Composition of scalar mesons and their effects on nuclear matter properties in an extended linear sigma model

TL;DR

This work extends the baryonic extended linear sigma model (bELSM) by incorporating antisymmetric-flavor tensor structures to treat iso-scalar and iso-vector mesons more realistically within a chiral framework. The LO Lagrangian includes new h, e, and a1-type terms and explicit three- and four-quark scalar components whose mixing yields the physical $\sigma$, $a_0$, and $f_0$ mesons; vacuum alignments $\langle\sigma'\rangle=\sqrt{3}\alpha$ and $\langle\hat{\sigma}'\rangle=\sqrt{3}\beta$ are fixed, and the 11-parameter space is constrained by hadron masses and NM properties at $n_0$. The model reproduces NM properties at saturation, predicts a plateau in the symmetry energy around $n\approx 2n_0$, and, for suitable parameter choices (notably including a nonzero $a_0$ and balanced $e$/$g$ terms with moderate $\tilde{g}_3$), NS structures that satisfy GW170817 and MSP J0740+6620 constraints; the high-density sound velocity can approach the conformal limit $v_s^2\rightarrow 1/3$ for certain sets like el-g30eg. The analysis also reveals that the $\sigma$ is roughly a 50/50 two-quark/four-quark mixture, while $a_0$ is predominantly four-quark, underscoring the link between QCD-like chiral structure and macroscopic dense-matter phenomenology.

Abstract

It has been argued that the iso-scalar and iso-vector mesons play significant roles in nuclear matter and neutron star structures. We improve the extended linear sigma model with baryons, proposed in our previous work, by introducing the flavor structures constructed from antisymmetric tensors of chiral representations to study these physics. The parameter space of this model is refined with well-reproduced nuclear matter properties at saturation density by the lowest order Lagrangian, ensuring consistency with vacuum results, such as $f_π\approx 134 \, \text{MeV}$. The anticipated plateau-like behaviors of the symmetry energy are predicted at intermediate densities, which is crucial for the consistency of GW170817 and the neutron skin thickness of $\text{Pb}^{208}$. Subsequently, neutron star structures are calculated using several parameter sets, and the results for the nuclear matter properties at saturation density align with empirical values. It is found that the neutron star structures are sensitive to the couplings between the iso-vector $a_0$ meson and nucleons and the four-vector meson couplings: small values of both are favorable. Meanwhile, nuclear matter properties at saturation density favor larger values of the latter and are not sensitive to the former. This signifies the statistical significance of neutron star observations when obtaining realistic chiral effective field theories or models at various densities. The parameter set favored by neutron star observations also aligns the behavior of the sound velocity with the conformal limit at high densities relevant to cores of massive stars. It is hoped that the results of this work can guide future studies on the relationship between the microscopic symmetry of strong interactions and macroscopic phenomena.

Figures (3)

• Figure 1: The M-R relation of NSs. The constraints MSP J0740+6620 are from Ref. NANOGrav:2019jur and GW170817 are from Ref. LIGOScientific:2018cki. Both are at $95\%$ confidence level.
• Figure 2: The $E_{\rm sym}(n)$ for different cases.
• Figure 3: The $v_s^2$ from different cases. The conformal limit is due to the asymptotic freedom of QCD at high energies.