We consider quantum chromodynamics (QCD) with $N_{\mathrm{c}}$ colors and $N_{\mathrm{f}}$ quark flavors at finite quark chemical potential ${\mu }_{\mathrm{q}}$ or isospin chemical potential ${\mu }_{\mathrm{I}}$. We specifically address the nature of the “silver blaze” behavior in the framework of $1/N_{\mathrm{c}}$ expansions. Starting with the QCD partition function, we implement Veneziano’s $N_{\mathrm{f}}/N_{\mathrm{c}}$ expansion to identify the density onset. We find the baryon mass $M_{\mathrm{B}}$ and the pion mass $m_{\pi }$ appearing from different orders of Veneziano’s expansion. We argue that the confining properties are responsible for the silver blaze behavior in the region of $m_{\pi }/2<{\mu }_{\mathrm{q}}<M_{\mathrm{B}}/N_{\mathrm{c}}$. We point out, however, that Veneziano’s expansion brings about a subtlety along the same line as the baryon problem in finite-density quenched lattice simulations. We emphasize that the large-$N_{\mathrm{c}}$ limit can allow for the physical ordering of $M_{\mathrm{B}}$ and $m_{\pi }$ thanks to the similarity between the large-$N_{\mathrm{c}}$ limit and the quenched approximation, while unphysical ghost quarks contaminate the baryon sector if $N_{\mathrm{c}}$ is finite. We also discuss the “orientifold” large-$N_{\mathrm{c}}$ limit that does not quench quark loops.

• Received 16 March 2014

DOI:https://doi.org/10.1103/PhysRevD.89.105001