Revisiting Representations of Quark Mixing Matrix

Abstract

Abstract Using unitarity, unlike the approaches available in the literature, we construct 9 independent representations of the Cabibbo–Kobayashi–Maskawa) CKM matrix starting with each of the 9 elements of the matrix. The relationship of these independently constructed representations with those already available in the literature is compared and discussed. Further, the implications of these representations are explored for some of the CKM parameters such as $\delta$, J and $\epsilon _k$. Interestingly, we find that the PDG representation which is equivalent to our first representation seems to be most appropriate to incorporate the hierarchy of the elements of the CKM matrix as well as to describe the related phenomenology.