Eur. Phys. J. A (2018) 54: 186
https://doi.org/10.1140/epja/i2018-12632-1

Regular Article - Theoretical Physics

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

¹ Institut für Theoretische Physik II, Fakultät für Physik und Astronomie, Ruhr-Universität Bochum, 44780, Bochum, Germany
² Institute for Theoretical and Experimental Physics, B. Cheremushkinskaya 25, 117218, Moscow, Russia
³ Institute for Advanced Simulation, Institut für Kernphysik and Jülich Center for Hadron Physics, Forschungszentrum Jülich, D-52425, Jülich, Germany
⁴ Tbilisi State University, 0186, Tbilisi, Georgia
⁵ Helmholtz Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, D-53115, Bonn, Germany

^* e-mail: jgegelia@hotmail.com

Received: 22 January 2018
Accepted: 5 October 2018
Published online: 2 November 2018

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.