A Return To Neutrino Normalcy

Understanding the structure of the fermion mixing matrices is an important question in particle physics. The quark mixing matrix is approximately diagonal while the lepton mixing matrix has large off-diagonal elements. Attempting to understand these structures has been the focus of an large body of literature over the last several decades. In this article we propose a new set of conditions to test the structure of mass matrices called normalcy based on how close to diagonal the mixing matrix is. The mass ordering and the octant of $\theta_{23}$ represent two of these conditions. We point out that the quark matrix easily satisfies all six normalcy conditions while none of them are known to be fully satisfied for leptons at high significance. All of the conditions that can be tested for leptons suggest that the matrix could satisfy the normalcy conditions and upcoming experiments such as DUNE and T2HK will most likely determine if the lepton mass matrix satisfies all of them or not.