How large is "large $N_c$" for Nuclear matter?

TL;DR

The paper identifies a new scale related to the number of neighbors in dense systems, explaining why large $N_c$ approximations work in vacuum QCD but not at high densities, impacting phenomenological models.

Contribution

It introduces a previously neglected scale—the number of neighbors—that affects the convergence of the large $N_c$ expansion at high chemical potential.

Findings

Large $N_c$ expansion converges only when $N_c$ exceeds this new scale (~10).

Explains failure of large $N_c$ methods in high-density nuclear matter.

Cautions against relying on large $N_c$ extrapolations for dense matter phenomenology.

Abstract

We argue that a so far neglected dimensionless scale, the number of neighbors in a closely packed system, is relevant for the convergence of the large $N_c$ expansion at high chemical potential. It is only when the number of colors is large w.r.t. this new scale ($\sim \order{10}$) that a convergent large $N_c$ limit is reached. This provides an explanation as to why the large $N_c$ expansion, qualitatively successful in in vacuum QCD, fails to describe high baryo-chemical potential systems, such as nuclear matter. It also means that phenomenological claims about high density matter based on large $N_c$ extrapolations should be treated with caution.