Unveiling time-varying signals of ultralight bosonic dark matter at collider and beam dump experiments

Ultralight bosons are compelling dark matter (DM) candidates due to their macroscopic wave-like behavior, potentially altering small-scale structure. Prior proposals suggest that ultralight DM can induce time variations in fundamental constants and Standard Model parameters, detectable in atomic, molecular, optical, geophysical (Oklo), and astrophysical systems. The authors focus instead on collider and beam-dump probes by considering a dark-sector mediator—specifically a kinetically mixed dark photon—whose mass oscillates in time if coupled to an ultralight scalar DM charged under U(1)'. The central research question is how a time-varying mediator mass modifies collider/beam-dump signatures and limits, and whether exploiting event time-stamps can recover sensitivity lost by traditional, time-blind resonance searches. The study proposes that mass oscillations lead to characteristic multi-peak (typically double-peak) invariant-mass spectra and reduced per-bin exposure, altering constraints. It introduces analysis strategies that use time information to enhance sensitivity and explores implications for the dark photon explanation of the muon (g−2) anomaly.

The paper situates its work within several strands: (i) Ultralight DM phenomenology, including wave-like effects and induced variations of constants (e.g., atomic clocks, interferometry, astrophysical probes). (ii) Kinetic-mixing dark photon models and existing collider/beam-dump searches that set stringent bounds on mixing ε and mass, excluding traditional dark-photon explanations of (g−2)μ. (iii) Prior ideas on time-varying SM couplings/masses from ultralight fields and transient topological defects. (iv) Experimental programs at BaBar, LHCb, A1/Mainz, NA48/2 and others for visible dark photon searches, as well as invisible-decay searches (BaBar, BESIII, NA64, NA62). The study builds on these by introducing mediator mass oscillations driven by ultralight scalar DM and by leveraging time-stamped collider data to search for time-varying signals, a direction less explored than AMO or astrophysical probes.

Model setup: A kinetically mixed dark photon A' couples to the electromagnetic current with strength parameterized by ε. A complex ultralight scalar DM φ with small U(1)' charge Q induces a time-dependent A' mass via scalar QED interactions. The dark photon mass oscillates as m^2(t)=m0^2(1+κ cos^2(m_φ t)), where κ encodes the oscillation amplitude determined by g'Q, local DM density, and field parameters. The oscillation period is τ=π/m_φ. The mass ratio y(t)=m(t)/m0 spans [y_min=1, y_max=√(1+κ)]. Signal template and time exposure: For resonant searches, the event invariant mass follows the time-dependent m(t). The exposure in a mass bin [m_i,m_{i+1}] scales with |dt/dm|, producing a normalized probability density function f(y)=2y/[π(y^2−y_min^2)(y_max^2−y^2)], which diverges at y_min and y_max, yielding a characteristic double-peak spectrum after detector smearing. If data-taking duration t_expr ≫ τ, the invariant-mass spectrum is described by f(y) independent of initial phase and explicit time. Recasting visible A' searches (Double-Peak Method, DPM): The authors recast BaBar, LHCb, A1/Mainz, NA48/2 (and rescale for APEX, HADES, KLOE, PHENIX, WASA) dilepton resonance searches by fitting invariant-mass spectra with a background polynomial and the time-varying signal template f_s(m) (Gaussian-smeared f(y)). For each nominal mass m_A, two fits are performed corresponding to the left and right peaks at m0 and √(1+κ) m0. The stronger of the two derived ε^2 limits is taken. Likelihoods are compared using LLR = −2 ln(L/L0), with LLR=3.84 for 95% CL. Detector resolutions, fit windows, and mass ranges follow experimental configurations (Table 1). The method also applies to displaced A' at LHCb and beam-dump experiments via time-averaged event yields. Beam dump recast: For E774, E141, NA64, the A' production via eZ→eZA' and decay in flight is modeled with an empirical yield N_e(ε,m) calibrated to reproduce official limits, then generalized to the time-varying case by averaging over the oscillation: N(ε,m0,κ)=∫ N_e(ε,m(t)) dt = ∫_{1}^{1+κ} N_e(ε,m(y)) dm. Time-Dependent Method (TDM): To exploit time stamps, events are binned in 2D time–mass grids. For each hypothesized m0, κ, m_φ (hence τ), only bins intersecting the oscillation trajectory m_A'(t) are used ("red bins"). This preserves the expected signal yield while suppressing background, effectively improving sensitivity. Without full time information in published spectra, a conservative sensitivity estimate assumes background is uniform in time across each mass bin, and scales with the selected time exposure. The method is applied to CMS Open Data (2012 dimuon AOD): events are selected (pT>15 GeV, |η|<2.4), with detector mass resolution σ(m_μμ)=0.026 GeV + 0.013 m_μμ. For DPM, 1D invariant-mass fits are performed; for TDM, 2D bins use Δm=σ and Δt=τ/8, summing LLR over bins. Non-uniform instantaneous luminosity L(t) is accounted for by integrating signal expectations over the two solutions t^±(m) per period; when τ is shorter than the L(t) variation timescale (few hours), the resulting f(y) matches the ideal spectrum. Invisible A' case: For e^+e^−→γA' with invisible A', the photon energy E_γ=(s−m_A'^2)/(2√s) is broadened by m_A'(t) between Emin=(s−(1+κ)m0^2)/(2√s) and Emax=(s−m0^2)/(2√s), and the analysis proceeds analogously to visible decays by substituting photon-energy bins for invariant-mass bins. For NA64 (missing-energy), efficiencies are largely m_A'-independent at high E_miss; time variation mainly rescales production rate. For NA62 (π^0→γA'), the DPM on reconstructed m_A' applies. Validation and recasts: The traditional (κ=0) BaBar recast reproduces official limits within a factor ≲1.9 (1σ) across e^+e^− and μ^+μ^− channels. Beam-dump recasts reproduce official contours after calibrating empirical parameters. CMS Open Data analysis demonstrates feasibility of both DPM and TDM on real collider data with non-uniform L(t).

- Time-varying mediator mass produces a robust double-peak invariant-mass spectrum with peaks at the minimum and maximum masses (m0 and √(1+κ)m0). This spreads signal across bins and reduces per-bin time exposure relative to a fixed-mass resonance. - Recasts of visible A' searches (BaBar, LHCb, A1/Mainz, NA48/2, and others via rescaling) show that for m0 ≳ 10^−2 GeV and κ≈O(10), existing bounds on ε^2 are weakened by roughly 1 order (up to 1–2 orders) compared to traditional single-peak assumptions (κ=0). The envelope of traditional bounds is shown as a gray dashed baseline in figures. - The previously excluded dark-photon explanation of the muon (g−2) anomaly can re-open for masses around O(10 MeV) when accounting for mass oscillations, as illustrated where the (g−2)_μ band intersects weakened BaBar and NA48/2 limits. - Beam-dump limits (E774, E141, NA64) in the time-varying scenario are obtained via time-averaged yields; they are generally weakened compared to the static-mass case, consistent with DPM intuition. - Incorporating event time-stamps via the Time-Dependent Method (TDM) suppresses background while preserving signal, improving sensitivity by about 1 order of magnitude relative to time-blind DPM in the abstract, and by 1–2 orders in detailed projections (e.g., for NA48/2, BaBar, LHCb) assuming no excess. - Application to CMS Open Data (2012 dimuons) validates both DPM and TDM on real data with non-uniform instantaneous luminosity. For oscillation periods shorter than the L(t) variation timescale (few hours), the observed signal spectrum matches the ideal f(y); TDM limits exceed DPM by 1–2 orders in the demonstrated benchmarks (κ=15, 24, m_φ≈10^−19 eV). - For invisible A' searches (BaBar, BESIII, NA64, NA62), the time-varying scenario typically weakens limits due to spectral broadening or rate rescaling; nonetheless, the parameter space for a dark-photon (g−2)_μ solution with dominant invisible decays is excluded, implying visible decays must dominate in that case.

The study shows that if a dark mediator’s mass oscillates due to coupling with ultralight bosonic DM, collider and beam-dump resonance searches must be reinterpreted. The characteristic double-peak mass spectrum and reduced per-bin exposure explain why traditional, time-blind searches overconstrain ε^2. By explicitly modeling time dependence—either in a 1D DPM using the derived f(y) or in a 2D TDM using event time-stamps—one obtains both accurate reinterpretations and enhanced discovery potential. TDM specifically targets the oscillation trajectory, greatly suppressing background and recovering or exceeding the sensitivity lost to spectral spreading in DPM. This framework restores viability of portions of the dark-photon (g−2)_μ parameter space near tens of MeV that were previously excluded under fixed-mass assumptions, while providing a concrete path to test them with existing data. The methodology generalizes beyond visible decays to invisible channels and can be extended to other time-varying phenomena (e.g., couplings, widths). Real-data validation with CMS Open Data demonstrates practicality, including handling non-uniform instantaneous luminosity; when τ is shorter than luminosity-variation timescales, the idealized f(y) description holds, justifying use of DPM where time information is unavailable and motivating TDM reanalyses where it is.

The authors propose and realize a search strategy for ultralight bosonic dark matter signals at colliders and beam dumps via time-varying mediator masses. They derive a universal double-peak invariant-mass template for oscillating masses and show that traditional constraints weaken by about 1–2 orders compared to fixed-mass assumptions. They introduce a time-dependent analysis using event time-stamps (TDM) that suppresses background and restores sensitivity by roughly 1–2 orders over DPM, validated on CMS Open Data. In a concrete kinetic-mixing dark-photon model, parts of the (g−2)_μ-favored region around O(10 MeV) can re-emerge and are testable with TDM-based reanalyses. The approach also applies to invisible decays and can be generalized to other time-varying properties (e.g., couplings, rates). Future work should include collaboration-led reanalyses with full time information across experiments, optimization of binning/resolution trade-offs to manage statistical limitations, and exploration of additional models and experimental channels sensitive to time-varying signatures.

- Sensitivity gains from TDM depend on availability and precision of event time-stamps; many public datasets (beyond CMS) lack such information. Where only time-blind spectra exist, only DPM (less sensitive) can be used. - The DPM and TDM assume data-taking duration much longer than the oscillation period; if τ is comparable to or longer than run segments, sensitivity and spectral modeling can degrade and depend on initial phase and luminosity schedule. - Non-uniform instantaneous luminosity L(t) complicates time-domain analyses; while periods shorter than a few hours are robust, longer τ require careful integration over L(t) and may reduce sensitivity. - Very fine mass/time binning can lead to low counts per bin and large statistical uncertainties; optimal binning is experiment-dependent. - Model-specific assumptions (e.g., small g′Q to avoid thermalization, misalignment production, negligible early-Universe constraints due to logarithmic couplings) bound the parameter space; black hole superradiance excludes some ultralight mass ranges. - For invisible A' scenarios, while DPM applies, limits can still exclude (g−2)_μ regions, implying model dependence (e.g., visible decays must dominate) that may not generalize to all dark sectors.