Quark mean field model with pion and gluon corrections for $\mathrm{\Lambda }$ and ${\mathrm{\Xi }}^0$ hypernuclei and neutron stars

Properties of $\mathrm{\Lambda }$ and ${\mathrm{\Xi }}^0$ hypernuclei and neutron stars are investigated in a quark mean field model with pion and gluon corrections. First, $u, d$, and $s$ quarks are confined by relativistic harmonic oscillator potentials to generate baryons, such as nucleons and $\mathrm{\Lambda }, \mathrm{\Sigma }$, and $\mathrm{\Xi }$ hyperons. The effects of pion-quark coupling and one-gluon exchange are considered perturbatively. Then, the baryons interact with each other through exchanging $\sigma , \omega$, and $\rho$ mesons between quarks in hypernuclei and nuclear matter. The strengths of confinement potentials for $u, d$, and $s$ quarks are determined by the masses and radii of free baryons. The coupling constants between the quarks and mesons are fixed by the ground-state properties of several nuclei and single-hyperon potentials at nuclear saturation density, which yields three parameter sets for the coupling constants between mesons and quarks, named QMF-NK1S, QMF-NK2S, and QMF-NK3S. Compared to the results of the previous quark mean field model without pion and gluon corrections, it is found that properties of $\mathrm{\Lambda }$ hypernuclei, i.e., the single-$\mathrm{\Lambda }$ energies, are more consistent with the experimental observables. Properties of ${\mathrm{\Xi }}^0$ hypernuclei are also calculated and compared with the results in the previous quark mean field model. With these three parameter sets, the neutron stars containing hyperons are investigated through solving the Tolman-Oppenheimer-Volkoff equation. Maximum masses of neutron stars approach $2.1M_{\odot }$ with hyperons, and corresponding radii are around 13 km.

Figure 1

The effective masses of three hyperons ($\mathrm{\Lambda }, \mathrm{\Sigma }$, and $\mathrm{\Xi }$) with different parameter sets [set A (solid curve), set B (dashed curve), and set C (dotted curve)] as functions of the $u$ quark mass correction.

Figure 2

The results of theoretical calculation for energy levels of $\mathrm{\Lambda }$ hyperon for ${}_{\mathrm{\Lambda }}{}^{40}\mathrm{Ca}, {}_{\mathrm{\Lambda }}{}^{89}\mathrm{Y}$, and ${}_{\mathrm{\Lambda }}{}^{208}\mathrm{Pb}$ by QMF-NK1S, QMF-NK2S, and QMF-NK3S, compared with the experimental data and the results in the previous QMF model without pion and gluon effects.

Figure 3

The results of theoretical calculation for energy levels of ${\mathrm{\Xi }}^0$ hyperon for ${}_{{\mathrm{\Xi }}^0}{}^{40}\mathrm{Ca}, {}_{{\mathrm{\Xi }}^0}{}^{89}\mathrm{Y}$, and ${}_{{\mathrm{\Xi }}^0}{}^{208}\mathrm{Pb}$ by QMF-NK1S, QMF-NK2S, and QMF-NK3S, compared with the results in our previous QMF model without pion and gluon corrections.

Figure 4

The scalar and vector potentials, $U_S^{\mathrm{\Lambda }}$ and $U_V^{\mathrm{\Lambda }}$, for the $1s_{1/2} \mathrm{\Lambda }$ state in ${}_{\mathrm{\Lambda }}{}^{40}\mathrm{Ca}, {}_{\mathrm{\Lambda }}{}^{89}\mathrm{Y}$, and ${}_{\mathrm{\Lambda }}{}^{208}\mathrm{Pb}$ by QMF-NK1S, QMF-NK2S, and QMF-NK3S.

Figure 5

The scalar and vector potentials, $U_S^{{\mathrm{\Xi }}^0}$ and $U_V^{{\mathrm{\Xi }}^0}$, for the $1s_{1/2} {\mathrm{\Xi }}^0$ state in ${}_{{\mathrm{\Xi }}^0}{}^{40}\mathrm{Ca}, {}_{{\mathrm{\Xi }}^0}{}^{89}\mathrm{Y}$, and ${}_{{\mathrm{\Xi }}^0}{}^{208}\mathrm{Pb}$ by QMF-NK1S, QMF-NK2S, and QMF-NK3S.

Figure 6

Systematic calculations of the binding energies of $\mathrm{\Lambda }$ hypernuclei with the QMF-NK3S parameter set compared with the experimental data.

Figure 7

Pressures of $\beta$ equilibrated matter as functions of the energy density, for QMF-NK1S, QMF-NK2S, and QMF-NK3S parameter sets.

Figure 8

Fractions of leptons and baryons in neutron star matter as functions of total baryon density, for QMF-NK1S, QMF-NK2S, and QMF-NK3S parameter sets.

Figure 9

The masses of neutron stars as functions of density and radius, for QMF-NK1S, QMF-NK2S, and QMF-NK3S parameter sets.