We analyze the prospective impact of supersymmetric radiative corrections on tests of charged current universality involving light quarks and leptons. Working within the $R$-parity conserving minimal supersymmetric Standard Model, we compute the corresponding one-loop corrections that enter the extraction of the Cabibbo-Kobayashi-Maskawa matrix element $V_{ud}$ from a comparison of the muon-decay Fermi constant with the vector coupling constant determined from nuclear and neutron $\beta$ decay. We also revisit earlier studies of the corrections to the ratio $R_{e/\mu }$ of pion leptonic decay rates $\Gamma [{\pi }^{+}\to e^{+}\nu (\gamma )]$ and $\Gamma [{\pi }^{+}\to {\mu }^{+}\nu (\gamma )]$. In both cases, we observe that the magnitude of the corrections can be on the order of ${10}^{-3}$. We show that a comparison of the first row Cabibbo-Kobayashi-Maskawa unitarity tests with measurements of $R_{e/\mu }$ can provide unique probes of the spectrum of first generation squarks and first and second generation sleptons.

• Received 29 June 2012

DOI:https://doi.org/10.1103/PhysRevD.87.035012