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

TL;DR

This paper examines the conceptual foundations of renormalization in effective field theories for two nucleons, highlighting scheme dependence limitations and the importance of cutoff choices for maintaining low-energy theorems.

Contribution

It clarifies the scheme dependence in renormalization and demonstrates the impact of cutoff limits on low-energy theorems within an effective field theory framework.

Findings

Renormalization scheme dependence cannot be fully eliminated at finite order.

Finite cutoff preserves low-energy theorems, while removing the cutoff violates them.

Removing the cutoff yields finite results but conflicts with EFT principles.

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, 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 $\Lambda$ as long as it is chosen of the order of the hard scale in the problem. Removing the cutoff by taking the limit $\Lambda \to \infty$ 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.