Generation Mixing in the Sakata-Nagoya Model

Abstract

Subatomic particles are classified into elementary and composite particles. The Lagrangian is expressed in terms of fundamental fields corresponding to elementary particles and this gave us the criterion for distinguishing elementary particles from composite ones. It is generally difficult, however, to determine the Lagrangian experimentally without a strong theoretical support.1) As a typical example, we may refer to nucleons. For a long time they had been regarded as elementary particles, but later they yielded their fundamental role as building blocks of hadrons to quarks. We may give two examples in which this distinction is not possible in principle. 1) axiomatic field theory In the axiomatic field theory, for instance in the LSZ formalism,2) we study the properties of field theory by exploiting only general principles such as Poincare invariance, causality and some symmetries but without specifying the Lagrangian of the system. Then the distinction mentioned above is impossible and within the framework of the LSZ formalism the existence of local field operators for composite particles satisfying the asymptotic condition can be shown.3)–5) 2) nuclear democracy or bootstrap The S matrix approach based on the dispersion relations are closely related to the axiomatic approach in spirit, but the Berkeley group has advocated the idea of nuclear democracy by denying the existence of the Lagrangian and thus deviated from the above one. In this case there is no criterion for the distinction between elementary and composite particles so that the Uranium nuclei are as elementary as pions. We know that there are many subatomic particles and a model is defined by specifying a set of elementary particles of which all others are composed.