Halo-independent comparison of direct detection experiments in the effective theory of dark matter-nucleon interactions

The theoretical interpretation of dark matter direct detection experiments is hindered by uncertainties of the microphysics governing the dark matter-nucleon interaction, and of the dark matter density and velocity distribution inside the Solar System. These uncertainties are especially relevant when confronting a detection claim to the null results from other experiments, since seemingly conflicting experimental results may be reconciled when relaxing the assumptions about the form of the interaction and/or the velocity distribution. We present in this paper a halo-independent method to calculate the maximum number of events in a direct detection experiment given a set of null search results, allowing for the first time the scattering to be mediated by an arbitrary combination of various interactions (concretely we consider up to 64). We illustrate this method to examine the compatibility of the dark matter interpretation of the three events detected by the silicon detectors in the CDMS-II experiment with the null results from XENON1T and PICO-60.