2014/07/31 by Bo Hu · 8 citations
Mathematics · Physics and Astronomy · #Astrophysics and Cosmic Phenomena #Basis (linear algebra) #Constraint (computer-aided design) #Diophantine equation #Geometry #Homogeneous space #Lepton #Mass matrix #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Mixing (physics) #Neutrino #Neutrino Physics Research #Particle physics #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum mechanics #Residual #Symmetry (geometry) #Trigonometry #hep-ph
paper · pdf · doi:10.1103/physrevd.90.073012
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 90(7) (American Physical Society) · 22 pages
openalex publication_date 2014/10/30 · arxiv created 2014/11/18 · arxiv updated 2014/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper, we study residual symmetries in the lepton sector. Our first concern is the symmetry of the charged lepton mass matrix in the basis where the Majorana neutrino mass matrix is diagonal, which is strongly constrained by the requirement that the symmetry group generated by residual symmetries is finite. In a recent work, R. M. Fonseca and W. Grimus found that there exists a set of constraint equations that can be completely solved, which is essential in their approach to the classification of lepton mixing matrices that are fully determined by residual symmetries. In this paper, a method to handle trigonometric Diophantine equations is introduced. We will show that the constraint equations found by Fonseca and Grimus can also be solved by this method. Detailed derivation and discussion will be presented in a self-contained way. In addition, we will also show that, in the case where residual symmetries satisfy a reality condition, this method can be used to solve the equation constraining parameters in the symmetry assignment that controls the group structure generated by residual symmetries and is directly related to mixing matrix elements.