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There is no known reason that dark matter interactions with the StandardModel should couple to neutrons and protons in the same way. This isospinviolation can have large consequences, modifying the sensitivity of existingand future direct detection experimental constraints by orders of magnitude.Previous works in the literature have focused on the zero-momentum limit whichhas its limitations when extending the analysis to the Non-RelativisticEffective Field Theory basis (NREFT). In this paper, we study isospin violationin a detailed manner, paying specific attention to the experimental setups ofliquid noble detectors. We analyse two effective Standard Model gauge invariantmodels as interesting case studies as well as the more model-independent NREFToperators. This work demonstrates the high degree of complementarity betweenthe target nuclei xenon and argon. Most notably, we show that the StandardModel gauge-invariant formulation of the standard spin-dependent interactionoften generates a sizeable response from argon, a target nuclei with zero spin.This work is meant as an update and a useful reference to model builders andexperimentalists.

Isospin-violating dark matter at liquid noble detectors: new constraints, future projections, and an exploration of target complementarity