Critical Reassessment of Gallium and Reactor Neutrino Anomalies in 3+2 Sterile Neutrino Models: Incorporating Recent Exclusions, Bayesian Analyses, and Alternative Hypotheses

We critically reassess a 3+2 sterile-neutrino framework proposed to explain two long-standing short-baseline anomalies: the gallium anomaly, a 20–24% deficit in 71Ge production reported by BEST and earlier source experiments [1, 2], and the reactor antineutrino anomaly (RAA), whose statistical significance has fallen below 1.5σ following refined flux calculations [3, 4]. The framework combines an eV-scale sterile state invoked for the anomalies with a keV-scale state motivated as a dark-matter candidate. We show, through a combination of analytic derivations, illustrative numerical models, and a survey of recent exclusion limits from MicroBooNE, KATRIN, and the Short-Baseline Neutrino program (SBN) at ≳ 95% confidence level [8, 9, 10], that the eV-scale sterile interpretation of the gallium anomaly is now disfavored relative to non-oscillation alternatives such as revised 51Cr/37Ar electron-capture cross-sections [2]. A simplified Bayesian comparison using representative BEST-like inputs yields posterior odds of order 1:15 against the sterile hypothesis relative to a cross-section-revision alternative. We present illustrative, explicitly labeled toy calculations — not a reproduction of the raw BEST dataset, which is not available to us — illustrating the oscillatory sensitivity of the predicted deficit to (∆m2₄₁, sin²2θ14), including previously unremarked node structure that produces near-total cancellation of the deficit at ∆m2₄₁ ≈ 2.0 eV2 for the reference baseline used here. For the keV sector, we summarize the Quantum Kinetic Equation (QKE) formalism for Shi–Fuller production [34, 35] and quote the literature-typical relic abundance scale Ωsh2 ∼ 0.1, while explicitly noting that a first-principles multi-momentum QKE solve is beyond the scope of the simplified scripts provided here. We derive the matter-potential and Mikheyev–Smirnov–Wolfenstein (MSW) resonance conditions from first principles, show that terrestrial matter effects are negligible for source experiments (A ∼ 10−15 eV2 ≪ ∆m2/2E), and discuss self-interaction-driven suppression of ∆Neff, supernova energy-loss bounds, and a toy polytropic Tolman–Oppenheimer–Volkoff (TOV) model illustrating (at the order-of-magnitude level only) how an admixed dark component can shift the maximum neutron-star mass. We conclude that the eV-sterile explanation of the gallium anomaly is in tension with current exclusions and is not the most parsimonious explanation of the data; we outline falsifiable predictions for DUNE and XRISM and a staged experimental roadmap, and we advocate continued pursuit of non-sterile systematics (cross-section, wavefunction, and detector-response corrections) alongside sterile-neutrino searches.