Abstract
We present the expansion of the two-pion exchange three-nucleon potential (TPE-3NP) to chiral order ${q}^{4}$, which corresponds to a subset of all possibilities at this order and is based on the $\ensuremath{\pi}N$ amplitude at $\mathcal{O}({q}^{3})$. Results encompass both numerical corrections to strength coefficients of previous $\mathcal{O}({q}^{3})$ terms and new structures in the profile functions. The former are typically smaller than 10% whereas the latter arise from either loop functions or nonlocal gradients acting on the wave function. The influence of the new TPE-3NP over static and scattering three-body observables has been assessed and found to be small, as expected from perturbative corrections.
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