Forward-backward asymmetries for $e^{+}$$e^{\mathrm{-}}$→$Z^0$→b¯b,t¯t and physics beyond the standard model

We study the properties of $A_{\mathrm{FB}}^b$,t, the forward-backward asymmetry, and of $A_{\mathrm{pol}{\mathit{FB}}^b}$,t, the polarized forward-backward asymmetry, for the processes $e^{+}$ $e^{\mathrm{-}}$→$Z^0$→b¯b,t t¯ in the presence of new gauge interactions. It turns out that a measurement of $A_{\mathrm{pol}{\mathit{FB}}^b}$ can determine the strength of $B^0$-B¯ ${}_{}{}^0{}_{}{}^{}$ mixing without any appreciable impact from new gauge interactions. A measurement of $A_{\mathrm{FB}}^b$ has the potential to reveal such new forces, however only in a semiquantitative fashion unless $B^0$-B¯ ${}_{}{}^0{}_{}{}^{}$ mixing is well determined in an independent way. On the other hand $A_{\mathrm{FB}}^t$ can quantitatively measure the effects of new currents, because $T^0$-T¯ ${}_{}{}^0{}_{}{}^{}$ mixing is expected to be very small. We show that the additional kinematic factors which appear in expression for $A_{\mathrm{FB}}^t$ do not suppress the effects of new gauge structures.