Quark structure of isoscalar- and isovector-scalar mesons and nuclear matter property

It was found that 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 the relativistic mean field method. The nuclear matter properties at saturation density and hadron spectra are well reproduced with this model simultaneously, and only the two-quark component of the scalar mesons couples to baryon fields and dominates the nuclear force. A plateaulike structure is found in the symmetry energy of nuclear matter due to the multimeson couplings, and it is crucial for understanding the neutron skin thickness of ${}^{208}\mathrm{Pb}$ and the tidal deformation of neutron star from GW170817. At high-density regions, 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.

Figure 1

(a)–(e) Comparison between models with (opt) and without ${\widehat{h}}_2$ (opt-N4) terms.

Figure 2

Parameter effects on the binding energy. TM1 is the result from Ref. [41], where $\rho$, $\omega$, and $\sigma$ mesons are considered with ${\mathrm{n}}_0=0.145{\mathrm{fm}}^{-3}$. $\mathrm{FSU}\text{−}\delta 6.7$ is the result from Ref. [28], where $\delta$ [here, $a_0(980)$] meson is added with ${\mathrm{n}}_0=0.148{\mathrm{fm}}^{-3}$.

Figure 3

Parameter effects on symmetry energy $E_{\mathrm{sym}}$. (a) $\alpha$ variation. (b) $\beta$ variation. (c) $c_4$ variation. (d) $e_3$ variation. (e) $c$ variation. (f) $g_3$ variation. (g) $h_2$ variation. (h) ${\hat{h}}_2$ variation.

Figure 4

Parameter effects on the slope of the symmetry energy $L$. (a) $\alpha$ variation. (b) $\beta$ variation. (c) $c_4$ variation. (d) $e_3$ variation. (e) $c$ variation. (f) $g_3$ variation. (g) $h_2$ variation. (h) ${\hat{h}}_2$ variation.

Figure 5

Parameter effects on incompressibility coefficient $K$. (a) $\alpha$ variation. (b) $\beta$ variation. (c) $c_4$ variation. (d) $e_3$ variation. (e) $c$ variation. (f) $g_3$ variation. (g) $h_2$ variation. (h) ${\hat{h}}_2$ variation.

Figure 6

Parameter effects on skewness coefficient $J$. (a) $\alpha$ variation. (b) $\beta$ variation. (c) $c_4$ variation. (d) $e_3$ variation. (e) $c$ variation. (f) $g_3$ variation. (g) $h_2$ variation. (h) ${\hat{h}}_2$ variation.