Natural Ultralight Dark Matter: The Quadratic Twin

TL;DR

This work tackles the naturalness problem of ultralight dark matter (ULDM) with substantial quadratic couplings to the Standard Model by introducing a twin-Higgs-inspired mechanism. The ULDM is realized as a pseudo-Nambu-Goldstone boson whose mass corrections are protected by a mirror-$\mathbb{Z}_2$ symmetry between the SM and a twin SM, causing linear sensitivity to cancel and leaving leading mass shifts quadratic in the couplings. Explicit $U(1)$ and $U(2)$ constructions demonstrate how the mass corrections are highly suppressed, opening roughly $25$ orders of magnitude in the coupling-mass parameter space for $m_\phi$ in the range $\sim(10^{-20}-10^{-15})$ eV, within reach of clocks, interferometers, and future nuclear-clock probes. The framework predicts density-dependent effects with potential screening and gradient enhancements on Earth, providing concrete phenomenology for current and upcoming tabletop experiments, and it points to a rich cosmological history in the twin sector that warrants further study. Overall, the paper presents a natural, testable path to ULDM that is compatible with experimental sensitivities and offers new directions for early-Universe dynamics.

Abstract

Scalar ultralight dark matter (ULDM) is uniquely accessible to tabletop experiments such as clocks and interferometers, and its search has been the focus of a vast experimental effort. However, the scalar ULDM mass is not protected from radiative corrections, and the entirety of the parameter space within reach of experiments suffers from a severe naturalness problem. In this paper, we propose a new twin mechanism that protects the mass of the scalar ULDM. Our scalar ULDM is a pseudo-Nambu-Goldstone boson with quadratic couplings to the Standard Model (SM) and to a twin copy of the SM, with a mirror $\mathbb{Z}_2$ symmetry exchanging each SM particle with its twin. Due to the mirror symmetry, the leading-order mass correction is quadratic in the (tiny) coupling while the linear order is canceled. This opens up vast regions of parameter space for natural quadratically coupled ultralight dark matter, within the sensitivity of existing and future experiments.

Figures (5)

• Figure 1: The parameter space of quadratically coupled ULDM: coupling to electrons $|d_{m_e}^{(2)}|$ vs. mass $m_\phi$. The red lines are the naturalness bounds from our quadratic twin ULDM for a cutoff $\Lambda=10\,\text{TeV}$ and various values of $f$. For comparison, we plot the Goldstone naturalness bound (gray) for the same cutoff and various values of $f$ without the twin mechanism, see App. \ref{['app:naturalness']}. DM amplitude-sensitive bounds, subject to screening, are shown in solid lines, while dashed lines of the same color neglect screening Hees:2018fpgBanerjee:2025dlo, see Sec. \ref{['sec:Pheno']}. Among them are atomic clock bounds H/SiKennedy:2020bac, quartzCampbell:2020fvq, molecularOswald:2021vtcOswald:2025bih, and interferometers Geo600Vermeulen:2021epa and AurigaBranca:2016rez. Additionally, we show gradient-sensitive constraints from MICROSCOPEBanerjee:2025dloGue:2025nxq for $d_{m_e}^{(2)}>0$, and the projected sensitivity of the ${}^{229}$$\rm Th$ nuclear clock (dot-dashed).
• Figure 2: (Left) Dark matter profile and gradient at Earth's surface for increasing ($(qR)^2<0$) and decreasing ($(qR)^2>0$) scalar mass as function of $qR$. (Right) Same but as a function of $d_{m_e}^{(2)}$ for both signs.
• Figure 3: Same as Fig. \ref{['fig:parspace']} but including regions where for both signs ($d_{m_e}^{(2)}>0$ in the left panel and $d_{m_e}^{(2)}<0$ in the right panel) the DM field amplitude is screened (above blue line), DM field gradients are enhanced (above green line) and where the quadratic twin ULDM is sourced within Earth (region above the dark purple line in the right panel for $d_{m_e}^{(2)}<0$). In the right panel the light blue line is the bound from MICROSCOPE (Banerjee:2025dloGue:2025nxq), which is not valid within the dark purple region in which the field is sourced. In this region the effective mass is larger than the vacuum mass and positive since one expands around the finite density minimum.
• Figure 4: Eötvös parameter as a function of negative (left) and positive (right) $d_{m_e}^{(2)}$. The red region is excluded by MICROSCOPE.
• Figure 5: Scalar potential at zero electron density $n_e=0$ (blue), sub-critical density $n_e<n_e^c$ (orange) and super-critical density $n_e>n_e^c$ (green). As explained in the text, the finite density contribution to the potential destabilizes the minimum at $\phi_0=0$ for super-critical densities and new minima show up at $\phi=\pm\pi f/2$.