Perturbative renormalization of chiral nuclear forces at subleading order in 3S1-3D1 channel

TL;DR

This paper studies the renormalization of chiral nuclear forces in the coupled 3S1-3D1 channel, addressing issues with artificial correlations at exceptional cutoffs and improving phase shift stability.

Contribution

It extends a solution for exceptional cutoff issues from the 3P0 channel to the coupled 3S1-3D1 channel, enhancing renormalization consistency in chiral EFT.

Findings

Reduced cutoff variation in phase shifts

Removal of artificial correlations between low-energy constants

Application of a proven method to a coupled channel

Abstract

We investigate renormalization of chiral nuclear forces in the coupled channel of 3S1-3D1 of nucleon-nucleon scattering. The one-pion exchange potential is treated nonperturbatively at leading order while subleading potentials are perturbations. Very much like the uncoupled channel of 3P0 , the singular attraction of one-pion exchange gives rise to the so-called genuine exceptional cutoffs, where artificial correlations between subleading contact operators emerge and they result in ill-defined values of the low-energy constants. To address this issue we follow the solution proposed for 3P0 in Ref. [1] and apply it to 3S1-3D1 . The truncation uncertainty of an effective field theory allows certain degrees of freedom in choosing renormalization conditions, or fitting schemes of the low-energy constants. By exploiting this freedom near the exceptional cutoffs, we are able to remove the said correlations. A much mitigated cutoff variation of the phase shifts, which is acceptable to the power counting, is thus obtained.