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

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