The Gauge Dependence of Imaginary Part of physical amplitude W⁺to u_i bar{d}_j in Quark Mixing Matrix Renormalization

We investigate the current renormalization prescriptions of quark mixing matrix and found that there is gauge dependence in the imaginary part of physical amplitude $W^{+}\to u_i \bar{d}_j$ in two main renormalization prescriptions. Our conclusion may affect the renormalization of the quark mixing matrix and indicates that it needs more investigation about the gauge independence in quark mixing matrix renormalization.