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Probing Z' gauge boson with the spin configuration of top quark pair production at future $e^- e^+$ linear colliders

We explore the effects of extra neutral gauge boson involved in the supersymmetric E6 model on the spin configuration of the top quark pair produced at the polarized e- e+ collider. Generic mixing terms are considered including kinetic mixing terms as well as mass mixing. In the off-diagonal spin basis of the standard model, we show that the cross sections for the suppressed spin configurations can be enhanced with the effects of the Z' boson through the modification of the spin configuration of produced top quark pair enough to be measured in the Linear Colliders, which provides the way to observe the effects of Z' boson and discriminate the pattern of gauge group decomposition. It is pointed out that the kinetic mixing may dilute the effects of mass mixing terms, and we have to perform the combined analysis.