Remarks on nuclear matter: How an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>ω</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math> condensate can spike the speed of sound, and a model of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Z</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> baryons
Robert D. Pisarski
Abstract
I make two comments about nuclear matter. First, I consider the effects of a coupling between the $O(4)$ chiral field, $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\phi}}$, and the ${\ensuremath{\omega}}_{\ensuremath{\mu}}$ meson, $\ensuremath{\sim}+{\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\phi}}}^{2}{\ensuremath{\omega}}_{\ensuremath{\mu}}^{2}$; for any net baryon density, a condensate for ${\ensuremath{\omega}}_{0}$ is unavoidably generated. I assume that with increasing density, a decrease of the chiral condensate and the effective ${\ensuremath{\omega}}_{0}$ mass gives a stiff equation of state (EOS). In order to match that onto a soft EOS for quarkyonic matter, I consider an $O(N)$ field at large $N$, where at nonzero temperature quantum fluctuations disorder, any putative pion ``condensates'' into a quantum pion liquid ($\mathrm{Q}\ensuremath{\pi}\mathrm{L}$) [R. D. Pisarski et al., Phys. Rev. D 102, 016015 (2020)]. In this paper, I show that the $\mathrm{Q}\ensuremath{\pi}\mathrm{L}$ persists at zero temperature. If valid qualitatively at $N=4$, the ${\ensuremath{\omega}}_{0}$ mass goes up sharply and suppresses the ${\ensuremath{\omega}}_{0}$ condensate. This could generate a spike in the speed of sound at high density, which is of relevance to neutron stars. Second, I propose a toy model of a $Z(3)$ gauge theory with three flavors of fermions, where $Z(3)$ vortices confine fermions into baryons. In $1+1$ dimensions, this model can be studied numerically with present techniques, using either classical or quantum computers.