Higher Derivative Operators as loop counterterms in one-dimensional field theory orbifolds

Abstract

Using a 5D N=1 supersymmetric toy-model compactified on S_1/(Z_2 x Z_2'), with a ``brane-localised'' superpotential, it is shown that higher (dimension) derivative operators are generated as one-loop counterterms to the (mass)^2 of the zero-mode scalar field, to ensure the quantum consistency of the model. Such operators are just a result of the compactification and integration of the bulk modes. They are relevant for the UV momentum scale dependence of the (mass)^2 of the zero-mode scalar field, regarded as a Higgs field in more realistic models. While suppressed for a small compactification radius R, these operators can affect the predictive power of models with a large value for R. A general method is also provided for a careful evaluation of infinite sums of 4D divergent loop-integrals (of Feynman diagrams) present in field theory orbifolds. With minimal changes, this method can be applied to specific orbifold models for a simple evaluation of their radiative corrections and the overall divergences.