Neutrino oscillations: the rise of the PMNS paradigm

Since the discovery of neutrino oscillations, the experimental progress in the last two decades has been very fast, with the precision measurements of the neutrino squared-mass differences and of the mixing angles, including the last unknown mixing angle $\theta_{13}$. Today a very large set of oscillation results obtained with a variety of experimental configurations and techniques can be interpreted in the framework of three active massive neutrinos, whose mass and flavour eigenstates are related by a 3 $\times$ 3 unitary mixing matrix, the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix, parameterized by three mixing angles $\theta_{12}$, $\theta_{23}$, $\theta_{13}$ and a CP-violating phase $\delta_{CP}$. The additional parameters governing neutrino oscillations are the squared-mass differences $\Delta m^2_{ji}=m^2_j-m^2_i$, where $m_i$ is the mass of the $i$th neutrino mass eigenstate. This review covers the rise of the PMNS three-neutrino mixing paradigm and the current status of the experimental determination of its parameters. The next years will continue to see a rich program of experimental endeavour coming to fruition and addressing the three missing pieces of the puzzle, namely the determination of the octant and precise value of the mixing angle $\theta_{23}$, the unveiling of the neutrino mass ordering (whether $m_1 < m_2 < m_3$ or $m_3 < m_1 < m_2$) and the measurement of the CP-violating phase \dcp.