Irreducible Constraints on Hadronically Interacting Sub-GeV Dark Matter

TL;DR

This work develops a UV-insensitive framework to bound sub-GeV DM–nucleon scattering using SU(3) chiral EFT, establishing that hadronic leading-order couplings imply electromagnetic interactions at next-to-leading order and invoking BBN, irreducible freeze-in, and meson-decay constraints to derive cross-section limits around 10^{-36} cm^2 for DM masses from keV to ~100 MeV. By analyzing vector, axial-vector, pseudoscalar, and gluon operators with representative flavor structures, the authors show that regions accessible to traditional direct-detection experiments are already excluded, often by many orders of magnitude, independent of specific UV completions. The results imply that any future low-mass direct-detection program must reach exceedingly small cross-sections in this mass range to probe new parameter space, and they emphasize the complementary role of low-energy observables in constraining hadronically interacting DM. The approach provides a conservative, model-independent baseline for interpreting sub-GeV DM searches and highlights the significance of meson decays, freeze-in, and BBN as powerful probes of DM–nucleon interactions.

Abstract

We derive conservative upper limits on the dark-matter--nucleon scattering cross-section for sub-GeV mass dark matter. Working exclusively within the low-energy chiral effective theory, we derive bounds that are independent of the details of the dark matter interactions in the UV. Dark matter that interacts only hadronically at leading order also inevitably interacts with photons or electrons at next-to-leading-order. We show that these electromagnetic interactions lead to strong constraints from big bang nucleosynthesis and over-production of dark matter via freeze-in at low temperatures, while the leading-order hadronic couplings face stringent constraints from meson decays. Combining these constraints, we rule out both spin-independent and spin-dependent dark-matter--nucleon scattering cross-sections $\gtrsim 10^{-36}\,{\rm cm}^2$ for dark matter masses in the keV - 100 MeV range. These bounds are several orders of magnitude stronger than the existing constraints from astrophysics and cosmology and have significant implications for future low-mass direct detection experiments.

Figures (8)

• Figure 1: Feynman diagrams that contribute to the DM thermalisation and freeze-in production process $e^+e^- \to \chi \bar{\chi}$ for DM interacting via the quark vector current.
• Figure 2: Feynman diagrams contributing to DM thermalisation and freeze-in production (left) and pion decay (right) for the vector operator via the WZW term.
• Figure 3: Top: Constraints on the DM-nucleon spin-independent cross-section $\sigma^{\chi N}_{\rm SI}$ for complex scalar (left-panel) and Dirac fermion (right-panel) DM that interacts with the quark vector current with $C^V = \mathbb{1}$. Red shaded regions are excluded by BBN and olive-green shaded regions by the upper-limit on the branching ratio of $\pi^0 \to \gamma \nu\bar{\nu}$. Above the black dashed lines the DM attains thermal equilibrium with the SM plasma below $T \sim 10\,{\rm MeV}$ and within the grey-shaded regions the irreducible DM abundance overcloses the Universe. Bottom: Same as top panel, but for $C^V = Q_q$. In this case, the DM freeze-out line is shown by the nearly flat dot-dashed grey line in the right panel, with the hatched region above excluded by CMB constraints Slatyer:2015jla. In all panels, the blue and light-green regions are excluded by existing bounds from structure formation Rogers:2021byl and direct-detection experiments DAMIC-M:2025luvSENSEI:2023zdfPandaX:2023xgl, respectively.
• Figure 4: Left: Feynman diagram contributing to DM thermalisation and freeze-in production for interactions with the quark axial-vector, pseudoscalar and $G_{a\,\mu\nu}\tilde{G}^{a\,\mu\nu}$ operators. Right: Feynman diagram contributing to the invisible $\pi^0,\eta$ decays for interactions with the quark axial-vector, pseudoscalar and $G_{a\,\mu\nu}\tilde{G}^{a\,\mu\nu}$ operators.
• Figure 5: Constraints on the DM-nucleon spin-dependent cross-section $\sigma^{\chi N}_{\rm SD}$ for Dirac fermion DM interacting with the quark axial-vector current. The olive-green and deep-green shaded regions are excluded by the upper-limits on the $\pi^0 \to \nu\bar{\nu}$ and $\eta \to \nu\bar{\nu}$ branching ratios, respectively, and orange shaded regions by the measurement of the $K^+ \to \pi^+ \nu\bar{\nu}$ branching ratio. The grey shaded regions denote the parameter space where the irreducible DM abundance overcloses the Universe, and above the black dashed lines the DM attains thermal equilibrium with the SM plasma below $T \sim 10\,{\rm MeV}$. Red shaded regions are excluded by BBN. The left panel is for $C^A = \mathbb{1}$ and the right panel $C^A = Q_q$. Existing bounds from structure formation Rogers:2021byl and direct-detection experiments Wang:2021oha are shown in blue and light-green, respectively.