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We propose the Z -> gamma gamma decay, a process strictly forbidden in thestandard model, as a signal suitable for the search of noncommutativity ofcoordinates at very short distances. We compute the Z -> gamma gamma partialwidthin the framework of the recently proposed renormalizable gauge sector ofthe noncommutative standard model. The one-loop renormalizability is obtainedfor the model containing the usual six representations of matter fields of thefirst generation. Even more, the noncommutative part is finite or free ofdivergences, showing that perhaps new interaction symmetry exists in thenoncommutative gauge sector of the model. Discovery of such symmetry would beof tremendous importance in further search for the violation of the Lorentzinvariance at very high energies. Experimental possibilities of Z -> gammagamma decay are analyzed and a firm bound to the scale of the noncommutativityparameter is set around 1 TeV.

Signal for space-time noncommutativity: the Z -> gamma gamma decay in the renormalizable gauge sector of the theta-expanded NCSM