<italic>Ab initio</italic> calculations with relativistic chiral forces in nuclear physics

Nuclear ab initio calculations, which aim to describe the structure and properties of atomic nuclei starting from the nucleon-nucleon interactions in free space, represent a major frontier in contemporary nuclear theory. Understanding nuclear forces, infinite nuclear matter, and finite nuclei within a unified framework has remained a central challenge in nuclear physics for decades. While most ab initio studies employ nonrelativistic Schrödinger-equation frameworks, this paper offers a relativistic perspective.Relativistic Brueckner-Hartree-Fock (RBHF) theory is one of the most important ab initio methods in the relativistic framework, where the saturation properties of nuclear matter could be described satisfactorily by considering two-body forces. This success in describing the nuclear equation of state using two-body forces marks a significant advantage. In recent years, RBHF theory has achieved great success in providing a unified description of nuclear matter and atomic nuclei. However, the predictive power and theoretical foundation of this success have been constrained by the nature of the underlying nuclear interactions. The realistic nuclear forces currently used in existing RBHF theories are based on the phenomenological meson-exchange Bonn potential, which lacks a direct connection to quantum chromodynamics and cannot be systematically improved. This impasse has been bridged by the development of chiral effective field theory (χEFT). As the low-energy effective theory of QCD, χEFT can provide order-by-order refined chiral nuclear forces needed in ab initio studies. Recently, significant progress has been made in constructing the relativistic chiral forces based on the covariant chiral effective field theory, enabling an accurate description of nucleon-nucleon scattering phase shifts. This paper briefly reviews the RBHF theory based on relativistic chiral forces and showcases a series of calculations performed with the relativistic leading-order (LO) chiral forces. We systematically present results for neutron-proton scattering phase shifts, the equation of state of symmetric nuclear matter, and binding energy per nucleon and charge radius of Ca isotopes. The performance of the LO relativistic chiral force is remarkably promising. It achieves a quantitative agreement with the neutron-proton scattering data up to laboratory energies of 300 MeV in S-waves, and a good description is also observed in channels such as 3P0 and 3D1 up to 100 MeV. The calculated saturation point of symmetric nuclear matter, along with the binding energies and charge radii of 40Ca, agrees reasonably well with experimental data, significantly improving the “Coester Line”. These results demonstrate that the relativistic approach, employing a leading-order chiral force with only four low-energy constants and no three-nucleon forces, can capture the most important dynamics and offer a complementary pathway to address longstanding challenges in nuclear ab initio studies. Future work will naturally proceed to higher orders in the chiral expansion and include consistent three-nucleon forces, promising even greater precision and a more fundamental understanding of nuclear phenomena.