Constraints from the Neutron EDM on Subleading Effective Operators for Direct Dark Matter Searches

Interactions between Dark Matter (DM) and nucleons relevant for direct search experiments can be organised in a model independent manner using a Galiliean invariant, non--relativistic effective field theory (NREFT). Here one expands the interactions in powers of the momentum transfer q and DM velocity v. This approach generates many operators. The potentially most important subleading operators are odd under T, and can thus only be present in a theory with CP violating interactions. We consider two such operators, called O₁₀ and O₁₁ in the literature, in simplified models with neutral spin-0 mediators; the couplings are chosen such that the coefficient of the leading spin independent (SI) operator, which survives for v 0, vanishes at tree level. However, it is generically induced at the next order in perturbation theory. We perform a numerical comparison of the number of scattering events between interactions involving the T-odd operators and the corresponding loop induced SI contributions. We find that for ''maximal'' CP violation the former can dominate over the latter. However, in two of the three models we consider, an electric dipole moment of the neutron (nEDM) is induced at two--loop order. We find that the experimental bound on the nEDM typically leads to undetectably small rates induced by O₁₀. On the other hand, the model leading to a nonvanishing coefficient of O₁₁ does not induce an nEDM.