Neutrino oscillations: the rise of the PMNS paradigm

Abstract: 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.