High-quality two-nucleon potentials up to fifth order of the chiral expansion (1703.05454v2)

Abstract: We present NN potentials through five orders of chiral effective field theory ranging from leading order (LO) to next-to-next-to-next-to-next-to-leading order (N4LO). The construction may be perceived as consistent in the sense that the same power counting scheme as well as the same cutoff procedures are applied in all orders. Moreover, the long-range parts of these potentials are fixed by the very accurate pi-N LECs as determined in the Roy-Steiner equations analysis by Hoferichter, Ruiz de Elvira and coworkers. In fact, the uncertainties of these LECs are so small that a variation within the errors leads to effects that are essentially negligible, reducing the error budget of predictions considerably. The NN potentials are fit to the world NN data below pion-production threshold of the year of 2016. The potential of the highest order (N4LO) reproduces the world NN data with the outstanding chi^2/datum of 1.15, which is the highest precision ever accomplished for any chiral NN potential to date. The NN potentials presented may serve as a solid basis for systematic ab initio calculations of nuclear structure and reactions that allow for a comprehensive error analysis. In particular, the consistent order by order development of the potentials will make possible a reliable determination of the truncation error at each order. Our family of potentials is non-local and, generally, of soft character. This feature is reflected in the fact that the predictions for the triton binding energy (from two-body forces only) converges to about 8.1 MeV at the highest orders. This leaves room for three-nucleon-force contributions of moderate size.

Overview of High-Quality Two-Nucleon Potentials up to Fifth Order of the Chiral Expansion

This paper presents a comprehensive paper on the construction of nucleon-nucleon ($NN$) potentials up to the fifth order of the chiral effective field theory (ChEFT). This development spans from leading order (LO) to next-to-next-to-next-to-next-to-leading order (N$^4$LO). The methodology is consistent, employing a uniform power counting scheme and cutoff procedure across all orders.

A significant detail of this research is its utilization of precise pion-nucleon low-energy constants (LECs), obtained through Roy-Steiner equations analysis conducted by Hoferichter, Ruiz de Elvira, and colleagues. The extreme accuracy of these LECs diminishes the error margin significantly, lending credibility to the predictions made by these potentials.

The $NN$ potentials are fitted against an extensive dataset of global $NN$ scattering data beneath the pion-production threshold as of 2016. The paper reports that the highest order potential (N$^4$LO) achieves an unprecedented precision, with a $\chi^2$/datum of 1.15, marking the finest accuracy attained for chiral $NN$ potentials.

The theoretical framework developed in this paper provides a solid base for systematic ab initio calculations of nuclear structure and reactions which, importantly, include exhaustive error analysis. A notable conclusion from this work is the consistent order-by-order development of the potentials, enabling reliable determination of the truncation error at each order.

Key features of the potential family described here include non-locality and a soft nature, made evident by the predictions for triton binding energy (from two-body forces alone) converging to around 8.1 MeV at higher orders. This converged presence necessitates three-nucleon-force contributions of moderate size.

Additionally, practical implications arise from the non-local, soft character of these potentials as compared to recent chiral potential constructions that are more local or semi-local. The availability of different families of chiral $NN$ potentials allows researchers to explore systematic studies addressing issues such as the radius problem and the overbinding of intermediate-mass nuclei.

Moreover, the paper discusses the intricacies involved in incorporating chiral three-body forces (3NFs). While the full potential at N$^4$LO is not immediately manageable, there exists an attempt to complete calculations for the two-pion-exchange (2PE) 3NF. This approach involves using effective LECs, derived by summing contributions from all relevant orders, establishing a pathway to incorporate crucial components of the 3NF.

The paper concludes with deliberations on uncertainty quantifications tied to experimental errors of $NN$ data, uncertainties in LECs, regulator dependence, and theoretical truncation errors. It suggests that truncation error is the dominant source of systematic uncertainty that researchers must consider, proposing methods and definitions for assessing this error reliably.

In summary, this paper demonstrates a thorough and systematic advancement in constructing chiral $NN$ potentials, emphasizing both theoretical precision and practical implementation in further nuclear calculations. Its contribution is likely to inform ongoing and future developments in nuclear theory and models.