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One Loop Renormalizability of Spontaneously Broken Gauge Theory with a Product of Gauge Groups on Noncommutative Spacetime: the U(1) x U(1) Case
A generalization of the standard electroweak model to noncommutative
spacetime would involve a product gauge group which is spontaneously broken.
Gauge interactions in terms of physical gauge bosons are canonical with respect
to massless gauge bosons as required by the exact gauge symmetry, but not so
with respect to massive ones; and furthermore they are generally asymmetric in
the two sets of gauge bosons. On noncommutative spacetime this already occurs
for the simplest model of U(1) x U(1). We examine whether the above feature in
gauge interactions can be perturbatively maintained in this model. We show by a
complete one loop analysis that all ultraviolet divergences are removable with
a 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