ALP-Mediated Dark Matter-Nucleon Scattering

• ALP-mediated dark matter-nucleon scattering is defined by dark matter interacting with nucleons via axion-like particles through both spin-dependent and loop-induced spin-independent channels.
• The methodology employs effective Lagrangians with derivative couplings and distinguishes between heavy and light mediator regimes to capture momentum transfer and coherence effects.
• Experimental strategies, ranging from tabletop optomechanical sensors to large-scale liquid xenon detectors and neutron star heating observations, enhance sensitivity to varied ALP mass and coupling landscapes.

Axion-like particle (ALP)-mediated dark matter–nucleon scattering encompasses a diverse range of theoretical, phenomenological, and experimental regimes. In such scenarios, dark matter (DM) interacts with Standard Model nucleons through the exchange of a pseudoscalar mediator—typically an ALP—resulting in both spin-dependent (SD) and loop-induced spin-independent (SI) scattering. The phenomenology is shaped by the ALP mass regime, tree-level versus loop-induced couplings, nuclear coherence, and the vastly distinct velocity landscapes of terrestrial and astrophysical environments.

1. Theoretical Foundations: ALP–Nucleon and ALP–DM Couplings

In canonical constructions, the relevant interactions are described by an effective Lagrangian with derivative couplings: $$\mathcal{L}_{aNN} = g_{aNN}\,\bar N\,\gamma^\mu\gamma^5 N\,\partial_\mu a$$ where $g_{aNN}$ is the (isoscalar or isovector) ALP–nucleon coupling, $N$ denotes the nucleon field, and $a$ is the ALP (Dutta et al., 31 Jan 2025, Jiang et al., 2021).

For DM composed of a Dirac fermion $\chi$, the coupling to the ALP is similarly of the form: $$\mathcal{L}_{a\chi\chi} = g_\chi\,\bar\chi\,\gamma^5\chi\,a$$ with $g_\chi$ parameterizing the DM–ALP interaction. The ALP–quark couplings propagate to the nucleon scale as $g_N = \sum_q g_q\,\Delta_q^N$, where $\Delta_q^N$ encodes the nucleon’s quark spin fractions (Coffey et al., 2022).

The tree-level amplitude for $\chi+N\to\chi+N$ via $a$-exchange is then governed by the effective operator $$O_6\sim(\vec S_\chi\cdot \vec q)(\vec S_N\cdot \vec q)/(m_\chi m_N)$$, resulting from the leading expansion of the $\gamma^5$ bilinears in the non-relativistic regime (Beenakker et al., 24 Nov 2025, Coffey et al., 2022).

2. Scattering Amplitudes, Cross Sections, and Mediator Mass Regimes

The tree-level differential cross section for ALP-mediated DM–nucleon scattering is: $$\frac{d\sigma_\text{SD}}{dE_R} \propto \frac{|g_\chi g_N|^2\,q^4}{(q^2+m_a^2)^2}$$ where $q^2=2 m_N E_R$ and $m_a$ is the ALP mass (Beenakker et al., 24 Nov 2025, Coffey et al., 2022).

Two regimes are distinguished:

• Heavy-mediator limit ($m_a \gg q$): The cross section scales as $q^4/m_a^4$, leading to severe velocity and momentum suppression, particularly relevant for terrestrial direct detection where $v_\text{halo}\sim 10^{-3}c$.
• Light-mediator or "massless" regime ($m_a \ll q$): The denominator scales as $q^4$, but the $q^4$ in both numerator and denominator cancels, resulting in a cross section $\propto 1/q^2$—thus enhancing the scattering rate relative to the naive $q^4$ scaling (Beenakker et al., 24 Nov 2025). This regime applies when the mediator mass is lower than the typical momentum transfer in the experiment.

At one-loop level, ALP exchange can induce SI operators, especially when the ALP couples flavor-off-diagonally (e.g., to the top quark). The resulting SI cross section features a significant $m_t/m_u$ enhancement (chirality-flip), leading to rates that can be directly probed by current and near-future xenon-based experiments (Beenakker et al., 24 Nov 2025).

3. Experimental Strategies and Sensitivity: Tabletop and Large-scale Detectors

Experimental efforts span diverse technologies and mass ranges. Optically levitated nanospheres present a table-top approach with unique sensitivity to low-momentum transfer recoils:

• Levitated SiO₂ nanospheres: Spheres of 200 nm diameter operate in the incoherent regime for $q \gtrsim 0.06$ keV, probing $g_{\text{aN}}, g_{p\chi_s}$ down to $10^{-5}$–$10^{-7}$ at $m_a\lesssim10$ keV. Small (15 nm) spheres—coherent for $q<0.8$ keV—offer $N_p^2$ rate enhancement, with a single sphere reaching $g_{p\chi_s}\sim10^{-6}$ at $m_\chi<100$ eV and $100\times100$ arrays probing down to $g_{p\chi_s}\sim10^{-8}$ (Dutta et al., 31 Jan 2025).

Configuration	Array Size	Run Time	$g_{aN}^{\min}$ $(m_a \lesssim 10$ keV$)$
Present	$4 \times 4$	10 yr	$3 \times 10^{-5}$
Upgrade I	$10 \times 10$	10 yr	$2 \times 10^{-5}$
Upgrade II	$100 \times 100$	1 yr	$1 \times 10^{-5}$
Ultimate	$1000\times1000$	1 yr	$5 \times 10^{-6}$

Similar scaling holds for $g_{p\chi_s}$, with the Standard Quantum Limit (SQL) for the impulse measurement determining the minimum accessible $q_\text{th}$. The fully-coherent regime provides $N_p^2$ event rate enhancement (Dutta et al., 31 Jan 2025).

Quantum spin-based amplifiers, such as those implemented with hyperpolarized $^{129}$Xe and $^{87}$Rb, have probed ALP masses in the $\sim$8 feV–744 feV range, setting $g_{aNN}$ limits at $2.9\times10^{-9}~\textrm{GeV}^{-1}$ (at $67.5$ feV, $95\%$ CL), more than $10^5$ times stronger than previous laboratory constraints and approaching astrophysical bounds (Jiang et al., 2021).

Large-scale liquid xenon detectors can probe loop-induced SI cross sections in the $10^{-46}$–$10^{-48}$ cm$^2$ regime, with flavor-changing ALP couplings offering exceptional reach due to $m_t$ enhancements (Beenakker et al., 24 Nov 2025).

4. Distinctive Features and Scaling Laws

The momentum and mass regime of the ALP crucially determines the scaling laws:

• Tree-level SD scattering: For generic (flavor-diagonal) pseudoscalar exchange, cross sections are $v^4$-suppressed in terrestrial direct detection, severely restricting experimental reach (Coffey et al., 2022, Beenakker et al., 24 Nov 2025).
• Light-mediator regime: The $q^2$ denominator in the cross section is reduced, partially alleviating momentum suppression and leading to a non-trivial scaling with $1/q^2$ for $m_a\ll q$, allowing certain experimental configurations (notably tabletop optomechanical sensors) to access otherwise hidden parameter space (Dutta et al., 31 Jan 2025, Beenakker et al., 24 Nov 2025).
• Coherence effects: In nanoparticle or nuclei, full target coherence ($q<2\pi/r_{sp}$) yields an $N_p^2$ event rate enhancement, while incoherent (nuclear) regimes revert to scaling with the number of nuclei (Dutta et al., 31 Jan 2025).
• Loop-induced SI enhancement: In cases with ALP flavor-changing couplings, e.g., off-diagonal top-quark interactions, the one-loop SI cross section receives chirality-flip enhancement, potentially elevating rates to the sensitivity levels of ongoing XENONnT and PandaX-4T searches. Specifically, for $f_a=1$ TeV and $\xi \sim 10^{-3}$, $\sigma_\text{SI}$ reaches $10^{-46}$ cm$^2$ (Beenakker et al., 24 Nov 2025).

5. Astrophysical Probes: Neutron Star Heating

Neutron star (NS) observations constitute a complementary avenue, uniquely insensitive to the velocity suppression that limits terrestrial searches. Infalling DM is accelerated by the deep NS potential ($v_\text{esc}\sim 0.6c$), so that the $v^4$ suppression in $\sigma_\text{SD}\propto v^4/m_a^4$ is lifted (Coffey et al., 2022).

Quantitatively, the capture rate $C$ and resultant heating luminosity $L_\text{NS}$ scale as: $$C \simeq \frac{\rho_\chi}{m_\chi} \langle v \rangle \pi R_\text{NS}^2 \frac{v_\text{esc}^2}{\langle v\rangle^2} \frac{\sigma_\text{SD}}{\sigma_\text{cap}}$$

$L_\text{NS} = C m_\chi (v_\text{esc}^2/2)$

For $g_N=10^{-3}, g_\chi=1, m_\chi=1$ GeV, and $m_a=100$ MeV, $\sigma_\text{SD}(v_\text{esc})\sim10^{-45}$ cm$^2$, resulting in $L_\text{NS}\sim10^{25}$ GeV/s, corresponding to an observable NS temperature $T_\infty\sim 10^3$ K. NS heating outperforms direct detection and beam-dump/meson-decay limits in large yet unconstrained regions, especially for $m_\chi=0.01$–10 GeV and $m_a=10$–1000 MeV (Coffey et al., 2022).

6. Current Bounds and Projected Sensitivities

ALP-mediated DM–nucleon scattering is constrained across multiple channels:

• Laboratory (quantum sensors, NMR, optically trapped spheres): For $m_a=67.5$ feV, $g_{aNN}<2.9\times10^{-9}~\textrm{GeV}^{-1}$ at $95\%$ CL, with corresponding $\sigma_\text{tot}\sim10^{-77}$ cm$^2$ (Jiang et al., 2021).
• Direct detection (XENONnT, PandaX-4T): With flavor-changing (e.g., top) ALP couplings, SI cross sections up to $10^{-46}$ cm$^2$ are accessible, constraining $\xi \lesssim 2\times10^{-3}$ for $m_\chi=100$ GeV and $f_a=1$ TeV (Beenakker et al., 24 Nov 2025).
• NS heating: Permits sensitivity to $g_\chi g_N\sim10^{-8}$–$10^{-4}$ for $m_\chi\sim10$ MeV–10 GeV and $m_a\sim10$–1000 MeV—parameter space inaccessible to current terrestrial searches (Coffey et al., 2022).
• Tabletop optomechanics: Sensitivity to $g_{aN},~g_{p\chi_s},~g_{p\chi_V}$ at $10^{-5}$–$10^{-8}$ for sub-keV ALP or vector-mediation masses, benefitting from coherence enhancement (Dutta et al., 31 Jan 2025).

7. Outlook and Unique Capabilities

ALP-mediated DM–nucleon scattering, while traditionally considered unobservable due to suppression by low velocities and momentum transfer, possesses experimentally and phenomenologically viable regions through:

• Light-mediator enhancement ($m_a\ll q$)
• Loop-induced SI processes with chirality-flip amplification for flavor-changing couplings
• Full target coherence in precision optomechanics
• Velocity-boosted capture in compact astrophysical objects (NSs)

Optical levitation platforms uniquely cover the $10$ eV–$100$ keV momentum transfer window with negligible background at the Standard Quantum Limit, and are best suited for small $m_a$ and low-mass DM (Dutta et al., 31 Jan 2025).

Astrophysical probes and next-generation large-mass DD experiments will continue to close the remaining parameter space, with coherent improvements in experimental sensitivity and theoretical modeling enabling stringent exclusion or potential discovery across a broad ALP mass-coupling landscape.

References:

(Dutta et al., 31 Jan 2025, Beenakker et al., 24 Nov 2025, Coffey et al., 2022, Jiang et al., 2021)