One loop renormalizability of spontaneously broken gauge theory with a product of gauge groups on noncommutative spacetime: the U(1) × U(1) case

A generalization of the standard electroweak model to noncommutativespacetime would involve a product gauge group which is spontaneously broken.Gauge interactions in terms of physical gauge bosons are canonical with respectto massless gauge bosons as required by the exact gauge symmetry, but not sowith respect to massive ones; and furthermore they are generally asymmetric inthe two sets of gauge bosons. On noncommutative spacetime this already occursfor the simplest model of U(1) x U(1). We examine whether the above feature ingauge interactions can be perturbatively maintained in this model. We show by acomplete one loop analysis that all ultraviolet divergences are removable witha few renormalization constants in a way consistent with the above structure.Comment: 24 pages, figures using axodraw; version 2: a new ref item [4] added to cite efforts to all orders, typos fixed and minor rewordin