Effective field theory of dark matter direct detection with collective excitations

Abstract

We develop a framework for computing light dark matter direct detection rates through single phonon and magnon excitations via general effective operators. Our work generalizes previous calculations focused on spin-independent interactions involving the total nucleon and electron numbers $N$ (the usual route to excite phonons) and spin-dependent interactions involving the total electron spin $\mathbit{S}$ (the usual route to excite magnons), leading us to identify new responses involving the orbital angular momenta $\mathbit{L}$, as well as spin-orbit couplings $\mathbit{L}\ensuremath{\bigotimes}\mathbit{S}$ in the target. All four types of responses can excite phonons, while couplings to electron's $\mathbit{S}$ and $\mathbit{L}$ can also excite magnons. We apply the effective field theory approach to a set of well-motivated relativistic benchmark models, including (pseudo) scalar mediated interactions, and models where dark matter interacts via a multipole moment, such as a dark electric dipole, magnetic dipole or anapole moment. We find that couplings to pointlike degrees of freedom $N$ and $\mathbit{S}$ often dominate dark matter detection rates, implying that exotic materials with orbital $\mathbit{L}$ order or large spin-orbit couplings $\mathbit{L}\ensuremath{\bigotimes}\mathbit{S}$ are not necessary to have strong reach to a broad class of DM models. We highlight that phonon based crystal experiments in active R (such as SPICE) will probe light dark matter models well beyond those having a simple spin-independent interaction, including e.g., models with dipole and anapole interactions. Lastly, we make publicly available a code, $\mathsf{PhonoDark}$, which computes single phonon production rates in a wide variety of materials with the effective field theory framework.