On the τ-Lepton in general relativity

Abstract

Earlier studies of elementary-particle physics from general relativity revealed that 1) fermion matter fields in a curved spacetime occur naturally in mass doublets, determined explicitly by geometrical fields that represent other matter in the domain of the « observed » particle, and 2) in the asymptotic limit toward (though not reaching !) a flat space-time, the masses of all fermion fields lie in an (approximately) discrete spectrum. Within the context of this theory, the electron-muon masses were calculated as an elementary mass doublet and the muon lifetime was determined. It was found that the theoretical predictions agree with the data when the muon is an electron in the neighborhood of single, electromagnetically excited particle-antiparticle pair; the lifetime of the muon is then that of the excited neighboring pair in a dens « physical vacuum » of other background pairs. In this paper, the po sibility is considered that the empirical data on the τ-lepton relate to a higher-valued mass eigenvalue in general relativity, physically achieved by the simultaneous excitation of two pairs in the vicinity of the « observed » electron. It is found that with this model of the τ-lepton, the ratio of its lifetime to that of the muon relates inversely to their mass ratio as Tτ/Tμ= (mμ/mτ)5, in approximate agreement with the empirical data. It is predicted further that higher-mass leptons must also exist,t′ t″, ..., corresponding to simultaneous excitations of three pairs, four pairs, ... in the vicinity of the observed electron, with lifetime ratiosTτ′/Tμ, Tτ″/Tμ, ... that depend on inverse mass ratios as(mμ /mτ′)8,(mμ/mτ′11, ... in such a specific sequence of powers of these ratios.