Loop corrections in a solvable UV-finite model and its effective field theory

TL;DR

This paper investigates how low-energy effective Lagrangians can lead to non-renormalizability in loop diagrams within a UV-finite scalar model, and demonstrates the matching of effective and full theory results at low energies.

Contribution

It provides a detailed analysis of non-renormalizability in an exactly solvable UV-finite model and derives a closed-form effective Lagrangian to all orders in perturbation theory.

Findings

Effective theories exhibit non-renormalizability due to low-energy approximations.

Matching effective and full theory results is possible at low energies.

A closed-form expression for the effective Lagrangian is derived.

Abstract

We examine some features of the non-renormalizability induced through the use of low-energy effective Lagrangians in loop diagrams, in the context of a scalar model which is ultraviolet finite and partially soluble. In this framework, one can directly demonstrate the mechanism leading to the non-renormalizability of the effective theory. This behavior is generated by approximations that are applicable at low energies but are generally inappropriate for evaluating loop diagrams that contain virtual high-energy particles. However, it is explicitly shown that one can match the results obtained in the renormalized effective theory with those found in the full theory at low energy. We argue that the infrared sectors of these theories are inherently similar, independently of the matching procedure. A closed-form expression is obtained, to leading order in the energy expansion, for the complete effective Lagrangian at all orders in perturbation theory. The model may be useful to clarify certain aspects of realistic, but more complex, effective field theories.