of \(\Delta\) resonances may play a crucial role in the stability of neutron stars. Strange mesons soften the EOS slightly, while \(\Delta\) resonances predominantly soften the EOS in the low-density region. By calculating tidal deformabilities and comparing with astronomical event GW170817, we find that the inclusion of \(\Delta\) resonances decreases the radius of neutron stars.