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

Understand

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.