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

摘要

We discuss conceptual aspects of renormalization in the context of effective field theories for thetwo-nucleon system. It is shown that, contrary to widespread belief, the renormalization scheme dependenceof the scattering amplitude can only be eliminated up to the order the calculations are performed. Wefurther consider an effective theory for an exactly solvable quantum mechanical model which possessesa long- and short-range interaction to simulate pionful effective field theory. We discuss the meaning oflow-energy theorems in this model and demonstrate their validity in calculations with a finite cutoff A aslong as it is chosen of the order of the hard scale in the problem. Removing the cutoff by taking the limitA→∞ 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.