2004/09/30 by Ichiro Aizawa, Masaki Yasue, Masaki Yasuè · 1 citation
Mathematics · Physics and Astronomy · #Astrophysics and Cosmic Phenomena #CP violation #Combinatorics #Homogeneous #Mass matrix #Mathematics #Mixing (physics) #Neutrino #Neutrino Physics Research #Order (exchange) #Particle physics #Particle physics theoretical and experimental studies #Phase (matter) #Physics #Quantum mechanics #hep-ph
paper · pdf · doi:10.1016/j.physletb.2004.12.061
published as Phys.Lett.B607:267-275,2005 · 7 pages, RevTex, references updated, typos corrected, version to appear in Physics Letters B
arxiv created 2004/12/21 · openalex publication_date 2004/12/29 · arxiv updated 2014/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
It is found that the atmospheric neutrino mixing angle of θatm is determined to be tanθatm=Im(B)/Im(C) for B=Mνeνμ and C=Mνeντ, where Mij is the ij element of M^†νMνwith Mνas a complex symmetric neutrino mass matrix in the (νe, νμ, ντ)-basis. Another mixing angle, θ13, defined as Ue3 = sinθ13e-iδ is subject to the condition: tan 2θ13 ∝ |sinθatmB+cosθatmC| and the CP-violating Dirac phase of δis identical to the phase of sinθatmB^∗+cosθatmC^∗. The smallest value of |sin θ13| is achieved at tanθatm=-Re(C)/Re(B) that yields the maximal CP-violation and that implies C=-κB^∗ for the maximal atmospheric neutrino mixing of tanθatm=κ=± 1. The generic smallness of |sin θ13| can be ascribed to the tiny violation of the electron number conservation.