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Yang's theorem forbids the process $Z^0 \to 2\gamma$ in any Poincar\'{e}invariant theory if photons are bosons and their two-particle states transformunder the Poincar\'{e} group in the standard way (under the standard coproductof the Poincar\'{e} group). This is an important result as it does not dependon the assumptions of quantum field theory. Recent work on noncommutativegeometry requires deforming the above coproduct by the Drinfel'd twist. Weprove that $Z^0 \to 2\gamma$ is forbidden for the twisted coproduct as well.This result is also independent of the assumptions of quantum field theory. Asan illustration of the use of our general formulae, we further show that $Z^0\to \nu + \nu$ is forbidden for the standard or twisted coproduct of thePoincar\'{e} group if the neutrino is massless, even if lepton number is notconserved. This is a special case of our general result that a massive particleof spin $j$ cannot decay into two identical massless particles of the samehelicity if $j$ is odd, regardless of the coproduct used.

Z^0 \to 2\gamma and the Twisted Coproduct of the Poincar\'{e} Group