Early appearance of Δ isobars in neutron stars

We discuss the formation of Delta isobars in neutron star matter. We show that their threshold density strictly correlates with the density derivative of the symmetry energy of nuclear matter: the L parameter. By restricting L to the range of values indicated by recent experimental and theoretical analysis, i.e., 40 MeV less than or similar to L less than or similar to 62 MeV, we find that Delta isobars appear at a density of the order of 2 to 3 times the nuclear matter saturation density, i.e., the same range as for the appearance of hyperons. The range of values of the couplings of the Delta s with the mesons is restricted by the analysis of the data obtained from photoabsorption, electron and pion scattering on nuclei. If the potential of the Delta in nuclear matter is close to the one indicated by the experimental data then the equation of state becomes soft enough that a "Delta puzzle" exists, similar to the "hyperon puzzle" widely discussed in the literature. Possible solutions to this puzzle are also discussed.