Eur. Phys. J. A (2009) 41: 341-354
https://doi.org/10.1140/epja/i2009-10833-3

Regular Article - Theoretical Physics

Regularization, renormalization and “peratization” in effective field theory for two nucleons

¹ Forschungszentrum Jülich, Institut für Kernphysik (Theorie) and Jülich Center for Hadron Physics, D-52425, Jülich, Germany
² Helmholtz-Institut für Strahlen- und Kernphysik (Theorie) and Bethe Center for Theoretical Physics, Universität Bonn, D-53115, Bonn, Germany
³ Institut für Kernphysik, Johannes Gutenberg-Universität, D-55099, Mainz, Germany
⁴ High Energy Physics Institute, Tbilisi State University, 0186, Tbilisi, Georgia

^* e-mail: e.epelbaum@fz-juelich.de

Received: 27 May 2009
Accepted: 15 June 2009
Published online: 23 July 2009

Abstract

We discuss conceptual aspects of renormalization in the context of effective field theories for the two-nucleon system. It is shown that, contrary to widespread belief, the renormalization scheme dependence of the scattering amplitude can only be eliminated up to the order the calculations are performed. We further consider an effective theory for an exactly solvable quantum mechanical model which possesses a long- and short-range interaction to simulate pionful effective field theory. We discuss the meaning of low-energy theorems in this model and demonstrate their validity in calculations with a finite cutoff as long as it is chosen of the order of the hard scale in the problem. Removing the cutoff by taking the limit ∞ yields a finite result for the scattering amplitude but violates the low-energy theorems and is, therefore, not compatible with the effective field theory framework.