Present and projected sensitivities of Dark Matter direct detection experiments to effective WIMP-nucleus couplings

Abstract: Assuming for Weakly Interacting Massive Particles (WIMPs) a Maxwellian velocity distribution in the Galaxy we explore in a systematic way the relative sensitivity of an extensive set of existing and projected Dark Matter (DM) direct detection experiments to each of the 14 couplings that parameterize the most general non-relativistic (NR) effective Hamiltonian allowed by Galilean invariance for a contact interaction driving the elastic scattering off nuclei of WIMPs of spin 1/2. We perform our analysis in terms of two free parameters: the WIMP mass $m_{\chi}$ and the ratio between the WIMP-neutron and the WIMP-proton couplings $c^n/c^p$. We include the modified signal spectral shape due to non-standard interactions when it is needed in the determination of the bound, such as in the case of background subtraction or of the application of the optimal-interval method. For each coupling, in the $m_{\chi}$-$c^n/c^p$ plane we provide contour plots of the most stringent 90 % C.L. bound on the WIMP-nucleon cross section and show the experiment providing it. We also introduce NRDD_constraints, a simple interpolating code written in Python that allows to obtain the numerical value of the bound as a function of the WIMP mass $m_{\chi}$ and of the coupling ratio $c^n/c^p$ for each NR coupling. We find that 9 experiments out of the 14 present Dark Matter searches considered in our analysis provide the most stringent bound on some of the effective couplings for a given choice of $(m_{\chi},c^n/c^p)$: this is evidence of the complementarity of different target nuclei and/or different combinations of count-rates and energy thresholds when the search of DM is extended to a wide range of possible interactions.