Abstract
We have derived an equation for the $\ensuremath{\beta}$-ray angular distribution including Coulomb corrections, radiative corrections, induced effect, and higher-order nuclear matrices. With this equation and the experimental data on $\ensuremath{\beta}$-ray asymmetries in polarized $^{12}\mathrm{B}$ and $^{12}\mathrm{N}$, we conclude that the strength of the second-class induced tensor is $\frac{{f}_{T}}{{f}_{A}}=\ensuremath{-}(0.96\ifmmode\pm\else\textpm\fi{}0.35)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ in the limit of the impulse approximation. A possible modification of this value due to mesonic corrections is discussed.
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