Prospects for detection of target-dependent annual modulation in direct dark matter searches

Abstract: Earth's rotation about the Sun produces an annual modulation in the expected scattering rate at direct dark matter detection experiments. The annual modulation as a function of the recoil energy $E_\text{R}$ imparted by the dark matter particle to a target nucleus is expected to vary depending on the detector material. However, for most interactions a change of variables from $E_\text{R}$ to $v_\text{min}$, the minimum speed a dark matter particle must have to impart a fixed $E_\text{R}$ to a target nucleus, produces an annual modulation independent of the target element. We recently showed that if the dark matter-nucleus cross section contains a non-factorizable target and dark matter velocity dependence, the annual modulation as a function of $v_\text{min}$ can be target dependent. Here we examine more extensively the necessary conditions for target-dependent modulation, its observability in present-day experiments, and the extent to which putative signals could identify a dark matter-nucleus differential cross section with a non-factorizable dependence on the dark matter velocity.