Target dependence of the annual modulation in direct dark matter
  searches
  Due to Earth's revolution around the Sun, the expected scattering rate in
direct dark matter searches is annually modulated. This modulation is expected
to differ between experiments when given as a function of recoil energy
$E_\text{R}$, e.g. due to the gravitational focusing effect of the Sun. A
better variable to compare results among experiments employing different
targets is the minimum speed $v_\text{min}$ a dark matter particle must have to
impart a recoil energy $E_\text{R}$ to a target nucleus. It is widely believed
that the modulation expressed as a function of $v_\text{min}$ is common to all
experiments, irrespective of the dark matter distribution. We point out that
the annual modulation as a function of $v_\text{min}$, and in particular the
times at which the rate is maximum and minimum, could be very different
depending on the detector material. This would be an indication of a scattering
cross section with non-factorizable velocity and target material dependence.
Observing an annual modulation with at least two different target elements
would be necessary to identify this type of cross section.
