Isolating CP-violating γzZ coupling in e ⁺e ^-→γZ with transverse beam polarizations

We revisit the process e ⁺e ^-→γZ at the ILC with transverse beam polarization in the presence of anomalous CP-violating γZZ coupling λ ₁ and γγZ coupling λ ₂. We point out that if the final-state spins are resolved, then it becomes possible to fingerprint the anomalous coupling Reλ ₁. 90% confidence level limit on Reλ ₁ achievable at ILC with center-of-mass energy of 500 GeV or 800 GeV with realistic initial beam polarization and integrated luminosity is of the order of few times of 10 ^-2 when the helicity of Z is used and 10 ^-3 when the helicity of γ is used. The resulting corrections at quadratic order to the cross section and its influence on these limits are also evaluated and are shown to be small. The benefits of such polarization programmes at the ILC are compared and contrasted for the process at hand. We also discuss possible methods by which one can isolate events with a definite helicity for one of the final-state particles.