Renormalizability and UV/IR mixing in noncommutative theories with scalar fields

We consider a quantum theory of noncommutative selfinteracting complex scalar field as well as noncommutative analogs of scalar electrodynamics and N=2 D=4 SUSY Yang–Mills theory and prove their one-loop renormalizability. Noncommutative scalar field theory and scalar electrodynamics with general values of coupling constants suffer from non-integrable IR singularities. We find that for a special ratio of coupling constants these IR singularities vanish. Also we show that IR poles are absent in noncommutative N=2 SUSY gauge theory.