Dark Glueball Direct Detection

We consider glueball dark matter (DM) in a Yang-Mills dark sector confined at $\Lambda_D$ scale and coupled to the Standard Model through electrically and dark-color charged vector-like fermion portals, with the mass scale $m_\psi$. In a simple case with two lightest mass-degenerate vector-like fermions with opposite electric charges the effective amplitudes with one $C$-odd glueball (oddball) and odd number of photons vanish, rendering the lightest $C$-odd spin-1 state with mass $m_\chi$ a viable DM candidate provided that $m_\psi\gtrsim 5.5 \Lambda_D$. We develop a controlled effective field theory framework with non-perturbative information supported by QCD phenomenology leading to a quantitative prediction for coherent elastic glueball scattering off nuclei. We find a steep scaling of the spin-independent cross section $\sigma_{\rm SI}\propto \Lambda_D^{2.15} m_\psi^{-8}$. This implies that the sensitivity of the current and next-generation xenon experiments in the range of $\sigma_{\rm SI} \sim 10^{-46} - 10^{-48}$ cm$^2$ corresponds to $m_\psi \simeq 3-30$ GeV, respectively, for $\Lambda_D\simeq 0.55-5.5$ GeV. We provide a minimal UV completion of the portal sector compatible with collider phenomenology. Our results pave a quantitative foundation for testing glueball DM in direct-detection experiments.