A weak, attractive, long-range force in Higgs condensates

Due to the peculiar nature of the underlying medium, density fluctuations in a `Higgs condensate' are predicted to propagate for infinitely long wavelengths with a group velocity $c_s\to \infty $. On the other hand, for any large but finite $c_s$ there is a weak, attractive $1/r$ potential of strength ${{1}\over{c^2_s}}$ and the energy spectrum deviates from the purely massive form $\sqrt{p}^2 + M^2_h}$ at momenta smaller than $\delta\sim {{M_h}\over{c_s}}$. Physically, the length scale $\delta^{-1}$ corresponds to the mean free-path for the elementary constituents in the condensate and would naturally be placed in the millimeter range.