Does an eV-scale sterile neutrino exist?

In plain words

A fourth neutrino that feels no force except gravity, with mass near 1 eV, could explain some anomalies. It would show up as extra appearance and disappearance at short distances.

Precise statement

Determine whether a fourth mass state with $\Delta m^2_{41} \sim 0.1 \text{ to } 10\,\mathrm{eV}^2$ and mixings |U_e4|, |U_mu4| large enough to produce sin^2(2 theta_mue) $\sim 10^{-3}$ exists. An answer is a $5\,\sigma$ oscillation signal or exclusion of the region preferred by LSND and gallium in both appearance and disappearance.

What would settle it

Combined SBN-program oscillation fits with near and far detectors, plus reactor (PROSPECT, STEREO) and atmospheric (IceCube) disappearance limits.

Status in the literature

Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.

Appearance-disappearance tension in global fits and the 2025 MicroBooNE result disfavor the simple 3+1 model.

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