Revisiting general dark matter-bound-electron interactions

Abstract

In this Letter we revisit general dark matter (DM)-bound-electron interactions studied previously in the influential work [R. Catena {\it 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 ($a_{0,1,2}$) and a linear combination (${\tilde{W}}_{0,1,2}$) of the four atomic response functions ($W_{1,2,3,4}$) given in that work, ${\tilde{W}}_0=W_1,{\tilde{W}}_1=|v_0^{\perp }{|}^2{W}_1-2\frac{m_{e}q\cdot v_0^{\perp }}{q^2}{W}_2+W_3,{\tilde{W}}_2=\frac{(q\cdot v_0^{\perp }{)}^2}{q^2}{W}_1-2\frac{m_{e}q\cdot v_0^{\perp }}{q^2}{W}_2+\frac{m_e^2}{q^2}{W}_4$. Furthermore, we find a crucial minus sign was missed for the calculation of $W_2$ 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 $W_2$ and $W_{3,4}$ terms, so that ${\tilde{W}}_{1,2}$ are dominated by the usual response function $W_1$ in some cases. Many DM scenarios involving DM or electron axial-vector current can yield $W_2$ 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.

v2: 7+2 pages, 4 figures, matches the published version as a letter in PRD

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