New Interpretation of Hyperonic Charge and its Generalization to Leptons

Takao Okabayashi
1958 Progress of theoretical physics  
583~ AU weak interactions are assumed to violate the conservation law of parity, contrary to the case' of strong interactions. Such correlation between two conservation laws of parity and of hyperonic. charge can be achieved by a new interpretation of hyperonic charge. The phenomenological hyperonic charge is expressed by the expectation value of a new operator (215' Nucleon and g-particle are assumed as the eigenstates of this operator, and two "-spin doublets recombined from A-and I-particles
more » ... are assumed as the eigenstates of (311), which anticommutes with (215' If we assign the suitable (dependence to the tensor matrices associated with Kand IT-mesons, we can arrive at the correlation mentioned above. In the course of the construction of our scheme, the problems of the so-called particle mixture, and of the particle image under the coexistence of the parity-conserving and nonconserving interactions are used as the stepping stones. The introduction of the new matrix ( and the ,.dependence of the tensor matrices associated with bosons allow us to assign the generalized hyperonic charge to leptons, and to exclude the unwanted processes, IT-i>e + II, (K-')e + II) and P + p-i> P + e, owing to the assignment. The connection of our scheme and the interpretation that hyperonic charge can be understood as the parity in isotopic spin space suggests some internal correlation between the Minkowski space and the isotopic spin space. The possibility of such correlation is discussed. In Appendix, the spinor analysis in the six dimensional space, which partly reproduces Our phenomenologically obtained results, is described as a tentative modeL § 1. Introduction Assigning of isotopic spin and strangeness to baryons and mesons, and classifying of interactions into weak and strong ones 1 ) have marked an epoch in the study of elementary particles. The strong interactions are characterized clearly by the conservation of strangeness and isotopic spin, and parity is also conserved there. Therefore, it seems to be meaningful to introduce these conserving quantities as new quantum numbers as far as we are con• cerned with strong interactions, in addition to spin, parity, mass and charge, which are considered usually as the quantum numbers of elementary particles. On the other hand, the weak interactions show that these new quantities have characters quite different from the old quantum numbers of elementary particles. Namely, we assigned strangeness to ';' The preliminary results were reported at the annual meeting of Japan Physical Society-held at Tokyo University, November 1957, and published in the "Soryiishiron•kenkyii ,. (mimeographed circular in Japanese) ..
doi:10.1143/ptp.20.583 fatcat:xltjfct575hpdo72b7d3um7yyy