Probing Dark Matter via Non-Relativistic Effective Field Theory:WIMP–Nucleus Scattering for Helium target

Abstract

Non-Relativistic Effective Field Theory (NREFT) provides a systematic framework for studying Weakly
Interacting Massive Particles (WIMPs) beyond the conventional spin-independent and spin-dependent
paradigms. In this work, we investigate the phenomenology of WIMP-nucleus scattering using a compre
hensive set of 15 interaction operators embedded within nuclear response functions. We focus on helium-4
as a target system, motivated by its light mass (4.0026 u), spin-zero ground state (J = 0), kinematic match
ing for low-massWIMPs(10–50GeV),anditsrelevancetoemergingsuperfluidheliumtechnologies.Using
the dmscatter code, we compute recoil-energy spectra and event rates for the full NREFT operator basis
(O1–O15). Our results demonstrate that the null spin of 4He strictly suppresses contributions from spin
dependent operators (e.g., O4,O6 → 0), offering a clean probe for scalar and momentum-dependent inter
actions. We observe distinct spectral features for momentum-dependent operators such as O3,O5,O8,O11,
and O15, alongside the characteristic velocity suppression of O2 (v⊥ ∼ 10−3c). These findings highlight
the complementarity of helium-4 with heavier targets for disentangling NREFT operators and provide
essential inputs for interpreting signals in next-generation direct detection experiments.