Quark mean field model with pion and gluon corrections for $\Lambda,~\Xi^0$ hypernuclei and neutron stars

Abstract

Properties of $\Lambda,~\Xi^0$ hypernuclei and neutron stars are investigated in quark mean field model with pion and gluon corrections. Firstly, $u, ~d$, and $s$ quarks are confined by relativistic harmonic oscillator potentials to generate the baryons, like nucleon, $\Lambda, ~\Sigma$, and $\Xi$ 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 arises three parameter sets for the coupling constants between mesons and quarks, named QMF-NK1S, QMF-NK2S, and QMF-NK3S. Compared to the results of previous quark mean field model without pion and gluon corrections, it is found that properties of $\Lambda$ hypernuclei, i.e. the single $\Lambda$ energies, are more consistent with the experimental observables. Properties of $\Xi^0$ hypernuclei are also calculated and compared with the results in 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.