Studying Hyperon Puzzle in a Unified SU(3)–SU(6) Baryon–Meson Coupling Scheme

We investigate the influence of hyperons on the equation of state (EOS) and global properties of neutron stars using the relativistic mean-field (RMF) framework. To address uncertainties in hyperon–meson interactions, we adopt a unified baryon–meson coupling scheme grounded in SU(3) flavour symmetry and partially broken SU(6) spin-flavour symmetry. Within this scheme, vector meson coupling constants are determined through SU(3) symmetry relations and parameterised by a single free parameter, α_v, while scalar couplings are constrained to reproduce empirical hyperon potential depths at nuclear saturation density.

Within this symmetry-guided framework, we construct the EOS for dense matter, incorporating the full baryon octet and leptons under conditions of β-equilibrium and charge neutrality. The resulting EOS is applied to the Tolman–Oppenheimer–Volkoff equations to determine neutron star mass–radius relations. Our findings indicate that the presence of hyperons softens the EOS, in agreement with the established hyperon puzzle, and decreases the maximum mass of neutron stars. The appearance of hyperons, especially the Λ baryon, occurs at densities several times higher than nuclear saturation density and substantially alters the internal composition of massive stars.

The dependence of stellar properties on the coupling parameter α_v is further analysed. Lower values of α_v result in a stiffer equation of state and higher maximum masses, which partially alleviates the hyperon puzzle. The model successfully reproduces current astrophysical constraints, including the existence of two-solar-mass neutron stars and established bounds on tidal deformability.

Overall, the unified SU(3)–SU(6) coupling scheme provides a consistent and less arbitrary framework for describing hyperonic matter in neutron stars, thereby offering deeper insight into the role of strangeness in dense astrophysical environments.