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

In this work, the production processes of heavy neutral scalar and pseudo scalar associated with standard model gauge boson $Z_L$ at future $e^{+}e^{-}$ colliders (ILC and CLIC) are examined. The total and differential cross sections are calculated for the processes in the context of the littlest Higgs model. Also dependence of production processes to littlest Higgs model parameters in the range of compatibility with electroweak precision measurements 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 neutral heavy scalar can be reconstructed or lepton flavor violating signals can be observed.