Complete EFT operator bases for dark matter and weakly-interacting light particle

The standard model can be extended to include weakly-interacting light particle (WILP): real or complex singlet scalar with a conserved U(1) charge, Majorana or Dirac neutral fermion, neutral or hidden-charged vector boson, etc. Imposing the Z2 symmetry, these particles can be lifted as the weakly-interacting massive particle (WIMP), the candidate of dark matter. Instead, imposing the shift symmetry on the scalar components gives rise to the axion-like particle, dark photon, etc. Utilizing these light degrees of freedom along with the standard model particles and imposing different symmetries, we construct the complete and independent sets of effective operators up to dimension eight with the Young tensor technique, consistent with counting from the Hilbert series.