  It was found that the isoscalar-scalar and isovector-scalar mesons play
significant roles in nuclear matter physics. However, the underlying structures
of these resonances are not yet well understood. We construct a three-flavor
baryonic extended linear sigma model including both the two- and four-quark
constitutes of scalar mesons with respect to the axial transformation and study
the nuclear matter properties with relativistic mean field method. The nuclear
matter properties at saturation density and hadron spectrums are well
reproduced with this model simultaneously and, only the two-quark component of
the scalar mesons couple to baryon fields and dominates the nuclear force. A
plateau-like structure is found in the symmetry energy of nuclear matter due to
the multi-meson couplings, and it's crucial for understanding the neutron skin
thickness of $^{208}\rm Pb$ and the tidal deformation of neutron star from
GW170817. At high density regions, the vector mesons are found to be rather
crucial, especially the ones coupling with four-quark configurations. This
model can be easily extended to study neutron stars, even with hyperons in
their interior.
