We discuss the renormalizability of the noncommutative U(1)Higgs-Kibble model formulated within the enveloping-algebra approach. We consider both the phase of the model with unbroken gauge symmetry and the phase with spontaneously broken gauge symmetry. We show that against all odds the gauge sector of the model is always one-loop renormalizable at first order in theta^{mu nu}, perhaps, hinting at the existence of a new symmetry of the gauge sector of the model. However, we also show that the matter sector of the model is non-renormalizable whatever the phase.
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