Quark mean-field model for nuclear matter with or without bag

We propose the new quark mean-field bag (QMFB) model by incorporating the bag confinement mechanism in the original quark mean-field model. Nuclear matter and neutron star properties are studied with the QMFB model. For the study of the bag effect, we newly fit 12 parameter sets by reproducing the empirical saturation properties of nuclear matter. Quark confinement is found to be mainly demonstrated by the bag after it is included in the model, instead of the confining potential. For nuclear matter, the bag decreases the binding energy and increases the symmetry energy. For neutron star, the bag affects significantly the radius $R$ of a $1.4M_\odot$ star, with the maximum mass only slightly modified. The bag also has a large suppression effect on the well-accepted $R$ vs $L$ dependence, with $L$ the symmetry energy slope at the saturation density.