Lorentz violating backgrounds from quadratic, shift-symmetric, ultralight dark matter

TL;DR

This work develops an EFT for a shift-symmetric, quadratically coupled real scalar ULDM field interacting with the QED sector, where leading CP-even interactions emerge at dimension-8. It analyzes the one-loop renormalization-group flow, showing a robust two-sector (\(j=0, j=2\)) structure with limited operator mixing, and provides a concrete UV completion via heavy spin-2 exchange that yields explicit Wilson coefficients. The ULDM background induces both oscillations of fundamental constants and Lorentz-violating effects, allowing terrestrial clock and LV experiments to bound the Wilson coefficients and translate these into keV-scale UV cutoffs, while astrophysical and collider bounds can reach higher scales though with model dependence. The framework unifies two distinct experimental probes under a consistent EFT, highlighting that current bounds probe keV to GeV scales and that future precision clocks or solar halo scenarios could substantially improve sensitivity. Key contributions include the operator basis at dimension-8, the RG structure, positivity constraints, and the linkage of oscillation and LV observables within a single, UV-mensible description.

Abstract

We consider an effective theory for a shift-symmetric, quadratically-coupled, ultralight spin-0 field. The leading CP-conserving interactions with Standard Model fields in the effective theory arise at dimension 8. We discuss the renormalization group evolution and positivity bounds on these operators, as well as their possible UV origins. Assuming that the spin-0 field is associated with an ultralight dark matter candidate, we discuss the effects of the dimension-8 operators on experiments searching for the oscillation of fundamental constants and Lorentz violation. We find that the direct bounds on these two effects are of similar strength but rather weak, corresponding to a UV cutoff scale of keV order, as they are mediated by dimension-8 operators.

Figures (6)

• Figure 1: At energies much lower than the mass of the KK graviton, tree-level exchange is approximated by a local interaction and represented as an effective operator.
• Figure 2: The bounds on Wilson coefficients from experiments searching for oscillations of fundamental constants for different dark matter mass $m_\phi$. Upper: Exclusion regions of $\mathcal{C}_3$ (left) and the corresponding cut-off $\Lambda\sim \sqrt{4\pi}\mathcal{C}_3^{-1/4}$ (right). Orange regions are obtained from Filzinger:2023zrs (comparison of Yb$^+$ E3/E2 as well as Yb$^+$/Sr) and blue regions from Sherrill:2023zah (comparison of Yb$^+$/Sr). Lower: Exclusion regions of $\mathcal{C}_1$ (left) and the corresponding cut-off $\Lambda\sim \sqrt{4\pi} \mathcal{C}_1^{-1/4}$ (right), obtained by comparing the frequencies of Yb/Cs Kobayashi:2022vsf (orange) or H/Si Kennedy2020 (blue). Also shown with gray shaded regions are bounds from the MICROSCOPE experiment, obtained from direct translation of the bounds given in Banerjee:2022sqgHees:2018fpg.
• Figure 3: Bounds on the cut-off scale $\Lambda$ corresponding to $\mathcal{C}_2$. In the regime $m_\phi \lesssim 10^{-21} {\rm eV}$, the DM behaves as constant LV background and the bound can be obtained by direct interpretation of the bound from the experiment comparing two $^{171}$Yb$^+$ clocks Sanner2019. In the regime $10^{-21} {\rm eV} \lesssim m_\phi \lesssim 10^{-15} {\rm eV}$, the oscillating nature of $\phi$ field cannot be ignored. In the regime $m_\phi \gtrsim 10^{-15} {\rm eV}$, the experiment is unable to resolve the fast oscillation of DM, but the signal will fluctuate at a time scale of the order of the DM coherence time. For the last two regimes, as indicated by the shaded region, a dedicated analysis of the experimental data needs to be done in the future to obtain the (precise) bound. With the blue region, we show that experiments comparing the frequencies of an H maser and silicon cavity Kennedy2020 can be used to provide complementary bounds.
• Figure 4: New vertices
• Figure 5: Electron-DM scattering diagrams