Does nuclear matter bind at large $N_c$?

TL;DR

This paper examines whether nuclear matter can exist at large $N_c$ using effective hadronic models, concluding that it does not bind at large $N_c$, highlighting the special nature of our physical world with $N_c=3$.

Contribution

The study analyzes the large $N_c$ behavior of nuclear matter binding within Walecka-type models, linking scalar meson properties to the existence of nuclear matter at different $N_c$ values.

Findings

Nuclear matter does not bind at large $N_c$ in realistic models.

The scalar meson sector's properties are crucial for binding.

Our universe's $N_c=3$ is uniquely suited for nuclear matter.

Abstract

The existence of nuclear matter at large $N_{c}$ is investigated in the framework of effective hadronic models of the Walecka type. This issue is strongly related to the nucleon-nucleon attraction in the scalar channel, and thus to the nature of the light scalar mesons. Different scenarios for the light scalar sector correspond to different large $N_{c}$ scaling properties of the parameters of the hadronic models. In all realistic phenomenological scenarios for the light scalar field(s) responsible for the attraction in the scalar channel it is found that nuclear matter does not bind in the large $N_{c}$ world. We thus conclude that $N_{c}=3$ is in this respect special: 3 is fortunately not large at all and allows for nuclear matter, while large $N_{c}$ would not.