Early appearance of Δ isobars in neutron stars

We discuss the formation of Δ 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., 40MeV≲L≲62MeV, we find that Δ 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 Δs 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 Δ in nuclear matter is close to the one indicated by the experimental data then the equation of state becomes soft enough that a “Δ puzzle” exists, similar to the “hyperon puzzle” widely discussed in the literature. Possible solutions to this puzzle are also discussed.