UV and IR divergences within Dimensional Regularization in Non-Commutative theories and phenomenological implications

Using Dimensional Regularization (DR) for some two-point functions of a prototype Non-Commutative (NC) φ4 scalar theory in 4 dimensions, we explicitly analyze, to one-loop, the IR and UV divergences of non-planar diagrams having quadratic divergences and compare to the case of the Pauli–Villars cut-off regularization (PVR). We also note that the IR structure 1/p∘p obtained from DR is reproduced by PVR in the limit where the UV cut-off Λ 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 from low-energy data is 1/θ≈ν⩾1015 GeV for NCQCD and 1010 GeV for NCQED, which comes from the absence of sidereal variations between the Cs and Hg atomic clocks.