Chiral interactions up to next-to-next-to-next-to-leading order and nuclear saturation

TL;DR

This paper introduces a Monte Carlo framework for perturbative calculations of infinite nuclear matter using chiral interactions up to N$^3$LO, enabling systematic uncertainty estimates and improved convergence.

Contribution

The authors develop a versatile Monte Carlo method for chiral nuclear interactions, allowing systematic order-by-order calculations and uncertainty quantification in nuclear matter studies.

Findings

Good many-body convergence up to fourth order.

Successful simultaneous fit to triton and saturation properties.

Reduced theoretical uncertainties at N$^3$LO.

Abstract

We present an efficient Monte Carlo framework for perturbative calculations of infinite nuclear matter based on chiral two-, three-, and four-nucleon interactions. The method enables the incorporation of all many-body contributions in a straightforward and transparent way, and makes it possible to extract systematic uncertainty estimates by performing order-by-order calculations in the chiral expansion as well as the many-body expansion. The versatility of this new framework is demonstrated by applying it to chiral low-momentum interactions, exhibiting a very good many-body convergence up to fourth order. Following these benchmarks, we explore new chiral interactions up to next-to-next-to-next-to-leading order (N$^3$LO). Remarkably, simultaneous fits to the triton and to saturation properties can be achieved, while all three-nucleon low-energy couplings remain natural. The theoretical uncertainties of nuclear matter are significantly reduced when going from next-to-next-to-leading order to N$^3$LO.