Effects of quark core sizes of baryons in neutron star matter

Abstract: We describe the quark substructure of hadrons and the equation of state of high density neutron star matter by using the Nambu$-$Jona-Lasinio (NJL) model, which is an effective quark theory based on QCD. The interaction between quarks fully respects the chiral and flavor symmetries. Guided by the success of various low energy theorems, we assume that the explicit breaking of these symmetries occurs only via the current quark masses, and all other symmetry breakings are of dynamical nature. In order to take into account the effects of the finite quark core sizes of the baryons on the equation of state, we make use of an excluded volume framework which respects thermodynamic consistency. The effects generated by the swelling quark cores generally act repulsively and lead to an increase of the pressure with increasing baryon density. On the other hand, in neutron star matter they also lead to a decrease of the density window where hyperons appear, because it becomes energetically more favorable to convert the faster moving nucleons into hyperons. Our quantitative analysis shows that the net effect of the excluded volume is too small to solve the long standing "hyperon puzzle," which is posed by the large observed masses of neutron stars. Thus the puzzle persists in a relativistic effective quark theory which takes into account the short range repulsion between baryons caused by their finite and swelling quark core sizes in a phenomenological way.