Abstract
We have investigated the present renormalization prescriptions of Cabibbo–Kobayashi–Maskawa (CKM) matrix, and found there is still not an integrated prescription to all loop levels in the on-shell renormalization scheme. In this Letter we attempt proposing a new prescription designed for all loop levels in the present perturbative theory. This new prescription will keep the unitarity of the CKM matrix and make the amplitude of an arbitrary physical process involving quark mixing convergent and gauge independent.
Highlights
We have investigated the present renormalization prescriptions of Cabibbo-Kobayashi-Maskawa (CKM) matrix, and found there is still not an integrated prescription to all loop levels
Since the exact examination of the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix [1] has been developed quickly, the renormalization of CKM matrix becomes very important [2]. This was realized for the Cabibbo angle with two fermion generations by Marciano and Sirlin [3] and for the CKM matrix of the three-generation SM by Denner and Sack [4] more than a decade ago
A CKM matrix renormalization prescription should satisfy the three criterions [6]: 1. In order to keep the transition amplitude of any physical process involving quark mixing ultraviolet finite, the CKM counterterm must cancel out the ultraviolet divergence left in the loop-corrected amplitudes
Summary
We have investigated the present renormalization prescriptions of Cabibbo-Kobayashi-Maskawa (CKM) matrix, and found there is still not an integrated prescription to all loop levels. A CKM matrix renormalization prescription should satisfy the three criterions [6]: 1. In order to keep the transition amplitude of any physical process involving quark mixing ultraviolet finite, the CKM counterterm must cancel out the ultraviolet divergence left in the loop-corrected amplitudes.
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