Two-loop corrections and predictability on orbifold

We study quantum loop corrections to two-point functions and extraction of physical quantities in a five-dimensional ${\varphi }^4$ theory on an orbifold. At two-loop level, we find that divergence for quartic derivative terms of $(p^2{)}^2$ appear as Lagrangian terms in the bulk. The counterterms are needed and these terms make propagators have two poles. With this effect taken into account, corrections to masses are derived. We show that for extraction of physical quantities for two-point functions an ultraviolet cutoff must be orders of magnitude larger compared to a compactification scale. Even higher derivative corrections at higher loop levels are also discussed.