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, $f(v)\ge 0$. 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, $m_{\chi }<m_{\mathrm{Ge}}$ can be in just as good agreement as light dark matter, while $m_{\chi }>m_{\mathrm{Ge}}$ depends on understanding the sensitivity of xenon to dark matter at very low recoil energies, $E_R\lesssim 6\mathrm{keVnr}$. 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.

• Received 19 November 2010

DOI:https://doi.org/10.1103/PhysRevD.83.034007