Cusp in the symmetry energy, speed of sound in neutron stars and emergent pseudo-conformal symmetry

Abstract

In this paper, we review how the “cusp” predicted in the nuclear symmetry energy generated by a topology change at density [Formula: see text] can have a surprising consequence, so far unrecognized in nuclear physics and astrophysics communities, on the structure of dense compact-star matter. The topology change translated into nuclear EFT with “effective” QCD degrees of freedom encoded in hidden local and scale symmetries predicts an EoS that is soft below and stiff above [Formula: see text], and yields the properties of neutron stars with no tension with all the astrophysical observations available up to date. Furthermore it describes the interior core of the massive stars populated by fractionally charged quasi-fermions that are neither baryonic nor quarkonic. It is argued that the cusp “buried” in the symmetry energy resulting from strong correlations with hidden heavy degrees of freedom leads, at [Formula: see text], to a “pseudo-conformal” sound speed, [Formula: see text], converged from below at [Formula: see text]. It is not conformal since the trace of energy–momentum tensor is not zero even in the chiral limit. It reflects an emergent scale symmetry. This observation with the topology change implies that the quantities accurately measured at [Formula: see text] cannot give a qualitatively stringent constraint for what takes place at the core density of compact stars [Formula: see text]. This is because there intervenes a change of degrees of freedom in the effective field theory. We discuss the implication of this on the recent PREX-II “dilemma” in the measured skin thickness of [Formula: see text].