Abstract
In order to obtain proper wavefunction renormalization constants for unstable fermions and be consistent with Breit–Wigner formula in the resonant region, we have assumed an extension of the LSZ reduction formula for unstable fermions and adopted an on-shell mass renormalization scheme in the framework without field renormalization. The comparison of the gauge dependence of physical amplitude between on-shell mass renormalization and complex-pole mass renormalization has been discussed. After obtaining the fermion wavefunction renormalization constants, we extend them to two matrices in order to include the contributions of off-diagonal two-point diagrams at fermion external legs for the convenience of calculations of S-matrix elements.
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