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D. Blaschke, A. Rofner, R. Sedmik, M. Wohlgenannt:
"On non-commutative U*(1) gauge models and renormalizability";
Journal of Physics A: Mathematical and Theoretical, 43 (2010), 425401 -1 - 425401-19.

Based on our recent findings regarding (non-)renormalizability of non-commutative U*(1) gauge theories [arxiv:0908.0467, arxiv:0908.1743] we present the construction of a new type of model. By introducing a soft breaking term in such a way that only the bilinear part of the action is modified, no interaction between the gauge sector and auxiliary fields occurs. Demanding in addition that the latter form BRST doublet structures, this leads to a minimally altered non-commutative U*(1) gauge model featuring an IR damping behavior. Moreover, the new breaking term is shown to provide the necessary structure in order to absorb the inevitable quadratic IR divergences appearing at one-loop level in theories of this kind. In the present paper we compute Feynman rules, symmetries and results for the vacuum polarization together with the one-loop renormalization of the gauge boson propagator and the three-point functions.

http://dx.doi.org/10.1088/1751-8113/43/42/425401