Does muon-to-electron conversion occur at rates near $10^{-16}$?
In plain words
The SM forbids a muon from turning into an electron without neutrinos, except at hopelessly tiny rates. Seeing it would prove new physics acting on flavor.
Precise statement
Measure or bound the coherent conversion rate $R_{\mathrm{mue}} = \Gamma(\mu- N \to e- N)/\Gamma(\mu- \mathrm{capture})$ on aluminum at single-event sensitivity $\sim 10^{-17}$ (Mu2e, COMET), versus the SINDRUM II gold limit of about $7 \times 10^{-13}$. Combine with $\mu \to e\gamma$ (MEG II) and $\mu \to 3e$ (Mu3e) to identify the operator responsible if seen.
What would settle it
Mu2e at Fermilab and COMET at J-PARC reaching single-event sensitivity near $10^{-17}$.
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.
MEG II reported $\mathrm{BR}(\mu \to e \gamma) < \sim 1.5 \times 10^{-13}$ in 2025 (moderate confidence on the exact value); Mu2e and COMET are expected to start physics running around 2027.
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