Semilocal momentum-space regularized chiral two-nucleon potentials up to fifth order

Abstract: We introduce new semilocal two-nucleon potentials up to fifth order in the chiral expansion. We employ a simple regularization approach for the pion-exchange contributions which (i) maintains the long-range part of the interaction, (ii) is implemented in momentum space and (iii) can be straightforwardly applied to regularize many-body forces and current operators. We discuss in detail the two-nucleon contact interactions at fourth order and demonstrate that three terms out of fifteen used in previous calculations can be eliminated via suitably chosen unitary transformations. The removal of the redundant contact terms results in a drastic simplification of the fits to scattering data and leads to interactions which are much softer (i.e. more perturbative) than our recent semilocal coordinate-space regularized potentials. Using the pion-nucleon low-energy constants from matching pion-nucleon Roy-Steiner equations to chiral perturbation theory, we perform a comprehensive analysis of nucleon-nucleon scattering and the deuteron properties up to fifth chiral order and study the impact of the leading F-wave two-nucleon contact interactions which appear at sixth order. The resulting chiral potentials lead to an outstanding description of the proton-proton and neutron-proton scattering data from the self-consistent Granada-2013 database below the pion production threshold, which is significantly better than for any other chiral potential. For the first time, the chiral potentials match in precision and even outperform the available high-precision phenomenological potentials, while the number of adjustable parameters is, at the same time, reduced by about ~40%. Last but not least, we perform a detailed error analysis and, in particular, quantify for the first time the statistical uncertainties of the fourth- and the considered sixth-order contact interactions.

• The paper develops semilocal momentum-space regularized chiral NN potentials up to fifth order, streamlining the formulation by eliminating redundant contact terms.
• The study rigorously tests the potentials against the Granada-2013 database, achieving an outstanding fit for neutron-proton and proton-proton scattering data.
• The method preserves long-range pion exchange and maintains perturbative behavior, enhancing computational efficiency in many-body nuclear calculations.

Analysis of Semilocal Momentum-Space Regularized Chiral Two-Nucleon Potentials

The paper by P. Reinert, H. Krebs, and E. Epelbaum presents a comprehensive analysis of semilocal momentum-space regularized chiral two-nucleon potentials up to the fifth order in the chiral expansion. This study involves the development of a new family of nucleon-nucleon (NN) interactions intended to address the complexities and limitations associated with higher chiral orders and cut-off dependencies while maintaining simplicity in implementation for nuclear many-body physics applications.

The authors introduce a momentum-space regularization framework to manage pion-exchange contributions, which are a crucial component of the nucleon-nucleon potential in chiral effective field theory (EFT). The work is built upon previous developments in chiral expansions up to N$^4$LO, but with marked improvements to ensure that the regularization technique preserves the long-range nature of pion-induced interactions. This is particularly achieved by modifying the propagators of the exchanged pions, thereby maintaining their physical long-range attributes and structural properties even within a high-degree cut-off environment.

One salient point made in the study is the identification and treatment of redundant contact interactions at the fourth order of the chiral expansion. The authors determine that three of the fifteen originally used terms can be removed through unitary transformations without impacting physical observables. This observation potentially simplifies the computational framework and reduces the computational overhead of fitting the potential to empirical data.

The capability of the potential to converge effectively at high chiral orders is meticulously tested against the Granada-2013 database, one of the most precise NN scattering databases available. Through this rigorous methodology, the paper concludes that N$^4$LO potentials provide an outstanding fit for both neutron-proton (np) and proton-proton (pp) experimental observations, notably outperforming older models and comparable nonlocal NN potentials in terms of precision. This family of potentials not only reduces the number of adjustable parameters by approximately 40% compared to phenomenological potentials but also demonstrates small statistical uncertainties in extracted low-energy constants (LECs). This reduction brings significant computational efficiency while satisfying a high degree of accuracy—a considerable achievement in nuclear interaction modeling.

A crucial aspect explored in this study is the perturbative nature of the NN interactions, assessed through the Weinberg eigenvalue analysis. The outcomes suggest that the introduced semilocal momentum-space regularized potentials can maintain perturbativeness while cutting down on artifacts arising from high-momentum regularization, enabling more accurate predictions extending into the many-body domain of nuclear physics.

Speculating upon potential ramifications, this robust methodological advancement may equip researchers with a refined tool for exploring many-body and multi-nucleon interactions, paving the way for applications that previously faced limitations due to complexities rooted in chiral theory formulations at high orders. Furthermore, it enhances the theoretical underpinnings accessible for deducing nuclear structures and scattering with higher reliability and efficiency.

In conclusion, this work is positioned to significantly impact future advances in high-precision nuclear physics, providing a methodology that combines rigorous theoretical consistency with computational expedience. This positions it as a noteworthy candidate for inclusion in widespread computational frameworks and anticipated experimental validations. Future work may explore extending these strategies to further simplify three-body force calculations and implement them in the study of nuclear reactions and few- to many-body systems.