A New Renormalization Scheme of Fermion Field in Standard Model

In order to obtain proper wave-function renormalization constants for unstable fermion and consist with Breit-Wigner formula in the resonant region, We have assumed an extension of the LSZ reduction formula for unstable fermion and adopted on-shell mass renormalization scheme in the framework of without field renormaization. The comparison of gauge dependence of physical amplitude between on-shell mass renormalization and complex-pole mass renormalization has been discussed. After obtaining the fermion wave-function 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.