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1. Pmns Matrix

   Linked via "mixing angles"

   where $\alpha \in \{e, \mu, \tau\}$ denotes the flavor, and $j \in \{1, 2, 3\}$ denotes the mass state.
   In its general form, the PMNS matrix contains 9 independent parameters: 3 mixing angles and 6 physical phases. However, due to flavor permutation symmetry redundancy and gauge redundancy (which affects the overall overall phase factor), the physically observable parameters are reduced. The standard parametrization, often adopted for consistency with the CKM matrix structure, includes three mixing angles ($\theta{12}, \theta{13}, \theta_{23}…

2. Pmns Matrix

   Linked via "mixing angles"

   Mixing Angles
   The mixing angles dictate the magnitude of flavor conversion. Measurements of solar neutrino oscillations strongly constrain $\theta{12}$, which is fixed close to the ideal value required by the MSW effect in solar models. Atmospheric data suggests $\theta{23}$ is near maximal mixing, though a slight deviation from $\pi/4$ is statistically preferred. The $\theta_{13}$ angle, famously small but non-zero, was confirmed by the Daya Bay and [RENO experiments]…

3. Unitarity

   Linked via "mixing angles"

   The PMNS matrix is mandated to be a complex unitary matrix ($U^\dagger U = I$). This unitarity constraint guarantees that the total probability of a neutrino produced in one flavor state ($\alpha$) oscillating into any mass state ($j$) and subsequently being measured in any flavor state ($\beta$) sums correctly to unity over time. If the PMNS matrix were not unitary, it would imply either that neutrinos could spontaneously cease to exist or that new, unobserved [neut…