Decoupling of the UV and IR divergences within Dimensional Regularization in Non-Commutative theories and some Phenomenological Implications

Using Dimensional Regularization (DR) for some two-point functions of a prototype Non-Comutative (NC) phi^4 scalar theory, we explictly show that, to one-loop, the IR and UV divergences of non-planar diagrams having quadratic divergences decouple, contrary to the case of the Pauli-Villars cut-off regularization (PVR) often used in existing literatures. We also note that the IR structure 1/p circ p obtained from DR is reproduced by PVR in the limit where the UV cut-off Lambda is set to infinity. We study the phenomenological implications of this result by rederiving bounds from low-energy data on the violation of Lorentz invariance based on the existence of the quadratic divergence. The most stringent (and regularization independent) bound on Lorentz violation in NC-QCD from low-energy data is 1/sqrt(theta) approximately nu >= 10^{15} GeV, which comes from the absence of sidereal variations between the Cs and Hg atomic clocks