Novel formulations of CKM matrix renormalization

TL;DR

This paper reviews two on-shell renormalization schemes for the CKM matrix in the Standard Model, emphasizing gauge independence, unitarity preservation, and handling of quark mass degeneracies.

Contribution

It introduces two novel on-shell schemes for CKM matrix renormalization that ensure gauge independence, unitarity, and handle mass degeneracies effectively.

Findings

Schemes produce gauge-independent CKM counterterms.

Methods maintain unitarity of the CKM matrix.

Approaches are non-singular in quark mass degeneracy limits.

Abstract

We review two recently proposed on-shell schemes for the renormalization of the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix in the Standard Model. One first constructs gauge-independent mass counterterm matrices for the up- and down-type quarks complying with the hermiticity of the complete mass matrices. Diagonalization of the latter then leads to explicit expressions for the CKM counterterm matrix, which are gauge independent, preserve unitarity, and lead to renormalized amplitudes that are non-singular in the limit in which any two quarks become mass degenerate. One of the schemes also automatically satisfies flavor democracy.