We present a method to derive conservative upper limits on the coupling constants of the effective theory of dark matter-nucleon interactions, taking into account the interference among operators. The method can be applied in any basis, and can be easily particularized to any UV complete model. To illustrate our method, we use the IceCube constraints on an exotic neutrino flux from dark matter annihilations in the Sun to derive conservative upper limits on the dark matter-nucleon coupling constants of the effective theory, as well as to derive conservative upper limits on the dark matter-proton and dark matter-neutron scattering cross-sections.

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.

For dark matter particles with spin up to 1/2, the non-relativistic effective field theory provides 28 coupling strengths for the dark matter-nucleon interactions. The standard assumption of collaborations is that dark matter couples equally to protons and neutrons. Since this is not necessarily true, we developed a method to derive limits taking the interference among operators into account. Using this method and data provided from XENON1T and PICO60, the relaxation of the published cross-section limits can be up to four orders of magnitude. Further we extended the developed method which now allows to do a combined analysis of several experiments. The combination of experiments can strengthen the limits by up to four orders of magnitude.