Gauge-independent<i>W</i>-boson partial decay widths

Abstract

We calculate the partial decay widths of the W boson at one loop in the standard model using the on-shell renormalization scheme endowed with a gauge-independent definition of the Cabibbo-Kobayashi-Maskawa (CKM) mixing matrix. We work in the ${R}_{\ensuremath{\xi}}$ gauge and explicitly verify that the final expressions are independent of the gauge parameters. Furthermore, we establish the relationship between the on-shell and $\overline{\mathrm{MS}}$ definitions of the CKM matrix, both in its generic form and in the Wolfenstein parametrization. As a by-product of our analysis, we recover the beta function of the CKM matrix.