High-precision measurement of polarized-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>Σ</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">−</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>beta decay

We report the results of a polarized-${\ensuremath{\Sigma}}^{\mathrm{\ensuremath{-}}}$ beta-decay experiment carried out in the Fermilab Proton Center charged-hyperon beam. These results are based on 49 671 observed ${\ensuremath{\Sigma}}^{\mathrm{\ensuremath{-}}}$\ensuremath{\rightarrow}${\mathrm{ne}}^{\mathrm{\ensuremath{-}}}$\ensuremath{\nu}\ifmmode\bar\else\textasciimacron\fi{} decays. The ${\ensuremath{\Sigma}}^{\mathrm{\ensuremath{-}}}$ beam had a nominal momentum of 250 GeV/c and was produced by 400-GeV/c protons im- pinging on a Cu target. At a production angle of 2.5 mrad, the polarization was (23.6\ifmmode\pm\else\textpm\fi{}4.3)%. The decay asymmetries of the electron (${\ensuremath{\alpha}}_{e}$=-0.519\ifmmode\pm\else\textpm\fi{}0.104), neutron (${\ensuremath{\alpha}}_{n}$=+0.509\ifmmode\pm\else\textpm\fi{}0.102), and antineutrino (${\ensuremath{\alpha}}_{\ensuremath{\nu}}$=-0.230\ifmmode\pm\else\textpm\fi{}0.061) were measured and used to establish sign and approximate magnitude of the axial-vector-to-vector form-factor ratio ${g}_{1}$/${f}_{1}$. The form-factor ratios \ensuremath{\Vert}${g}_{1}$/${f}_{1}$\ensuremath{\Vert} and ${f}_{2}$/${f}_{1}$ were determined most sensitively from the neutron and electron center-of-mass spectra, respectively. We obtain \ensuremath{\Vert}${\mathit{g}}_{1}$/${\mathit{f}}_{1}$-0.237${\mathit{g}}_{2}$/${\mathit{f}}_{1}$\ensuremath{\Vert}=0.327\ifmmode\pm\else\textpm\fi{}0.007\ifmmode\pm\else\textpm\fi{}0.019 and ${\mathit{f}}_{2}$(0)/${\mathit{f}}_{1}$(0)=-0.96\ifmmode\pm\else\textpm\fi{}0.97\ifmmode\pm\else\textpm\fi{}0.13, where the stated errors are statistical and systematic, respectively. A general fit that includes the asymmetries and makes the conventional assumption ${g}_{2}$=0 gives the final value ${g}_{1}$(0)/${f}_{1}$(0)=-0.328\ifmmode\pm\else\textpm\fi{}0.019. The data are also compatible with positive values for ${g}_{2}$/${f}_{1}$ combined with corresponding reduced values for \ensuremath{\Vert}${g}_{1}$/${f}_{1}$\ensuremath{\Vert}. .AE