S-matrix bootstrap bounds on self-interacting dark matter

Self-interacting dark matter turns the structure of galactic halos into a direct requirement on a low-energy scattering amplitude. We show that, for weakly coupled scalar dark matter, this requirement implies a much stronger mass bound on the dark matter particle than partial-wave unitarity alone. Using analyticity, crossing symmetry, locality and partial-wave unitarity, we compute the maximal allowed threshold amplitude with a dispersive primal S-matrix bootstrap, assuming only a weakly coupled EFT below a scale $\Lambda$ and allowing arbitrary UV particle content above $\Lambda$. For the benchmark self-interaction cross section $\sigma_{\rm self}=10^{-24}(M/\mathrm{GeV})\mathrm{cm}^2$, the mass of a generic weakly coupled scalar satisfies $M\lesssim 0.3\,\mathrm{GeV}$ in the controlled EFT regime. If dark matter is a derivative-dominated pseudo-Nambu-Goldstone boson, the mass bound is lowered to the MeV scale or below, depending on the hierarchy $M/\Lambda$.