Regulator constraints for the perturbative renormalizability of attractive triplets

Abstract

Nuclear effective field theory organizes the calculation of observables as a power series in terms of the ratio of soft and hard momentum scales. The rigorous implementation of this idea requires a mixture of perturbative and non-perturbative methods: on the one hand, nuclei are bound states that require the iteration of part of the nuclear potential, while on the other corrections that are small in the aforementioned power series should be perturbative in principle. Recently, it has been noted that these corrections are not cutoff independent as there are a set of exceptional cutoffs for which the couplings cannot be determined, as exemplified with the subleading order $^3P_0$ phase shifts in two-nucleon scattering. Yet, here it is shown by means of concrete calculations that exceptional cutoffs are a regulator-dependent feature. There exists a well-defined limit when the cutoff is removed, which implies that not every regulator choice (understood not only as the regulator itself, but in tandem with renormalization conditions) is acceptable within the effective field theory framework. The practical implications are minor, though: except if one is trying to explicitly probe the cutoff independence of the theory, most sensible regulator and cutoff choices are compatible with the renormalized limit within truncation errors.