UV and IR divergences within Dimensional Regularization in Non-Commutative theories and Phenomenological Implications
arXiv:hep-ph/0208225 · doi:10.1016/S0370-2693(02)03150-7
Abstract
Using Dimensional Regularization (DR) for some two-point functions of a prototype Non-Comutative (NC) ϕ^4 scalar theory in 4-dimensions, we explictly 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/p0p obtained from DR is reproduced by PVR in the limit where the UV cut-off Λis 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/\sqrtθ\approx ν\geq 10^{15} GeV for NCQCD and 10^{10} GeV for NCQED, which comes from the absence of sidereal variations between the Cs and Hg atomic clocks.
5 pages latex file, espcrc2.sty, 2 eps.fig Revised and extended version