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Assuming for Weakly Interacting Massive Particles (WIMPs) a Maxwellianvelocity distribution in the Galaxy we provide an assessment of the sensitivityof existing Dark Matter (DM) direct detection (DD) experiments to operators upto dimension 7 of the relativistic effective field theory describing darkmatter interactions with quarks and gluons . In particular we focus on asystematic approach, including an extensive set of experiments and large numberof couplings, both exceeding for completeness similar analyses in theliterature. The relativistic effective theory requires to fix one coupling foreach quark flavor, so in principle for each different combination the boundsshould be recalculated starting from direct detection experimental data. Toaddress this problem we propose an approximate model-independent procedure thatallows to directly calculate the bounds for any combination of couplings interms of model-independent limits on the Wilson coefficients of thenon-relativistic theory expressed in terms of the WIMP mass and of theneutron-to-proton coupling ratio $c^n/c^p$. We test the result of theapproximate procedure against that of a full calculation, and discuss itspossible pitfalls and limitations. We also provide a simple interpolatinginterface in Python that allows to apply our method quantitatively.

astroparticle physics

On the sensitivity of present direct detection experiments to WIMP-quark  and WIMP-gluon effective interactions: a systematic assessment and new  model-independent approaches