Ultralight bosons, with their wave-like properties, represent a compelling dark matter (DM) candidate. Their wave nature could manifest as variations in DM activity at small scales, prompting research into their potential to induce time-varying fundamental constants. Detection methods currently explored include atomic, molecular, and optical physics, the Oklo phenomenon, and astrophysical observations. Ultralight bosonic DM might also cause oscillations in Standard Model (SM) gauge couplings and fermion masses, with periods linked to the DM mass, or temporal changes due to topological defects. The kinetic mixing dark photon model serves as an illustrative example of a mediator between the SM and dark sectors. Experiments have placed stringent limits on the mixing strength (ε) and mass (m) of the dark photon, ruling out solutions explaining the muon (g-2) excess. However, if an ultralight scalar DM φ is charged under a dark U(1)', periodic oscillations in the dark photon mass become possible, potentially relaxing collider and beam-dump constraints. This paper focuses on the implications of this time oscillation of the mediator mass, examining its effect on experimental constraints in high-energy collider and beam dump experiments rather than its direct coupling with the SM sector. This approach leads to a distinctive multi-peak (typically double-peak) spectrum in the invariant mass, differing from traditional single-peak resonance signatures.

Existing literature extensively covers ultralight dark matter, focusing on its wave-like behavior and implications for small-scale structure. Proposals suggest ultralight DM could lead to time-varying fundamental constants, detectable through various methods (atomic, molecular, optical physics; the Oklo phenomenon; astrophysical experiments). Oscillations in SM gauge couplings and fermion masses, linked to DM mass, have also been studied. The impact of topological defects on temporal changes has been modeled. The kinetic mixing dark photon model, a common framework for interaction between the SM and dark sector, is subject to significant experimental constraints, including the recently highly excluded parameter space that explains the muon (g-2) anomaly. The study of time-varying dark photon mass has the potential to significantly alter these established constraints.

The core methodology involves analyzing the implications of a time-oscillating dark photon mass on high-energy collider and beam dump experiments. The authors assume a time-dependent mass, *m*(t), for the resonant particle, modeled as a periodic oscillation with period τ. The usual resonance search strategy suffers from reduced time exposure in each mass bin due to the varying mass. The paper introduces a new approach, the double-peak method (DPM), which accounts for the spread in the signal template caused by the time-varying mass. Instead of focusing on a narrow resonance, DPM uses the time exposure (Δt) in each mass bin, leading to a double-peak spectral feature, reflecting the minimum and maximum of the resonant mass. The event number in each mass bin is then recalculated using the time exposure. A kinetic mixing dark photon A' model with U(1) interaction is considered, where the mass is influenced by a complex scalar DM φ (charged under the dark U(1)'). The DM's relic abundance is assumed to arise from a misalignment mechanism, and its behavior is described by a classical wave function. The scalar QED interaction leads to a time-oscillating A' mass, characterized by parameters *m*₀ (constant mass), κ (oscillation amplitude), and *m*φ (DM mass). The oscillation period (τ = π/*m*φ) is crucial. The probability density function (PDF) of the invariant mass exhibits a double-peak feature at the minimum and maximum of the resonant mass, diverging without detector resolution. This double-peak feature is the key distinction between the analysis in this paper and the traditional analysis. The effect of detector resolution on the shape of the double-peak is considered. The probability distribution is used to recast the constraints derived from existing dilepton experiments (BaBar, LHCb, A, NA48/2) and beam dump experiments (E774, E141, NA64). To improve sensitivity, the paper introduces a time-dependent method (TDM). This method utilizes event time stamps, unlike the time-blind approach. In the TDM, data are binned in both time and invariant mass, focusing on the regions where the signal is expected based on the time-varying mass. This significantly increases sensitivity. This method is validated using CMS Open Data of the 2012 dimuon events, demonstrating its effectiveness even with non-uniform instant luminosity. The applicability of TDM to experiments with invisible dark photon decays is also discussed. Furthermore, the authors address other potential constraints, including thermalization, freeze-in, black hole super-radiance, and loop-level corrections to SM fermion masses.

The key findings revolve around the novel double-peak method (DPM) and the time-dependent method (TDM) for detecting ultralight bosonic dark matter. The DPM addresses the time-varying mass of the dark photon by considering the time exposure in each mass bin, resulting in a distinctive double-peak spectrum. This significantly relaxes existing constraints on the parameter space, making previously excluded solutions, such as those related to the muon (g-2) anomaly, potentially viable. The TDM further enhances sensitivity by utilizing event time stamps, improving the reach by approximately one to two orders of magnitude compared to the time-blind approach and DPM. This is demonstrated using CMS Open Data. The time-dependent approach improves sensitivity because the signal events only happen at certain times and masses. This is verified using data from the CMS Open Data. The TDM approach effectively suppresses the background events while leaving the signal events unchanged. The analysis method is also extended to cases with invisible dark photon decays, demonstrating its adaptability. The methodology’s robustness is checked against experimental results, showing good agreement with official findings. The results indicate that the parameter space consistent with the muon (g-2) anomaly can become viable in the context of a time-varying dark photon mass.

This work significantly advances the search for ultralight bosonic dark matter by introducing novel analytical techniques. The double-peak spectral feature arising from the time-varying mass of the dark photon is a crucial observation, allowing for a more comprehensive exploration of the parameter space. The method effectively mitigates the limitations of traditional resonance searches by incorporating the time dependence of the signal. The utilization of event time stamps in the TDM leads to substantial improvements in sensitivity, potentially revealing previously hidden signals. The successful application of TDM using real CMS Open Data confirms the practical viability and robustness of the proposed methods. The finding that the parameter space for solutions to muon (g-2) anomaly could be explored again represents a major contribution to particle physics. The study extends to scenarios with invisible dark photon decays, widening the scope of application. The impact extends to various experimental setups, demonstrating a significant advancement in dark matter detection strategies.

This paper presents a novel approach to detect ultralight bosonic dark matter by focusing on the time-varying nature of the dark photon mass. The proposed double-peak method (DPM) and time-dependent method (TDM) offer significant improvements in sensitivity compared to traditional approaches. The successful application of TDM to CMS Open Data underscores the practicality of this innovative approach. Future research should focus on applying these methods to other collider and beam dump experiments to further explore the parameter space and potentially reveal additional evidence for ultralight dark matter. The methodology introduced here also offers a new perspective for exploring time-varying signals in other areas of particle physics.

The study relies on a specific model for the time-varying dark photon mass. The validity of the results hinges on the accuracy of this model. While the methods are applied to CMS Open Data, the non-uniformity of the instant luminosity might introduce some systematic uncertainties. The analysis is limited to specific experiments, and further work is required to expand the applicability of this approach to a broader range of experimental configurations. Future work should address the impact of potential systematic errors introduced by the non-uniform instant luminosity and refine the TDM to further improve its precision and accuracy.