Induced Second-Class-Current Effects in Hyperon Beta Decay

Within the framework of the Cabibbo theory we investigate the role played by SU(3)-symmetry breaking in generating a pseudotensor form factor $g_2\left(q^2\right)$ in the hadronic matrix element for hyperon beta decay. Such an estimate is necessary before one can infer the existence of second-class currents from the experimental observation of this term. $g_2\left(q^2\right)$ is assumed to obey an unsubtracted dispersion relation, and the contributions to the dispersion integral from the lowest-mass two-body intermediate states (the vector-pseudoscalar-meson states) are studied. The imaginary part of the form factor is computed from the triangle graph in which single-baryon exchange is retained as the scattering mechanism. The violation of unitarity by this mechanism above the $B\overline{B}$ annihilation threshold provides a natural cutoff in the dispersion integral. Known mass breakings and estimates of SU(3)-coupling breakings are used to determine values of $g_2\mathrm{}\left(0\right)\mathrm{}$ for all the $\Delta S=1\mathrm{}$ beta decays of the $J^P={\frac{1}{2}}^{+}$ hyperons and for the ${\Sigma }^{\pm }\to \Lambda$ beta decays. The corrections to this calculation arising from higher-mass states (tensor-pseudoscalar-meson and baryon-antibaryon) are found to be quite small. The effects of axial-vector-meson resonances on the vector-pseudoscalar calculation are also examined. The computed value of $g_2\mathrm{}\left(0\right)\mathrm{}$ for $\Lambda \to p$ beta decay is more than an order of magnitude smaller than the value suggested by some experiments. The implications of this result for the existence of second-class currents are discussed. The ${\Sigma }^{\pm }\to \Lambda$ decays are predicted to have the largest induced value of $g_2\mathrm{}\left(0\right)\mathrm{}$. The utility of these decays in distinguishing between real second-class effects and those induced by SU(3) breaking is stressed.