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

TL;DR

The paper tackles RG-invariance challenges in chiral NN forces within the coupled-channel $^{3}\!S_{1}$-$^{3}\!D_{1}$ channel by treating the one-pion exchange nonperturbatively at LO and subleading potentials as perturbations. It identifies genuine exceptional cutoffs (GECs) where subleading LECs become ill-defined due to regulator artifacts, extending prior work on the uncoupled $^{3}\!P_{0}$ channel. By adjusting renormalization conditions near GECs—moving the inputs $B^{(0)}$, $k_1$, and $k_2$ across several schemes—the authors remove artificial correlations and achieve finite, better-behaved N$^2$LO LECs and phase shifts. The modified strategy yields phase shifts in good agreement with Nijmegen PWA up to about $k\lesssim 300$ MeV, with controlled discontinuities within EFT uncertainties. These results demonstrate how careful renormalization choices can restore RG invariance and improve predictive reliability for coupled-channel chiral nuclear forces.

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.

Figures (10)

• Figure 1: $\mathcal{G}(\Lambda; k_1, k_2, B^{(0)})$ as a function of $\Lambda$ using Scheme I everywhere.
• Figure 2: $\mathcal{G}(\Lambda; k_1, k_2, B^{(0)})$ as a function of $\Lambda$ using the modified fitting strategy defined in Table \ref{['tab:NNLO_k1k2']}.
• Figure 3: The N$^2$LO ${{}^{3}\!{S}_{1}}$ phase shifts at $k=250$ MeV as a function of $\Lambda$. The solid lines correspond to the modified fitting strategy defined in Table \ref{['tab:NNLO_k1k2']}, and the dashed lines correspond to the original fitting strategy. The shaded bands are the background cutoff variations. See the text for more explanations.
• Figure 4: $\mathcal{G}(\Lambda; k_1, k_2, B^{(0)})$ versus $\Lambda$ for various values of $B^{(0)}$. The black solid, red dash-dotted, and blue dashed lines correspond to Scheme I, II and III, respectively.
• Figure 5: $\mathcal{G}(\Lambda; k_1, k_2, B^{(0)})$ versus $\Lambda$ for various values of $(k_1, k_2)$. The black solid, blue dashed and red dash-dotted lines correspond to Scheme I, IV and V, respectively.