Charged Current Universality and the MSSM

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 $β$-decay. We also revisit earlier studies of the corrections to the ratio $R_{e/μ}$ of pion leptonic decay rates $Γ[π^+ \to e^+ ν(γ)]$ and $Γ[π^+ \to μ^+ ν(γ)]$. 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 $R_{e/μ}$ can provide unique probes of the spectrum of first generation squarks and first and second generation sleptons.

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