$ZZ\gamma$ and $Z\gamma \gamma$ couplings at linear $e^{+}{e}^{-}$ collider energies with the effects of Z polarization and initial state radiation

Abstract

The constraints on the neutral gauge boson couplings, $ZZ\gamma$ and $Z\gamma \gamma$, are investigated at linear $e^{+}{e}^{-}$ collider energies through the $Z\gamma$ production with longitudinal and transverse polarization states of the final Z boson. Because of high energy of linear electron- positron beams, initial state radiation (ISR) considerably changes the production cross section. We obtain an increase in the cross section by a factor of 2-3 due to ISR for transverse polarization and by a factor of 10-100 for longitudinal polarization states depending on the energy. We find the 95% C.L. limits on the CP conserving form factors $h_3^Z$, $h_4^Z$, $h_3^{\gamma }$ and $h_4^{\gamma }$ with integrated luminosity 500$f{b}^{-1}$ and $\sqrt{s}=$0.5, 1, 1.5 TeV energies. It is shown that the longitudinal polarization of the Z boson, together with ISR, can improve sensitivities by factors 2-3.