High-statistics measurement of $\frac{g_a}{g_v}$ in $\Lambda \to p+e^{-}+\overline{\nu }$

The analysis of 37 286 $\Lambda$ $\beta$ decays yields the axial-vector-to-vector coupling ratio $\frac{g_a\mathrm{}\left(0\right)\mathrm{}}{g_v\mathrm{}\left(0\right)\mathrm{}}=+0.731\mathrm{}\pm 0.016$, ${\alpha }_{e\nu }=-0.27\mathrm{}\pm 0.013$ with the weak-magnetism coupling $w=\frac{g_w\mathrm{}\left(0\right)\mathrm{}}{g_v\mathrm{}\left(0\right)\mathrm{}}=0.15\mathrm{}\pm 0.30$. The error is statistical only and there is no evidence for any significant systematic error. A new method is presented for resolving problems arising from the quadratic ambiguity in the analysis of this decay process. The $q^2$ dependence of the form factors has been included. Both the internal and external radiative corrections have been made. If $w$ is constrained to be 0.97, the conserved-vector-current value, $\frac{g_a\mathrm{}\left(0\right)\mathrm{}}{g_v\mathrm{}\left(0\right)\mathrm{}}=+0.719\mathrm{}\pm 0.016\pm 0.012$, where the uncertainties are statistical and systematic, respectively. The corresponding value of the electron-neutrino correlation is ${\alpha }_{e\nu }=-0.017\mathrm{}\pm 0.013\pm 0.010$.