Subtractive renormalization of the chiral potentials up to next-to-next-to-leading order in higher NN partial waves

TL;DR

This paper introduces a subtractive renormalization scheme for P-wave nucleon-nucleon scattering using chiral effective theory potentials up to NNLO, enabling high cutoff evaluations and offering insights into cutoff dependence and renormalization.

Contribution

It develops a novel subtractive renormalization method for P-wave NN scattering with chiral potentials up to NNLO, allowing high cutoff analysis and alternative renormalization using generalized scattering lengths.

Findings

Renormalization achieved via generalized NN scattering lengths.

Cutoff dependence suggests a maximum cutoff of about 1 GeV for dimensional regularization.

Spectral-function regularization delays cutoff dependence onset.

Abstract

We develop a subtractive renormalization scheme to evaluate the P-wave NN scattering phase shifts using chiral effective theory potentials. This allows us to consider arbitrarily high cutoffs in the Lippmann-Schwinger equation (LSE). We employ NN potentials computed up to next-to-next-to-leading order (NNLO) in chiral effective theory, using both dimensional regularization and spectral-function regularization. Our results obtained from the subtracted P-wave LSE show that renormalization of the NNLO potential can be achieved by using the generalized NN scattering lengths as input--an alternative to fitting the constant that multiplies the P-wave contact interaction in the chiral effective theory NN force. However, in order to obtain a reasonable fit to the NN data at NNLO the generalized scattering lengths must be varied away from the values extracted from the so-called high-precision potentials. We investigate how the generalized scattering lengths extracted from NN data using various chiral potentials vary with the cutoff in the LSE. The cutoff-dependence of these observables, as well as of the phase shifts at $T_{lab} \approx 100$ MeV, suggests that for a chiral potential computed with dimensional regularization the highest LSE cutoff it is sensible to adopt is approximately 1 GeV. Using spectral-function regularization to compute the two-pion-exchange potentials postpones the onset of cutoff dependence in these quantities, but does not remove it.