One-Loop order effects from one extra universal dimension on λϕ 4 theory

Abstract

The self-interacting λ ϕ 4 scalar field theory is the prototype in the study of basic renormalisation issues in quantum field theories. In this paper we explore the one-loop order divergent impact to this theory from one universal extra dimension, , to the self-energy, four point vertex and the beta function. Such effects come as an infinite number of UV divergences corresponding to an infinite superposition of excited KK particles around the loop. We show that dimensional regularisation is adequate enough to control all of them in terms of the product of the one dimensional inhomogeneous Epstein zeta function times the gamma function. From the analytical properties of these functions, the UV divergences are extracted and the counterterms defined; the latter turn out to be of canonical dimension four at the Lagrangian level. We use both, the MS-scheme and a mass-dependent subtraction scheme to remove divergences. Only the latter manifestly satisfy the decoupling theorem.