Complementarity of experiments in probing the non-relativistic effective theory of dark matter-nucleon interactions

The non-relativistic effective theory of dark matter-nucleon interactions depends on 28 coupling strengths for dark matter spin up to 1/2. Due to the vast parameter space of the effective theory, most experiments searching for dark matter interpret the results assuming that only one of the coupling strengths is non-zero. On the other hand, dark matter models generically lead in the non-relativistic limit to several interactions which interfere with one another, therefore the published limits cannot be straightforwardly applied to model predictions. We present a method to determine a rigorous upper limit on the dark matter-nucleon interaction strength including all possible interferences among operators. We illustrate the method to derive model independent upper limits on the interaction strengths from the null search results from XENON1T, PICO-60 and IceCube. For some interactions, the limits on the coupling strengths are relaxed by more than one order of magnitude. We also present a method that allows to combine the results from different experiments, thus exploiting the synergy between different targets in exploring the parameter space of dark matter-nucleon interactions.