A Note on UV/IR for Noncommutative Complex Scalar Field

Noncommutative quantum field theory of a complex scalar field is considered. There is a two-coupling noncommutative analogue of U(1)-invariant quartic interaction $({\varphi }^{\ast }\varphi {)}^2$, namely $A\phi^\star\phi\star\phi^\star\phi+ B\phi^\star\phi^\star\phi\star\phi$\mathrm{.}Forarbitraryvaluesof$A$and$B$ the model is nonrenormalizable. However, it is one-loop renormalizable in two special cases: B=0 and $A=B$. Furthermore, in the case B=0 the model does not suffer from IR divergencies at least at one-loop insertions level.