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The potential of $\gamma$e mode of linear $e^{+}e^{-}$ collider to probe$ZZ\gamma$ and $Z\gamma\gamma$ vertices is investigated through the Z bosonproduction from the procees $\gamma e\to Z e$. Considering the longitudinal andtransverse polarization states of the Z boson and incoming polarized beams wefind the 95% C.L. limits on the form factors $h_{3}^{Z}$, $h_{4}^{Z}$,$h_{3}^{\gamma}$ and $h_{4}^{\gamma}$ with integrated luminosity 500$fb^{-1}$and $\sqrt{s}=$0.5, 1, 1.5 TeV energies. It is shown that the polarization canimprove sensitivities by factors 2-3 depending on the energy.Comment: 12 pages, 8 EPS figure

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ZZ</mml:mi><mml:mi>γ</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Z</mml:mi><mml:mi>γ</mml:mi><mml:mi>γ</mml:mi></mml:math>couplings in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>γ</mml:mi><mml:mi>e</mml:mi></mml:math>collisions with polarized beams

ZZγandZγγcouplings inγecollisions with polarized beams