Revisiting general dark matter-bound-electron interactions

In this Letter we revisit general dark matter (DM) -bound-electron interactions studied previously in the influential work R. Catena et al. , Atomic responses to general dark matter-electron interactions, Phys. Rev. Res. 2, 033195 (2020) For the most general DM-electron nonrelativistic or relativistic interactions for DM with spin up to 1, we find the average ionization matrix element squared can be organized into three terms, each of which is a product of a DM response function (a₀, ₁, ₂) and a linear combination (W₀, ₁, ₂) of the four atomic response functions (W₁, ₂, ₃, ₄) given in that work, W₀ = W₁, \, W₁ = |v₀^|² W₁ - 2 mₑ\, q v₀^ q² W₂ + W₃, \, W₂ = (q v₀^) ² q² W₁ - 2 mₑ\, q v₀^ q² W₂ + mₑ² q²W₄. Furthermore, we find a crucial minus sign was missed for the calculation of W₂ in that work, which has significant phenomenological consequences when explaining experimental bounds on specific DM scenarios. Due to the corrected sign, there can be significant cancellations between the W₂ and W₃, ₄ terms, so that W₁, ₂ are dominated by the usual response function W₁ in some cases. Many DM scenarios involving DM or electron axial-vector current can yield W₂ and thus are potentially affected by the sign. As an example, we show that the recent XENON1T constraint on the fermionic DM anapole moment is weakened by a factor of 2 or so. We also present a complete list of NR operators for spin-1 DM and compute their contributions to the DM response functions.