ALP-mediated Dark Matter-Nucleon Scattering

Abstract

We perform a comprehensive analysis of dark matter-nucleon scattering via the exchange of axion-like particles (ALPs). At first sight, this might appear of little practical use, as non-relativistic scattering through pseudo-scalar interactions is momentum-suppressed and spin-dependent, resulting in scattering rates below any experimental sensitivity. We show that the scattering rate can be drastically enhanced in two ways. First, light ALPs with masses below the typical momentum transfer at direct detection experiments lift the momentum suppression by acting as essentially massless mediators. Second, ALP exchange through loops induces coherent spin-independent scattering. If the ALP has flavor-changing couplings to up-type quarks, loop-induced scattering receives an extra strong enhancement by the top-quark mass. We deduce that, contrary to common lore, XENONnT and PandaX-4T are already sensitive to ALP-mediated dark matter-nucleon scattering. The next generation of direct detection experiments will probe far into the parameter space of the ALP effective theory, potentially exceeding the sensitivity of collider searches.

Figures (9)

• Figure 1: Feynman diagrams for ALP-mediated dark matter-quark scattering (left) and dark matter-gluon scattering (center and right) at $\mathcal{O}(c^2/f_a^2)$.
• Figure 2: Feynman diagrams for tree-level ALP-mediated and pion-mediated dark matter-nucleon scattering at $\mathcal{O}(c^2/f_a^2)$.
• Figure 3: Feynman diagrams for loop-induced dark matter-quark scattering via flavor-diagonal (left) and flavor-changing (right) ALP couplings at $\mathcal{O}(c^4/f_a^4)$. Crossed diagrams also contribute to the scattering amplitude.
• Figure 4: Feynman diagrams for loop-induced ALP-mediated dark matter-nucleon scattering with neutral meson exchange at $\mathcal{O}(c^4/f_a^4)$, where $\phi,\phi'=\pi^0,\eta$. Scalar $\chi \chi N N$ interactions are generated through various ALP-induced effective couplings in chiral perturbation theory: a $\chi\chi NN$ contact interaction (top left, bottom right), a $\chi\chi NN\phi$ contact interaction (top middle), two-meson exchange (top right), and a $NN\phi\phi^{(')}$ contact interaction (bottom left).
• Figure 5: Energy recoil distribution $\dd R / \dd E_R$ of Xenon nuclei due to dark matter scattering through flavor-diagonal ALP couplings; shown for ALP masses $m_a = 1\,$MeV (left) and $m_a = 10\,$GeV (right) and various dark matter masses, with $f_a = 1\,$TeV. Left panel: spin-dependent tree-level scattering in two scenarios, $c_{uu}(\Lambda)c_\chi = 1,\,c_{qq \ne uu}(\Lambda) = c_{GG} (\Lambda) = 0$ (solid) and $c_{GG} (\Lambda)c_\chi = 1,\,c_{qq}(\Lambda) = 0$ (dashed). Right panel: spin-dependent tree-level (solid) and spin-independent one-loop (dotted) scattering for $c_{uu}(\Lambda)c_\chi = 1,\,c_{qq \ne uu}(\Lambda) = c_{GG} (\Lambda) = 0$. Colored bands indicate renormalization scale variation within $\mu \in [0.5 , 2]m_a$ (darker shade) and nucleon form factor uncertainties (lighter shade).