Nuclear potentials are known to exhibit a considerable degree of scheme dependence. For one- and two-pion exchange nucleon-nucleon (NN) potentials, unitary ambiguities start showing up at the level of the leading relativistic corrections to the dominant static contributions. However, for the three-pion exchange potential, scheme-dependent contributions are expected to appear already at the static level. Here we analyze the leading and subleading chiral $3\pi$-exchange NN potentials using the method of unitary transformation. In line with the expectations, our results for selected classes of contributions differ from those obtained by Kaiser using $S$-matrix matching. We present analytical expressions for the $3\pi$-exchange potential, which are off-shell consistent with the interactions used by the Bochum group, and discuss the numerical importance of the observed differences.

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• Chiral perturbation theory
• Nuclear forces