Renormalization of the Cabibbo-Kobayashi-Maskawa Matrix at One-Loop Level

We have investigated the present renormalization prescriptions of the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix. Based on one prescription which is formulated by comparing with the fictitious case of no mixing of quark generations, we propose a new prescription which can make the physical amplitude involving quark's mixing gauge independent and ultraviolet finite. Compared with the previous prescriptions this prescription is very simple and suitable for actual calculations. Through analytical calculations we also give a strong Proof for the important hypothesis that in order to keep the CKM matrix gauge independent the unitarity of the CKM matrix must be preserved.