Astrophysics-independent determination of dark matter parameters from two direct detection signals

Next-generation dark matter direct detection experiments will explore several orders of magnitude in the dark matter–nucleus scattering cross section below current upper limits. In case a signal is discovered the immediate task will be to determine the dark matter mass and to study the underlying interactions. We develop a framework to determine the dark matter mass from signals in two experiments with different targets, independent of astrophysics. Our method relies on a distribution-free, nonparametric two-sample hypothesis test in velocity space, which neither requires binning of the data, nor any fitting of parametrizations of the velocity distribution. We apply our method to realistic configurations of xenon and argon detectors such as XENONnT/DARWIN and DarkSide, and estimate the precision with which the DM mass can be determined. Once the dark matter mass is identified, the ratio of coupling strengths to neutrons and protons can be constrained by using the same data. The test can be applied for event samples of order 20 events, but promising sensitivities require $\gtrsim 100$ events.