Higher Derivative Operators as Counterterms in Orbifold Compactifications

In the context of 5D N = 1 supersymmetric models compactified on S₁/Z₂ or S₁/(Z₂×Z₂‧) orbifolds and with brane-localized superpotential, higher derivative operators are generated radiatively as one-loop counterterms to the mass of the (brane or zero mode of the bulk) scalar field. It is shown that the presence of such operators which are brane-localised is not related to the mechanism of supersymmetry breaking considered (F-term, discrete or continuous Scherk-Schwarz breaking) and initial supersymmetry does not protect against the dynamical generation of such operators. Since in many realistic models the scalar field is commonly regarded as the Higgs field, and the higher derivative operators seem a generic presence in orbifold compactifications, we stress the importance of these operators for solving the hierarchy problem.