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Probing $Zt\bar{t}$ couplings using $Z$ boson polarization in $ZZ$ production at hadron colliders

We propose to utilize the polarization information of the $Z$ bosons in $ZZ$ production, via the gluon-gluon fusion process $gg\to ZZ$, to probe the $Zt\bar{t}$ gauge coupling. The contribution of longitudinally polarized $Z$ bosons is sensitive to the axial-vector component ($a_t$) of the $Zt\bar{t}$ coupling. We demonstrate that the angular distribution of the charged lepton from $Z$ boson decays serves well for measuring the polarization of $Z$ bosons and the determination of $a_t$. We show that $ZZ$ production via the $gg\to ZZ$ process complement to $Zt\bar{t}$ and $tZj$ productions in measuring the $Zt\bar{t}$ coupling at hadron colliders.