Evolved Chiral Hamiltonians at the Three-Body Level and Beyond

Based on the fundamental symmetries of QCD, chiral effective field theory (EFT) provides two- (NN), three- (3N), four- (4N), and many-nucleon interactions in a consistent and systematic scheme. Recent developments to construct chiral NN+3N interactions at different chiral orders and regularizations enable exciting nuclear structure investigations as well as a quantification of the fundamental uncertainties resulting from the chiral expansion and regularization. We present the complete toolchain to employ the present and future chiral NN, 3N, and 4N interactions in nuclear structure calculations and emphasize technical developments in the three- and four-body space, such as the similarity renormalization group (SRG), the frequency conversion, and the transformation to the JT-coupled scheme. We study the predictions of the chiral NN+3N interactions in ab initio nuclear structure calculations with the importance-truncated no-core shell model and coupled-cluster approach. We demonstrate that the inclusion of chiral 3N forces improves the overall agreement with experiment for excitation energies of p-shell nuclei and it qualitatively reproduces the systematics of nuclear binding energies throughout the nuclear chart up to heavy tin isotopes. In this context it is necessary to introduce truncations in the three-body model space and we carefully analyze their impact and confirm the reliability of the reported results. The SRG evolution induces many-nucleon forces that generally cannot be included in the calculations and constitute a major limitation for the applicability of SRG-evolved chiral forces. We study the origin and effect of the induced many-nucleon forces and propose a modification of the interaction, which suppresses the induced beyond-3N forces. This enables applications of the chiral interactions far beyond the mid-p shell. Furthermore, we test alternative formulations of SRG generators aiming to prevent the induced many-body forces from the outset. The extension of the SRG evolution and matrix-element treatment to the four-body space allows for an explicit inclusion of induced and initial 4N forces. We discuss the truncations and limitations in the four-body space and present first ab initio nuclear structure calculations for p-shell nuclei with induced 4N forces. By changing the parameters of the local 3N force we perform a comprehensive sensitivity analysis for nuclear spectra in the p shell that provides constraints for the construction of chiral interactions. Moreover, we identify certain correlations that prevent an accurate description of the experimental results by an adjustments of the local 3N force at N2LO. We report first results obtained with a next-generation NN+3N interaction at N3LO and compare the spectra obtained with several chiral interactions at different chiral orders, varying the regulator function and cutoff. These studies present a first step towards a systematic uncertainty quantification for the chiral forces and we show that p-shell spectroscopy is a sensitive diagnostic for chiral 3N interactions