[Paper Review] Effective Field Theory of Dark Matter Direct Detection With Collective Excitations

Tanner Trickle, Zhengkang Zhang+1 more|arXiv (Cornell University)|Sep 28, 2020

Atomic and Subatomic Physics Research5 citations

TL;DR

This paper develops an effective field theory framework to compute light dark matter direct detection rates via single phonon and magnon excitations in condensed matter targets, generalizing beyond standard spin-independent and spin-dependent couplings to include orbital angular momentum and spin-orbit coupling responses. It finds that couplings to nucleon and electron spin or number typically dominate detection rates, implying exotic materials with complex order are not required for strong sensitivity to a broad class of dark matter models, including dipole and anapole interactions.

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 $S$ (the usual route to excite magnons), leading us to identify new responses involving the orbital angular momenta $L$, as well as spin-orbit couplings $L\otimes S$ in the target. All four types of responses can excite phonons, while couplings to electron's $S$ and $L$ 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 point-like degrees of freedom $N$ and $S$ often dominate dark matter detection rates, implying that exotic materials with orbital $L$ order or large spin-orbit couplings $L\otimes S$ are not necessary to have strong reach to a broad class of DM models. We highlight that phonon based crystal experiments in active R&D (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, PhonoDark, which computes single phonon production rates in a wide variety of materials with the effective field theory framework.

Motivation & Objective

• To generalize dark matter direct detection beyond standard spin-independent and spin-dependent interactions to include responses involving orbital angular momentum and spin-orbit coupling.
• To develop a systematic effective field theory approach for computing single phonon and magnon excitation rates in crystalline and magnetic materials.
• To assess the reach of phonon-based experiments (e.g., SPICE) to a broad class of light dark matter models, including those with dipole and anapole interactions.
• To identify which effective operators—particularly those coupling to N, S, L, or L⊗S—dominate detection rates in realistic materials.
• To make publicly available a code, PhonoDark, for computing phonon production rates across diverse materials using the EFT framework.

Proposed method

• Construct a nonrelativistic effective field theory by matching relativistic dark matter models to effective operators involving nucleon number N, electron spin S, orbital angular momentum L, and spin-orbit coupling L⊗S.
• Match these effective operators to lattice degrees of freedom using nonrelativistic matching procedures, including projection of angular momentum operators onto crystal basis states.
• Quantize the lattice potential to derive the phonon and magnon excitation spectra, using the linear response formalism to compute transition rates.
• Apply the framework to benchmark models: standard spin-dependent interactions, scalar-mediated models, and multipole interactions (electric dipole, magnetic dipole, anapole moment).
• Compute single phonon excitation rates using the velocity-integrated response function, incorporating material-specific parameters such as sound speed, cell mass, and spin moment.
• Use the η-function formalism to compute the total event rate per unit target mass, accounting for the dark matter velocity distribution and kinematic thresholds.

Experimental results

Research questions

• RQ1 Which effective operators involving N, S, L, and L⊗S dominate dark matter detection rates via phonon and magnon excitations?
• RQ2 Can phonon-based experiments probe dark matter models beyond the standard spin-independent interaction, such as those with dipole or anapole couplings?
• RQ3 To what extent do couplings to orbital angular momentum L or spin-orbit coupling L⊗S enhance detection rates compared to standard N and S couplings?
• RQ4 How do the detection rates in materials like YIG depend on material parameters such as sound speed, spin moment, and cell mass?
• RQ5 What is the sensitivity reach of current and near-future phonon-based experiments (e.g., SPICE) to a broad class of light dark matter models?

Key findings

• Couplings to nucleon number N and electron spin S dominate detection rates in most models, implying that exotic materials with orbital L order or strong spin-orbit coupling are not necessary for strong sensitivity.
• Phonon-based experiments such as SPICE can probe light dark matter models with dipole and anapole interactions, extending beyond the reach of standard nuclear recoil experiments.
• The effective field theory framework successfully computes single phonon production rates across a wide range of materials, with the code PhonoDark enabling public access to these calculations.
• In YIG, the longitudinal acoustic phonon branch dominates the rate due to the alignment of the momentum and polarization vectors, leading to a rate scaling as ∝ q² η(v_min(q)).
• The detection rate for standard spin-dependent interactions in YIG scales as 1/c_s and is proportional to the square of the cell spin moment S_cell², with a maximum sensitivity limited by the first Brillouin zone edge.
• The inclusion of spin-orbit coupling and orbital angular momentum responses opens new channels for dark matter detection, though their contributions are typically subdominant compared to N and S couplings.