Neutron EDM constrains direct dark matter detection prospects

A non-relativistic effective field theory (NREFT) offers a bottom-up framework to classify Dark Matter (DM)-nucleon interactions relevant for scattering at direct detection experiments by organizing the interactions in powers of the momentum transfer $\vec{q}$ and DM velocity $\vec{v}$. This approach generates a number of operators including P-odd and T-odd operators; these can only be generated from a relativistic theory with CP violating interactions. We consider the leading order P-odd, T- odd operators viz. $\mathcal{O}_{10}$, $\mathcal{O}_{11}$ and $\mathcal{O}_{12}$ and compare the constraints on these operators from leading direct detection searches and from the bound on the neutron EDM (nEDM). We perform our analysis using simplified models with charged mediators and compute the loop diagrams contributing to the nEDM. We find that constraints on the DM scattering cross section from the bound on the nEDM are several orders of magnitude stronger than the limits from direct searches, and even well below the neutrino floor for such NREFT operators, for the entire sub-GeV to TeV DM mass range. This indicates that these operators need not be considered when analyzing data from present or future direct dark matter detection experiments.