We introduce new semilocal two-nucleon potentials up to fifth order in thechiral expansion. We employ a simple regularization approach for thepion-exchange contributions which (i) maintains the long-range part of theinteraction, (ii) is implemented in momentum space and (iii) can bestraightforwardly applied to regularize many-body forces and current operators.We discuss in detail the two-nucleon contact interactions at fourth order anddemonstrate that three terms out of fifteen used in previous calculations canbe eliminated via suitably chosen unitary transformations. The removal of theredundant contact terms results in a drastic simplification of the fits toscattering data and leads to interactions which are much softer (i.e. moreperturbative) than our recent semilocal coordinate-space regularizedpotentials. Using the pion-nucleon low-energy constants from matchingpion-nucleon Roy-Steiner equations to chiral perturbation theory, we perform acomprehensive analysis of nucleon-nucleon scattering and the deuteronproperties up to fifth chiral order and study the impact of the leading F-wavetwo-nucleon contact interactions which appear at sixth order. The resultingchiral potentials lead to an outstanding description of the proton-proton andneutron-proton scattering data from the self-consistent Granada-2013 databasebelow the pion production threshold, which is significantly better than for anyother chiral potential. For the first time, the chiral potentials match inprecision and even outperform the available high-precision phenomenologicalpotentials, while the number of adjustable parameters is, at the same time,reduced by about ~40%. Last but not least, we perform a detailed error analysisand, in particular, quantify for the first time the statistical uncertaintiesof the fourth- and the considered sixth-order contact interactions.
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