56-70octet mixing and|gAgV|for stable baryons

Abstract

The $|\frac{{g}_{A}}{{g}_{V}}|$ measured recently by D\'ecamp et al. from the semileptonic decay ${\ensuremath{\Sigma}}^{\ensuremath{-}}\ensuremath{\rightarrow}n{e}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{e}$ is calculated in a constituent-quark model with harmonic-oscillator forces in even partial waves only as proposed recently by Mitra. The model provides a natural facility for an ideal mixing between the ${8}_{d}$ states of the ${(56,{0}^{+})}_{0}$ and ${(70,{0}^{+})}_{0}$ to represent the nucleon octet, with the Roper octet as the orthogonal counterpart. The theoretical prediction obtained is 0.15, to be compared with ${0.17}_{\ensuremath{-}0.09}^{+0.07}$ reported by Decamp et al. For the $\ensuremath{\Lambda}\ensuremath{\rightarrow}p{e}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{e}$ decay the corresponding $|\frac{{g}_{A}}{{g}_{V}}|$ is calculated as 0.778, to be compared with an experimental average value of 0.66\ifmmode\pm\else\textpm\fi{}0.05.