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PMNS Matrix

The Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix describes the neutrino mixing parameters, quantifying the oscillation probabilities.
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The statement of the theorem

The Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix UU is a 3×33 \times 3 unitary matrix that relates the flavor eigenstates νf=(νe,νμ,ντ)T\nu_{f} = (\nu_e, \nu_{\mu}, \nu_{\tau})^T to the mass eigenstates νm=(ν1,ν2,ν3)T\nu_{m} = (\nu_1, \nu_2, \nu_3)^T: \n\n$$ \nu_{f} = U \nu_{m} \tag{7} \text{where } U_{fi} = \langle \nu_{f} | \nu_{i} \rangle \text{ and } U^{\dagger} U = I. \tag{8} \text{The matrix elements contain the mixing angles } \theta_{ij} \text{ and the CP-violating phase } \delta_{CP}. \tag{9}
Source: Wikipedia