Heavy Dark Baryons as Self-Interacting Dark Matter: A GeV-Scale Coincidence

Abstract

We study self-interacting dark matter composed of heavy baryons in a confining dark $SU(N)$ gauge theory with a single heavy vector-like quark, $m_Q \gg Λ_d$. In this regime, the dark baryons are compact Coulombic bound states whose long-distance interactions can be described by a multipole expansion. We derive the leading baryon-baryon interaction by adapting the quarkonium operator-product-expansion formalism to heavy baryons. The resulting force contains non-retarded London dispersion, retarded Casimir-Polder, and Yukawa contributions from dark glueball exchange. We find that the self-interaction phenomenology depends strongly on the number of colors. For $N=2,3$, the attractive interaction is too weak to overcome the short-distance Pauli repulsion, and no phenomenologically relevant velocity dependence is obtained within our minimal set-up. For sufficiently large $N$, the attractive interaction remains competitive with the repulsive core and can generate strong velocity dependent cross sections. Taking $SU(10)$ as a representative finite-$N$ realization, we find regions compatible with self-interaction requirements inferred from dwarf galaxies and clusters, while allowing much larger cross sections at low velocities relevant for gravothermal evolution. These regions correspond to GeV-scale dark baryons and a confinement scale close to that of QCD, which naturally motivate an asymmetric dark matter origin.