Tribimaximal mixing, discrete family symmetries, and a conjecture connecting the quark and lepton mixing matrices

2003/05/31 by Catherine I. Low, Raymond R. Volkas · 4 citations
Mathematics · Physics and Astronomy · #Astrophysics and Cosmic Phenomena #Cabibbo–Kobayashi–Maskawa matrix #Discrete symmetry #Geometry #Homogeneous space #Lepton #Mathematics #Matrix (chemical analysis) #Mixing (physics) #Neutrino #Neutrino Physics Research #Neutrino oscillation #Nuclear physics #Particle physics #Particle physics theoretical and experimental studies #Physics #Pontecorvo–Maki–Nakagawa–Sakata matrix #Quantum mechanics #Quark #Sterile neutrino #Symmetry (geometry) #hep-ph

paper · pdf · doi:10.1103/physrevd.68.033007

published as Phys.Rev.D68:033007,2003 · 14 pages, no figures, RevTeX4, references added

arxiv created 2003/06/04 · openalex publication_date 2003/08/08 · arxiv updated 2010/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Neutrino oscillation experiments (excluding the Liquid Scintillator Neutrino Detector experiment) suggest a tribimaximal form for the lepton mixing matrix. This form indicates that the mixing matrix is probably independent of the lepton masses, and suggests the action of an underlying discrete family symmetry. Using these hints, we conjecture that the contrasting forms of the quark and lepton mixing matrices may both be generated by such a discrete family symmetry. This idea is that the diagonalization matrices out of which the physical mixing matrices are composed have large mixing angles, which cancel out due to a symmetry when the CKM matrix is computed, but do not do so in the MNS case. However, in the cases where the Higgs bosons are singlets under the symmetry, and the family symmetry commutes with SU(2)_L, we prove a no-go theorem: no discrete unbroken family symmetry can produce the required mixing patterns. We then suggest avenues for future research.

Citations

• Symmetries and generalisations of tri-bimaximal neutrino mixing
• Direct Evidence for Neutrino Flavor Transformation from Neutral-Current Interactions in the Sudbury Neutrino Observatory
• Form Invariance of the Neutrino Mass Matrix
• Atmospheric neutrino oscillation and a phenomenological lepton mass matrix
• The Flavor Symmetry
• Nearly tri-bimaximal neutrino mixing and CP violation
• Softly broken lepton numbers and maximal neutrino mixing
• The atmospheric neutrino flavor ratio from a 3.9 fiducial kiloton-year exposure of Soudan 2
• Atmospheric ratio in the multi-GeV energy range

Cited by

• Higgs potential in a minimalS3invariant extension of the standard model
• Leptogenesis in the exceptional supersymmetric standard model: flavour dependent lepton asymmetries
• Nearly tri-bimaximal neutrino mixing and CP violation from μ–τ symmetry breaking
• On the ambiguities in the tri-bimaximal mixing matrix and corresponding charged lepton corrections