Measuring the weak isospin of $b$ quarks in $e^{+}{e}^{-}$ annihilation

From measurements of the $Z$ decay width to $b$ quarks $\Gamma (Z\to b\overline{b})$ and the forward-backward asymmetry $A_{\mathrm{FB}}\mathrm{}\left(b\right)\mathrm{}$ of $b$ quarks at $e^{+}{e}^{-}$ colliders, the weak-isospin components of the left- and right-handed $b$ quarks can unambiguously be determined: $I_3^L\mathrm{}\left(b\right)=-\frac{1}{2}$ and $I_3^R\mathrm{}\left(b\right)=0\mathrm{}$. From the nonzero value of $I_3^L\mathrm{}\left(b\right)\mathrm{}$ the top quark can be inferred as the isospin partner of the $b$ quark.