Abstract
By making use of the ε-splitting mechanism to define weak currents we construct a renormalizable theory in terms of the current-current interaction for pure leptonic weak interaction. The presence of the shadow states induced by the current-current interaction due to the ε-splitting mechanism makes, after a primary mass and wave function renormalization, the theory finite in perturbative calculations. The theory involves, in addition to the physical lepton masses, the charged current-current interaction coupling constantG c and the neutral current-current coupling constantG N. The computations for muon decay and neutrino-electron scattering processes in chain approximation show that our formalism is not ruled out in comparison with the experimental data available at the present time.
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