Particle dark matter coherent scattering direct searches rely on the scattering of the DM particle off a nucleus (Xe, Si, Ge, NaI etc). The wisdom is this is coherent scattering: so the rate ~atomic mass squared, since $q^2 \approx zero$. Is this completely sensible? Despite $q^2 \approx 0$ for galactic wind DM particles, thus with a size of interaction supposedly $\approx \hbar/q^2 > R$ nucleus, is it really sensible for a tiny heavy object exchanging a similarly tiny object to extend over the entire nucleus??? Argument for no:
- $\approx 100$ GeV particle: Compton wavelength < 1F the size of a single nucleon.
- object exchanged, Z or H, also on shell size < 1F.
- neutralino - esp. if it could be a 4th gen. Dirac or Majorana neutrino**, will have an oscillation length < 1 F - i.e. its wavefunctions will be changing on a scale small with the nucleus
- compared with e-m scattering, like e, mu, proton off nuclei, the e-m field clearly could encompass the entire nucleus at low $q^2$.
- compared with light neutrino scattering, even though W,Z heavy, the neutrino itself at low q^2 is larger than the nucleus.
** if the neutrino mixing angles $\sin^2\theta \approx (1/\Delta m^2)^2$ or $(1/\Delta m^2)1.5$, which they do for gen 1-3, then a 4th gen 100 GeV neutrino has a lifetime $\approx T_{top} \times 10^{44} > T_{universe}$, assuming the charged partner mass $ > M_{ne_u}$.
