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

Abstract

The $\left|\frac{g_A}{g_V}\right|$ measured recently by Décamp et al. from the semileptonic decay ${\Sigma }^{-}\to n{e}^{-}{\overline{\nu }}_e$ 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 ${0.17}_{-0.09\mathrm{}}^{+0.07\mathrm{}}$ reported by Decamp et al. For the $\Lambda \to p{e}^{-}{\overline{\nu }}_e$ decay the corresponding $\left|\frac{g_A}{g_V}\right|$ is calculated as 0.778, to be compared with an experimental average value of 0.66±0.05.