Charged Current Universality and the MSSM

Abstract

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 CKM 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.