Heavy Dark Baryons at Large $N$: Self-Interactions across All Scales

We show that heavy dark baryons in a confining $SU(N)$ sector with a moderately large number of colors, $N\sim 10$–$100$, can generate self-interactions spanning the full range of astrophysical velocities. Their chromo-electric polarizability induces van der Waals interactions that yield $\sigma \mathrm{/}{m}_{\mathrm{D}\mathrm{M}}\sim 30$-$100\mathrm{c}{\mathrm{m}}^2\mathrm{/}\mathrm{g}$ at dwarf-galaxy velocities, decrease to the values required by galaxy clusters, and rise to $100$-$1000\mathrm{c}{\mathrm{m}}^2\mathrm{/}\mathrm{g}$ at velocities of a few $\mathrm{k}\mathrm{m}\mathrm{/}\mathrm{s}$, as suggested by the second perturber of JVAS B1938+666. Remarkably, for a given ratio $m_Q\mathrm{/}{\mathrm{\Lambda }}_d$, these observations can be used to infer the value of $N$. The resulting self-interaction phenomenology favors GeV-scale dark baryons, independently of the relic-abundance requirement. At these masses, a dark baryon asymmetry comparable to the visible one can account for the observed dark-matter abundance.