Phonon Excitation in Cubic Crystal Targets via Dark Matter Scattering

The scattering of dark matter (DM) particles to excite collective vibrational modes knownas phonons in crystal targets is a motivated method of observing DM with masses mχ < 1 MeV. This is due to the matching between the typical energy and momentum imparted into the target and those of the phonons. For heavier dark matter particles with masses mχ ≳ 1 GeV, the scattering is instead point-like off of the individual nuclei in the crystal, rather than collective scattering from many atoms. While the single phonon and nuclear recoil responses are understood, the transition between the two is not. An understanding of this intermediate regime requires a consideration of multiphonon processes, in particular as higher-order corrections that increasingly contribute to the total scattering rate as the typical energy depositions increase. We utilize several simplifying approximations to arrive at analytic descriptions for multiphonon excitation, allowing us to fully characterize the crystal’s phonon response across the relevant mass spectrum for incident DM. Our results allow us to identify the dominant signals to look for in experimental DM searches with cubic crystal targets as a function of the detector energy thresholds