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

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.