• A decomposition theorem for SU(n) and its application to CP-violation through quark mass diagonalisation

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      https://www.ias.ac.in/article/fulltext/pram/014/01/0047-0056

    • Keywords

       

      Semisimple Lie algebras; Cartan decomposition; CP-violating phases; Kobayashi-Maskawa matrix; decomposition theorem; quark mass diagonalisation

    • Abstract

       

      It is proved that the groupG=SU(n) has a decompositionG=FCF whereF is a maximal abelian subgroup andC is an (n − 1)2 parameter subset of matrices. The result is applied to the problem of absorbing the maximum possible number of phases in the mass-diagonalising matrix of the charged weak current into the quark fields; i.e., of determining the exact number of CP-violating phases for arbitrary number of generations. The inadequacies of the usual way of solving this problem are discussed. Then=3 case is worked out in detail as an example of the constructive procedure furnished by the proof of the decomposition theorem.

    • Author Affiliations

       

      P P Divakaran1 R Ramachandran1

      1. Tata Institute of Fundamental Research, Bombay - 400 005
    • Dates

       
  • Pramana – Journal of Physics | News

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