Two-loop corrections and predictability on orbifold

TL;DR

This paper investigates two-loop quantum corrections in a five-dimensional orbifold $\

Contribution

It identifies the emergence of higher-derivative divergence terms at two loops and discusses their impact on propagator poles and physical quantity extraction.

Findings

Divergences for $(p^2)^2$ terms appear at two loops.

Counterterms introduce two poles in propagators.

Physical quantities require a large UV cutoff.

Abstract

We study quantum loop corrections to two-point functions and extraction of physical quantities in a five-dimensional $\phi^4$ 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.