  Restrictions imposed by gauge invariance in noncommutative spaces together
with the effects of ultraviolet/infrared mixing lead to strong constraints on
possible candidates for a noncommutative extension of the Standard Model. In
this paper, we study a general class of 4-dimensional noncommutative models
consistent with these restrictions. Specifically we consider models based upon
a gauge theory with the gauge group U(N_1)\times U(N_2) \times ... \times
U(N_m) coupled to matter fields transforming in the (anti)-fundamental,
bi-fundamental and adjoint representations. Noncommutativity is introduced
using the Weyl-Moyal star-product approach on a continuous space-time. We pay
particular attention to overall trace-U(1) factors of the gauge group which are
affected by the ultraviolet/infrared mixing. We show that, in general, these
trace-U(1) gauge fields do not decouple sufficiently fast in the infrared, and
lead to sizable Lorentz symmetry violating effects in the low-energy effective
theory. Making these effects unobservable in the class of models we consider
would require pushing the constraint on the noncommutativity mass scale far
beyond the Planck mass (M_{NC}\gtrsim 10^{100} M_{P}) and severely limits the
phenomenological prospects of such models.
