Effective Theory for Light Portal Dark Matter Detection

TL;DR

This work formulates a general effective-theory framework for direct detection of light portal dark matter with a light mediator, explicitly retaining the mediator propagator to handle finite momentum transfer. It couples DM bilinears to quark and gluon operators, uses QCD equations of motion to prune the operator basis, and employs lattice QCD–driven nucleon form factors to construct hadronic tensors at finite $Q^2$. The nucleon-level structure is then mapped to the nuclear level through an extended relativistic Fermi gas model, enabling calculation of $d\sigma_{nuclear}/dQ^2$ and facilitating high-threshold experimental probes like large-volume neutrino detectors for boosted sub-GeV DM. The paper illustrates the framework with UV-complete spin-1 and spin-2 portal examples, connecting their momentum-transfer–dependent cross sections to astrophysical core–cusp self-interaction considerations and highlighting practical paths to experimental constraints.

Abstract

We develop a general framework for the computation of light portal dark matter direct detection, incorporating a consistent treatment of finite momentum transfer. In this framework, dark matter interacts with Standard Model matter through a light mediator, which simultaneously serves as the force carrier for dark matter self-interaction, potentially with a distinct coupling strength. The corresponding effective theory relevant for detecting this class of dark matter is systematically constructed. Our analysis focuses on light (semi)relativistic dark matter, which may originate from cosmic-ray boosting and can be probed in high threshold experiments such as large-volume neutrino detectors. In this context, the nucleon matrix elements of the effective operators at finite momentum transfer are required, made available through recent advances in lattice QCD and related nonperturbative methods. The relativistic Fermi gas model is used to convert the nucleon-level momentum transfer to the nuclear level, thereby incorporating nuclear effects pertinent to heavy target experiments. To demonstrate the utility of the framework, we present ultraviolet-complete examples featuring spin-1 and spin-2 portal dark matter. For these models, we compute the differential cross sections with respect to momentum transfer, adopting parameter choices that address the so-called core-cusp problem in astrophysical observations via dark matter self-interactions.

Figures (4)

• Figure 1: Dark matter and quarks/gluons interaction via a light mediator in t-channel, where the black squares denote effective vertexes which could be spin-0, spin-1 and spin-2 currents.
• Figure 2: The differential cross section of spin-1 portal (semi)relativistic dark matter and Argon nucleus scattering, with three types of interaction: pure vector, pure axial-vector and mixed.
• Figure 3: Massive spin-2 currents matched onto QCD effective operators.
• Figure 4: Differential cross sections for spin-2 portal (semi)relativistic dark matter and Argon nucleus scattering.