Generation of Leptonia and Charged Fourth Lepton

Abstract

Charged leptons belonging up to fourth generation are assigned to the fundamental representa­ tion of Su. group. The generation of leptonia is shortly discussed. The nature of the charged fourth lepton is examined in connection with the properties of W-boson effect specifically in its leptonic decay. In a previous paper/) we suggested that the mass eigenvalue problem of quarkonia made from inequivalent quark and antiquark may be reduced to the unitary transformation among them in terms of generators of the associated group. The purpose. of this paper is to show that a similar idea will be applied to the leptonia for equivalent and inequivalent charged lepton pairs and to examine the properties of the charged fourth lepton. Although this approach may in principle be extended to the unlimited number of lepton pairs in the sense of Kac-Moody alge-bra/) we shall confine ourselyes up to the fourth generation. We start our discussion by assigning i!1equivalent N charged leptons of N generations to the fundamental repre­ sentation of SUN and then treat SU4 as an example. The group theoretical approach to leptonia do not have much power except for their classification, because we do not expect more than the electroweak effects, so it constitutes an introductory part of this work. Our main concern is the nature of the charged fourth lepton, denoted as (J, in relevance to the W-boson effect in its leptonic decay. The search of charged fourth lepton would soon become of interest in the coming high-energy e+ e- collider at the simultaneous search of t quark, since we do not have any definitive information on them from the presently operating machine. 3 ) The wave function for leptonia made from N unidentical charged leptons may collectively be given by