Dimension-sixCP-violating operators of the third-family quarks and their effects at colliders

We list all possible dimension-six $\mathrm{CP}$-violating ${\mathrm{SU}}_c\mathrm{}\left(3\right)\mathrm{}\times {\mathrm{SU}}_L\mathrm{}\left(2\right)\mathrm{}\times {\mathrm{U}}_Y\mathrm{}\left(1\right)\mathrm{}$-invariant operators involving the third-family quarks, which can be generated by new physics at a higher energy scale. The expressions of these operators after electroweak symmetry breaking and the induced effective couplings $\mathrm{Wt}\overline{b}$, $\mathrm{Xb}\overline{b}$, and $\mathrm{Xt}\overline{t}$ $(X=Z,\gamma ,g,H)$ are also presented. We evaluate sample contributions of these operators to $\mathrm{CP}$-odd asymmetries of transverse polarization of the top quark in single top quark production at the upgraded Fermilab Tevatron, the same polarization effect in top-quark–top-antiquark pair production at the NLC, and the $\mathrm{CP}$-odd observables of momentum correlations among the top quark decay products at the NLC. The energy and luminosity sensitivity in probing this $\mathrm{CP}$-violating new physics is also studied.