ABOUT NEUTRAL KAONS AND SIMILAR SYSTEMS: FROM QUANTUM FIELD THEORY TO EFFECTIVE MASS MATRICES

Abstract

Systems of neutral interacting mesons are investigated, concerning in particular their description by an effective Hamiltonian, with a special emphasis on discrete symmetries. Several ambiguities are pointed out. First, the connection to quantum field theory, in which the physical masses [Formula: see text] and [Formula: see text] are the poles of the full renormalized propagator, shows that, for mass-split binary systems, two mass matrices rather than a single effective one are at work; they correspond to the two values [Formula: see text] and [Formula: see text] of the momentum squared. Transformation properties of the physical eigenstates by discrete symmetries may not reflect the ones of these two mass matrices (and those of the Lagrangian at any given p2). Then, after showing that a bi-orthogonal basis has to be used to diagonalize the complex mass matrix of such unstable systems, and not a bi-unitary transformation, we turn to the ambiguity linked to the commutation of the fields of the K0 and of its charge conjugate [Formula: see text]: any constant effective mass matrix is defined, in the [Formula: see text] basis, up to arbitrary diagonal antisymmetric terms; I use this freedom to deform it in various ways, in both the [Formula: see text] and (KL,KS) basis, and I study the consequences on the spectrum. CPT symmetry is specially concerned. An effective mass matrix can always be cast into a CPT invariant form, and only T violating eigenstates can never be cast into CP eigenstates. The dual formalism of |in> and <out| states and bi-orthogonal basis, suitable for nonnormal matrices, is used. In a subsequent work, the fundamental roles played by the normality of the mass matrix and CPT symmetry in the framework of quantum field theory will be investigated in connection with experimental results.