Interpreting dark matter direct detection independently of the local velocity and density distribution

Abstract

We demonstrate precisely what particle physics information can be extracted from a single direct detection observation of dark matter while making absolutely no assumptions about the local velocity distribution and local density of dark matter. Our central conclusions follow from a very simple observation: the velocity distribution of dark matter is positive definite, $f(v)\ensuremath{\ge}0$. We demonstrate the utility of this result in several ways. First, we show a falling deconvoluted recoil spectrum (deconvoluted of the nuclear form factor), such as from ordinary elastic scattering, can be ``mocked up'' by any mass of dark matter above a kinematic minimum. As an example, we show that dark matter much heavier than previously considered can explain the CoGeNT excess. Specifically, ${m}_{\ensuremath{\chi}}<{m}_{\mathrm{Ge}}$ can be in just as good agreement as light dark matter, while ${m}_{\ensuremath{\chi}}>{m}_{\mathrm{Ge}}$ depends on understanding the sensitivity of xenon to dark matter at very low recoil energies, ${E}_{R}\ensuremath{\lesssim}6\text{ }\text{ }\mathrm{keVnr}$. Second, we show that any rise in the deconvoluted recoil spectrum represents distinct particle physics information that cannot be faked by an arbitrary $f(v)$. As examples of resulting nontrivial particle physics, we show that inelastic dark matter and dark matter with a form factor can both yield such a rise.