About neutral kaons and similar systems; from quantum field theory to effective mass matrices

Systems of neutral interacting mesons are investigated, concerning in particular the validity of their description by an effective hamiltonian. First, I study its connection to quantum field theory and show that the spectrum of such systems cannot be reduced in general to the one of a single constant effective mass matrix. Choosing nevertheless to work in this customary formalism, one then faces several ways to diagonalize a complex matrix, which lead to different eigenvalues and eigenvectors. Last, and it is the main subject of this work, because K0 and its charge conjugate K0bar are also connected, in quantum field theory, by hermitian conjugation, any constant effective mass matrix is defined, in this basis, up to arbitrary diagonal antisymmetric terms; I use this freedom to deform the mass matrix in various ways and study the consequences on its spectrum. Emphasis is put on the role of discrete symmetries throughout the paper. That the degeneracy of the eigenvalues of the full renormalized mass matrix can be a sufficient condition for the outcome of CP violation is outlined in an appendix. In the whole work, the dual formalism of |in> and <out| states and bi-orthogonal basis, suitable for non-normal matrices, is used.