We investigate renormalization of chiral nuclear forces in the coupled channel of ${}^3{S}_1-{}^3{D}_1$ 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 ${}^3{P}_0$, 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 ${}^3{P}_0$ in [Peng et al., Phys. Rev. C 110, 054001 (2024)] and apply it to ${}^3{S}_1-{}^3{D}_1$. 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.

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• Effective field theory
• Nuclear forces
• Nucleon-nucleon interactions