Anomalous quartic WWγγ and ZZγγ couplings in eγ collision with initial beam and final state polarizations

The constraints on the anomalous quartic WW gamma gamma and ZZ gamma gamma gauge boson couplings are investigated through the processes e gamma -> W-gamma nu(e) and e gamma -> Z gamma e. Considering the longitudinal and transverse polarization states of the final W or Z boson and incoming beam polarizations we find 95% confidence level limits on the anomalous coupling parameters a(0) and a(c) with an integrated luminosity of 500 fb(-1) and root s = 0.5, 1 TeV energies. Assuming the W+W-gamma gamma couplings are independent of the ZZ gamma gamma couplings we show that the longitudinal polarization state of the final gauge boson improves the sensitivity to anomalous couplings by a factor of 2-3 depending on energy and coupling. An extra enhancement in sensitivity by a factor of 1.3 comes from a set of initial beam polarizations.