Density of Saturated Nuclear Matter at Large $N_{c}$ and Heavy Quark Mass Limits

Abstract

We exhibit the existence of stable, saturated nuclear matter in the large $N_{c}$ and heavy quark mass limits of QCD. In this limit, baryons (with the same spin flavor structure) interact at leading order in $N_{c}$ via a repulsive interaction due to the Pauli exclusion principle and at subleading order in $1/N_c$ via the exchange of glueballs. Assuming that the lightest glueball is a scalar, which implies that the subleading baryon interaction is attractive, we find that nuclear matter saturates since the subleading attractive interaction is longer ranged than the leading order repulsive one. We find that the saturated matter is in the form of a crystal with either a face-centered cubic or a hexagonal-close-packed symmetry with baryon densities of $\mathcal{O}((\, \tilde{\alpha}_{s} m_q (\ln (N_{c}m_{q}\Lambda_{\textrm{QCD}}^{-1}))^{-1})^3 )$. Remarkably, the leading order expression for the density of saturated nuclear matter is independent of the lighest glueball mass and scalar-glueball-baryon coupling in the extreme large $N_{c}$ limit or heavy quark limit (or both), which we define precisely in this work.