WIMPonium

TL;DR

This work introduces WIMPonium, bound states of weakly interacting dark matter arising from a Yukawa-type long-range force, and develops a NRQCD-inspired effective theory to study their formation, production, and decays. By mapping the problem to non-relativistic EFT with higher-dimension WIMP–SM operators, the paper derives scaling rules for binding energies, state spectra, and collider cross sections, and analyzes how vector and scalar WIMPonium could manifest at the LHC or future colliders. The results connect bound-state spectroscopy to underlying WIMP–SM couplings, showing that WIMPonium can reveal the UV structure of the dark sector through resonance signals, mixing with Z or Higgs states, and characteristic decay patterns, while also highlighting implications for cosmology via Sommerfeld enhancements and possible indirect detection signatures. Overall, WIMPonium offers a tractable, model-agnostic probe of dark matter dynamics with tangible collider and astroparticle phenomenology.

Abstract

We explore the possibility that weakly interacting dark matter can form bound states - WIMPonium. Such states are expected in a wide class of models of particle dark matter, including some limits of the Minimal Supersymmetric Standard Model. We examine the conditions under which we expect bound states to occur, and use analogues of NRQCD applied to heavy quarkonia to provide estimates for their properties, including couplings to the Standard Model. We further find that it may be possible to produce WIMPonium at the LHC, and explore the properties of the WIMP that can be inferred from measurements of the WIMPonium states.

Figures (3)

• Figure 1: The minimum value of $\alpha_\chi$ for which there is an $1s$ WIMPonium state (solid lines), $2s$ states (dashed lines), and $2p$ states (dotted lines) as a function of the WIMP mass $M$ and for Yukawa screening mass (bottom curve to top curve) $m= 1, 10$, and $100$ GeV.
• Figure 2: Sample reconstructed invariant mass of the $\ell^+ \ell^-$ for the Standard Model (blue) and a vector WIMPonium $^3S_1$ state signal for a mass of 200 GeV, universal $\Lambda_f = M$, and $\alpha_\chi = 0.2$ (red) at the LHC for an integrated luminosity of 100 fb$^{-1}$. Note that the intrinsic width of the WIMPonium and the experimental resolution are much smaller than the bin width.
• Figure 3: Minimum coupling for a weakly coupled vector WIMPononium state to be visible at $5\sigma$ against the SM background in the $\ell^+ \ell^-$ channel as a function of the WIMPonium mass, assuming universal coupling to all SM fermions, no coupling to SM bosons, and no non-SM decay modes (red curve). Also shown are the CDF limits from $Z^\prime$ searches as a function of mass (blue points and interpolating curve).