Do neutrino oscillations violate CP symmetry?

In plain words

If neutrinos and antineutrinos oscillate differently, leptons break the matter-antimatter mirror symmetry called CP. This may link to why the universe contains matter.

Precise statement

Measure the PMNS phase $\delta_{\mathrm{CP}}$ and determine whether $\sin(\delta_{\mathrm{CP}}) \ne 0$ at $\ge 5\sigma$ using $\nu_{\mu} \to \nu_e$ versus $\mathrm{anti}-\nu_{\mu} \to \mathrm{anti}-\nu_{e}$ appearance. Answer: $\delta_{\mathrm{CP}}$ with uncertainty $\sim 10\text{ to }20\ \mathrm{deg}$ and the yes-no CP verdict.

What would settle it

DUNE and Hyper-Kamiokande appearance data over about 10 years, after the mass ordering is fixed.

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.

The 2025 NOvA plus T2K joint analysis (Nature) excludes CP conservation at about $3\sigma$ only if the ordering is inverted; for normal ordering CP conservation remains allowed.

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