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., $40\text{MeV}\lesssim L\lesssim 62\text{MeV}$, 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 $\Delta \mathrm{s}$ 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 “Δ puzzle” exists, similar to the “hyperon puzzle” widely discussed in the literature. Possible solutions to this puzzle are also discussed.

• Received 15 July 2014
• Revised 1 December 2014

DOI:https://doi.org/10.1103/PhysRevC.90.065809