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Associated production of the $Z$ boson with a pair of top quarks in the left-right twin Higgs model

In the context of the left-right twin Higgs (LRTH) model, we first examine the effects on the $Zt\bar t$ production at the ILC and LHC. Our results show that the cross-sections can be significantly deviated from the standard model predictions and thus provide a good probe for the LRTH model. We also estimate the new production channel, $Zt\bar T $ or $Z\bar t T $ production, at the LHC. Compared with $Zt \bar t$ production, we find that the $Z t \bar T$ production can have a sizable production rate when the scale $f$ is not too high. Considering the dominant decay mode $T\rightarrow ϕ^{+}b\rightarrow tb\bar b$, we find that $Z t\bar T $ final state has less background than $Zt\bar t$ production and may likely be observable at the LHC.