Is there a "$\Delta$-isobar puzzle" in the physics of neutron stars?

TL;DR

This paper investigates the conditions under which $\Delta$ isobars appear in neutron star matter, revealing their correlation with the symmetry energy's density derivative and highlighting a potential $\Delta$ puzzle akin to the hyperon puzzle.

Contribution

It establishes a link between the threshold density of $\Delta$ isobars and the symmetry energy slope parameter, and discusses the implications for the neutron star equation of state.

Findings

$\Delta$ isobars appear at 2-3 times nuclear saturation density.

The appearance of $\Delta$ isobars correlates with the symmetry energy slope $L$.

A potential $\Delta$ puzzle similar to the hyperon puzzle is identified.

Abstract

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 $\lesssim L \lesssim 62$ MeV, we find that $\Delta$ isobars appear at a density of the order of 2$\div$3 times nuclear matter saturation density, i.e. the same range 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.