Effective Field Theory for Dark Matter Absorption on Single Phonons

Single phonon excitations, with energies in the $1-100 \, \text{meV}$ range, are a powerful probe of light dark matter (DM). Utilizing effective field theory, we derive a framework to compute DM absorption rates into single phonons starting from general DM-electron, proton, and neutron interactions. We apply the framework to a variety of DM models: Yukawa coupled scalars, axionlike particles (ALPs) with derivative interactions, and vector DM coupling via gauge interactions or Standard Model electric and magnetic dipole moments. We find that GaAs or $\text{Al}_2\text{O}_3$ targets can set powerful constraints on a $U(1)_{B-L}$ model, and targets with electronic spin ordering are similarly sensitive to DM coupling to the electron magnetic dipole moment. Lastly, we make the code, \textsf{PhonoDark-abs} (an extension of the existing \textsf{PhonoDark} code which computes general DM-single phonon scattering rates), publicly available.