Two-loop Higgs mass in supersymmetric Kaluza-Klein theories

We perform an explicit two-loop computation of the Higgs mass in a five-dimensional supersymmetric theory compactified on the orbifold S1/Z2, with superpotential localized on a fixed-point brane and supersymmetry broken in the bulk of the extra dimension by Scherk-Schwarz boundary conditions. At one-loop, the Higgs mass is finite and proportional to 1/R2, R being the radius of the extra dimension. The two-loop corrections contain finite (∝1/R2) and linearly divergent (∝Λ/R) terms, where Λ is the cutoff of the five-dimensional theory. The divergent terms are cancelled by diagrams containing one-loop wave-function renormalization counterterms, i.e., by linear threshold effects of Yukawa (and gauge) couplings, at the scale 1/R. As a result there is no counterterm for the Higgs mass, which is finite and calculable to the considered order