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

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 Λ as long as it is chosen of the order of the hard scale in the problem. Removing the cutoff by taking the limit Λ → ∞ 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.

Low-energy theorems for nucleon-nucleon scattering atMπ=450MeV

“…[24], we have tested this approach by predicting the effective range parameters for S-wave NN scattering in the spin-triplet and the spin-singlet channels, see also Refs. [25][26][27][28][29][30] for earlier studies along this line. Further, we generalized the LETs to unphysical pion masses and applied the resulting approach to selected lattice-QCD results.…”

“…[24], see also Refs. [25][26][27][28][29][30] for related earlier studies. In this section we formulate the main idea of the LETs from a somewhat different perspective as compared to Ref.…”

“…[10], which will be referred to as BBSvK, where the expansion of the nuclear force around the chiral limit was employed, see, however, Ref. [28] for a criticism. This approach was used in Ref.…”

StrangenessS=−1hyperon-nucleon scattering in covariant chiral effective field theory

“…For other works on renormalization of chiral nuclear forces, see Refs. [34][35][36][37][38][39][40][41][42][43][44].…”

Chiral effective field theory for nuclear forces: Achievements and challenges

“…The lack of order-by-order convergence and discrepancies in lower partial-waves demonstrate that the potential should not be used beyond the limits of the effective theory [44] (see Ref. [45] for a related discussion). The conclusion then is that cutoffs should be limited to Λ Λ χ (but see also Ref.…”