How (not) to renormalize integral equations with singular potentials in effective field theory

TL;DR

This paper explores the challenges and methods of renormalizing integral equations with singular potentials in low-energy effective field theories of strong interactions, highlighting conceptual issues and providing practical examples.

Contribution

It clarifies the connection between perturbative and non-perturbative renormalization in effective theories, with detailed analysis and examples involving singular potentials and the Skornyakov-Ter-Martyrosian equation.

Findings

Analysis of renormalization methods for singular potentials

Examples illustrating effective field theory constructions

Revisiting the renormalization of the Skornyakov-Ter-Martyrosian equation

Abstract

We discuss the connection between the perturbative and non-perturbative renormalization and related conceptual issues in the few-nucleon sector of the low-energy effective field theory of the strong interactions. General arguments are supported by examples from effective theories with and without pions as dynamical degrees of freedom. A quantum mechanical potential with explicitly specified short- and long-range parts is considered as an "underlying fundamental theory" and the corresponding effective field theory potential is constructed. Further, the problem of the effective field theoretical renormalization of the Skornyakov-Ter-Martyrosian equation is revisited.