The Migdal effect in Semiconductors for the Effective Field Theory of Dark Matter Direct Detection

TL;DR

This paper develops a comprehensive effective field theory framework to describe the Migdal effect in semiconductors for dark matter detection, enabling systematic analysis of various interaction operators and deriving new experimental bounds.

Contribution

It combines vibrational and electronic degrees of freedom in semiconductors with non-relativistic effective field theory operators to analyze the Migdal effect across all kinematic regimes.

Findings

Derived new bounds on dark matter interactions from germanium detector data.

Showed factorization of scattering and ionization signals in semiconductors.

Compared limits to other direct detection constraints.

Abstract

The Migdal effect in semiconductors, prompt ionization from a primary nuclear scattering event, can be described across all kinematic regimes using an effective field theory that encodes the complex vibrational and electronic degrees of freedom of the crystal in measurable structure factors. Simultaneously, general dark matter-nucleus interactions can be systematically described using non-relativistic effective field theory operators. We combine these two effective field theory frameworks to calculate the Migdal effect in semiconductors for all ten dimension-six non-relativistic operators. From the effective Hamiltonian, we find that DM-nucleus scattering factorizes from the ionization and vibrational excitation signal as it does in the free-atom case. Using data from EDELWEISS that was taken with a germanium detector, we derive new experimental bounds on each operator and compare these limits to other direct-detection constraints in the literature. We find the accessible parameter space to be disfavored by bounds on heavy mediators contained in simple UV completions that generate the effective operators.