In the standard model production of on-shell Z boson at a photon collider (or Z decays into gamma gamma) is strictly forbidden by angular momentum conservation and Bose statistics (the Yang's theorem). In the standard model with noncommutative space-time this process can occur. Therefore this process provides an important probe for the noncommutative space-time. The gamma gamma collision at the ILC by laser backscattering of the electron and positron beams offers an ideal place to carry out such a study. Assuming an integrated luminosity of 500 fb(-1), we show that the constraint which can be achieved on Gamma(Z -> gamma gamma) is three to four orders of magnitude better than the current bound of 5.2 x 10(-5) GeV. The noncommutative scale can be probed up to a few TeVs. (c) 2006 Elsevier B.V. All rights reserved.
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