$SU(\mathcal{N})$ baryon formation in the early Universe and dark matter

Abstract

We study the formation of $\mathcal{N}$-quark baryons during the confinement crossover of an $SU(\mathcal{N})$ gauge theory containing quarks in the fundamental representation, with masses around or below the confinement scale. We assume stepwise baryon formation through the successive fusion of pairs of quark-clusters, with color interaction rates obeying quadratic Casimir scaling. We include the complete set of reactions between $SU(\mathcal{N})$ antisymmetric clusters dressed with their specific spin-flavor multiplicities. We show that at large $\mathcal{N}$, baryon formation is hindered by a Casimir bottleneck, such that fusion of few-quark clusters in the initial steps of the baryon assembly chain is strongly outweighed by cluster destruction processes. We find that for $\mathcal{N}=12\,(18)$ the baryon-to-meson yield ratio is suppressed down to $10^{-12}\,(10^{-23})$ of its value at $\mathcal{N}=3$. We embed the mechanism in a vectorlike three-flavor model whose lightest baryon can be electrically neutral, while axial-anomaly-induced couplings and dimension-six operators induce decays of the unstable mesons and charged baryons safely before big-bang nucleosynthesis. The relic density of cosmologically stable neutral $\mathcal{N}$-baryons is thus set during confinement at values so small that, for sufficiently large $\mathcal{N}$, the baryon masses required to saturate the dark matter energy density exceed by several orders of magnitude the unitarity bound on annihilation cross sections.