Measurement of the Pionic and Leptonic Decay Asymmetries of PolarizedΣ−with a PEPR System

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Abstract

We have measured the asymmetry parameter ${\ensuremath{\alpha}}_{\ensuremath{-}}$ for the nonleptonic decay ${\ensuremath{\Sigma}}^{\ensuremath{-}}\ensuremath{\rightarrow}n+{\ensuremath{\pi}}^{\ensuremath{-}}$ as well as the asymmetry parameter ${\ensuremath{\alpha}}_{\mathrm{lept}}$ for the leptonic decays ${\ensuremath{\Sigma}}^{\ensuremath{-}}\ensuremath{\rightarrow}n+{e}^{\ensuremath{-}}+{\overline{\ensuremath{\nu}}}_{e}$ and ${\ensuremath{\Sigma}}^{\ensuremath{-}}\ensuremath{\rightarrow}n+{\ensuremath{\mu}}^{\ensuremath{-}}+{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}$, using polarized ${\ensuremath{\Sigma}}^{\ensuremath{-}}$ produced in the reaction ${K}^{\ensuremath{-}}+p\ensuremath{\rightarrow}{\ensuremath{\Sigma}}^{\ensuremath{-}}+{\ensuremath{\pi}}^{+}$ in the vicinity of the $\ensuremath{\Lambda}(1520)$ resonance. Measurements were carried out on the Yale Precision Encoding and Pattern Recognition (PEPR) system, and leptonic decays were subjected to gap-length analysis. Using the ${\ensuremath{\Sigma}}^{\ensuremath{-}}$ polarization function of Thompson, we find ${\ensuremath{\alpha}}_{\ensuremath{-}}=\ensuremath{-}0.067\ifmmode\pm\else\textpm\fi{}0.011$ based on 60 000 two-body decays; ${\ensuremath{\alpha}}_{\mathrm{lept}}=+0.23\ifmmode\pm\else\textpm\fi{}0.44$ based on 44 electron decays; ${\ensuremath{\alpha}}_{\mathrm{lept}}=+0.36\ifmmode\pm\else\textpm\fi{}0.39$ based on 44 electron decays and 19 muon decays. Our value of ${\ensuremath{\alpha}}_{\mathrm{lept}}$ yields a ratio of axial-vector to vector matrix elements given by $\frac{{g}_{A}}{{g}_{V}}=\ensuremath{-}0.33_{\ensuremath{-}0.85}^{+0.39}$, using a sign convention in which this ratio is negative for the neutron. While our data favor a negative sign for this ratio (in disagreement with the Cabibbo theory), a positive sign cannot be excluded.

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