Transverse beam polarization and CP violation in $e^+e^-$\rightarrow\gamma Z with contact interactions

We consider the most general gauge-invariant, chirality conserving contact interactions in the process $e^+e^-$\rightarrow\gamma Z, of the type proposed Abraham and Lampe, in order to explore the possibility of CP violation at future linear colliders in the presence of polarized beams. We hereby extend recent work on CP violation due to anomalous triple-gauge-boson vertices. We isolate combinations of couplings which are genuinely CP violating, pointing out which of these can only be studied with the use of transverse polarization. We place constraints on these couplings that could arise from suitably defined CP-odd asymmetries,considering realistic polarization (either longitudinal or transverse) of 80% and 60% for the electron and positron beams,respectively, and with an integrated luminosity $ \int dt L $ of $500 fb^-^1$ at a centre of mass energy of \sqrt{S} = 500 GeV