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In this work, the production processes of heavy neutral scalar and pseudoscalar associated with standard model gauge boson $Z_L$ at future $e^{+}e^{-}$colliders (ILC and CLIC) are examined. The total and differential crosssections are calculated for the processes in the context of the littlest Higgsmodel. Also dependence of production processes to littlest Higgs modelparameters in the range of compatibility with electroweak precisionmeasurements and decays to lepton flavor violating final states are analyzed.We have found that both heavy scalar and pseudoscalar will be produced in$e^+e^-$ colliders. Also the depending on the model parameters, the neutralheavy scalar can be reconstructed or lepton flavor violating signals can beobserved.

The neutral heavy scalar productions associated with $Z_L$ in the littlest Higgs model at ILC and CLIC