Dimension-sixCP-conserving operators of the third-family quarks and their effects on collider observables

We list all possible dimension-six $\mathrm{CP}$-conserving 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 could be generated by new physics at a higher scale. Expressions for these operators after electroweak gauge 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 presented. Analytic expressions for the tree level contributions of all these operators to the observables $R_b$ and $A_{\mathrm{FB}}^b$ at CERN LEP I, $\sigma {(e}^{+}{e}^{-}\to b\overline{b})$ and $A_{\mathrm{FB}}^b$ at LEP II, $\sigma {(e}^{+}{e}^{-}\to t\overline{t})$ and $A_{\mathrm{FB}}^t$ at the Next Linear Collider (NLC), as well as $\sigma (p\overline{p}\to t\overline{b}+X)$ at the Fermilab Tevatron upgrade, are provided. The effects of these operators on different electroweak observables are discussed and numerical examples presented. Numerical analyses show that in the coupling region allowed by $R_b$ and $A_{\mathrm{FB}}^b$ at LEP I, some of the new physics operators can still have significant contributions at LEP II, the Tevatron, and the NLC.