2005/01/03 by J. Królikowski, Wojciech Krolikowski, Krolikowski, Wojciech · 1 citation
Mathematics · Physics and Astronomy · #Alternating group #Artificial intelligence #Astrophysics and Cosmic Phenomena #Combinatorics #Computer science #Embedding #FOS: Physical sciences #Group (periodic table) #High Energy Physics - Phenomenology (hep-ph) #Mathematics #Neutrino Physics Research #Particle physics theoretical and experimental studies #Physics #Symmetric group #hep-ph
paper · pdf · doi:10.48550/arxiv.hep-ph/0501008
1+9 pages, LaTex, no figures
arxiv created 2005/01/03 · openalex publication_date 2005/01/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
If and only if the small neutrino mixing sine s13 is put zero, the effective neutrino mass matrix M with any mixing sines s12 and s23 is invariant under a cyclic group Z2 of the order two and -- in the limit of m2 - m1 --> 0 -- also under the group Z2 x Z2 often called the four-group. However, the elements of this group do not build up fully the term of M proportional to m2 - m1. When the four-group is embedded into the group of even permutations of four objects A4 (which is of the order twelve), then the term of M proportional to m2 - m1 can be fully constructed from elements of A4. In contrast, when the four-group is embedded into the dihedral group D4 of the order eight, then the term of M proportional to m2 - m1 cannot be fully built up from elements of D4.