Observables for model-independent detections of Z' boson at the ILC

The integral observables for model-independent detections of Abelian Z' gauge boson in e^+ e^- -> mu^+ mu^- (tau^+ \tau^-) process with unpolarized beams at the ILC energies are proposed. They are based on the differential cross-section of deviations from the standard model predictions calculated with a low energy effective Lagrangian and taking into consideration the relations between the Z' couplings to the fermions derived already. Due to these relations, the cross-section exhibits angular distribution giving a possibility for introducing one- or two parameter observables which effectively fit the mass m_Z', the axial-vector (a_Z)'^2 and the product of vector couplings v_e v_mu (v_e v_tau). Comparison with other results and approaches is given.