A systematic investigation on vector dark matter-nucleus scattering in effective field theories

TL;DR

The paper develops a comprehensive EFT framework for vector (spin-1) DM interactions with nuclei, combining nonrelativistic and relativistic descriptions. It constructs a complete NR operator basis for vector DM–nucleon scattering, derives NR reductions of leading relativistic DM–quark/photon operators, and formulates the DM–nucleus scattering formalism in terms of nuclear and DM response functions. By confronting elastic scattering and Migdal-effect data from PandaX-4T, XENONnT, LZ, and DarkSide-50, it derives stringent bounds on NR and relativistic EFT coefficients across DM masses from MeV to TeV, with Migdal data extending sensitivity to ~20 MeV. A UV-complete model with a dark SU(2) sector is introduced, illustrating how the vector DM and its electromagnetic properties arise and how the low-energy operators are generated, thereby linking fundamental theory to direct-detection observables.

Abstract

In this paper, we systematically investigate the general spin-one dark matter-nucleus interactions within the framework of effective field theories (EFT). We consider both the nonrelativistic (NR) and the relativistic EFT descriptions of the DM interactions with nucleons and quarks. In the NREFT framework, we present a complete list of NR operators for spin-one DM coupling to nucleons and compute their contributions to the DM response functions. Next, we consider all possible leading-order relativistic EFT operators between DM and light quarks and the photon, and perform NR reductions to match them onto the NREFT. We then derive the nuclear scattering rate from these interactions, and employ recent DM direct detection data (from both the nuclear recoil and the Migdal effect) to constrain all these EFT operators and DM electromagnetic properties. We find the elastic nuclear recoil data (from PandaX-4T, XENONnT, LZ, and DarkSide-50) set stringent bounds on the EFT coefficients for a DM mass above a few GeV while the Migdal effect datasets (from PandaX-4T, XENONnT, and DarkSide-50) can probe the DM mass region as small as 20 MeV. Lastly, we construct a UV complete model that can provide a complex spin-one DM candidate, and at the same time generate DM-quark/photon operators discussed in this work.

Figures (9)

• Figure 1: Constraints on the dimensionless WCs of SI NREFT operators from DM-nucleus elastic scattering (solid curves) and the Migdal effect (dashed curves). The panels are organized according to the $(q,v)$ power counting, which is indicated in the parentheses following the operator label, along with the corresponding dominant nuclear response function.
• Figure 2: Same as \ref{['fig:con-NR-SI']}, but for SD NREFT operators. Notice that we have further categorized the operators based on their dominant nuclear response functions. Constraints on ${\cal O} _{25}$ and ${\cal O} _{26}$ are not shown, as they are too weak to be considered meaningful.
• Figure 3: Constraints on the WCs, $c_i$, associated with each NREFT operator for the isospin-specific case, featuring contributions from proton-only (upper) and neutron-only (lower) interactions. Each curve (either solid or dashed) represents the strongest constraint obtained by combining results from all considered experiments.
• Figure 4: Constraints on the coupling or effective scale related to each relativistic vector DM-photon operator from both the DM-nucleus elastic scattering (solid curves) and the Migdal effect (dashed curves).
• Figure 5: Constraints on the effective scale associated with each relativistic vector DM-quark operator in case A under the flavor-universal assumption with a universal coupling for $u$, $d$, and $s$ quarks. The solid curves represent results from the DM-nucleus elastic scattering, while the dashed curves correspond to the Migdal effect.