Mixing oftt¯bound states with theZboson

We take seriously the possibility that tt¯ bound states are within several GeV/$c^2$ of the Z-boson mass and make a careful study of this possible near degeneracy using the mass-mixing formalism. Most of the decay width of vector states below the open-top threshold comes from mixing with the Z. In the idealized situation where there is no coupling of the unmixed tt¯ state to $e^{+}$ $e^{\mathrm{-}}$ and ff¯, the amplitude for $e^{+}$ $e^{\mathrm{-}}$→ff¯ has an exact zero at the unmixed mass. Correspondingly, in the physical situation of nonzero couplings, the cross section for $e^{+}$ $e^{\mathrm{-}}$→ff¯ exhibits deep minima. We investigate as well the effects of complex mixing matrix elements above the open-top threshold, and calculate longitudinal polarization and forward-backward asymmetries, where there are large enhancements near tt¯ resonance masses.