Chiral EFT allows one to derive nuclear interactions by means of a perturbative expansion in powers of low momenta. The order of the expansion determines the accuracy of the resulting theoretical predictions. Two-nucleon forces have already been worked out to the fifth order, which is sufficient to achieve a sub-percent accuracy for two-nucleon scattering. For 3NFs, only the dominant third-order contributions have so far been taken into account. This severely limits the currently achievable accuracy of chiral EFT applications to nuclei heavier than the deuteron. The main hurdle preventing inclusion of higher-order corrections to the 3NF is related to spurious short-range contributions. As a low-energy approximation, chiral EFT cannot describe the short-distance dynamics between pions and nucleons, which is parametrized by universal coefficients called low-energy constants (LECs). When deriving the 3NF expressions, the undesired short-range contributions must be removed in a procedure known as regularization. However, the regularization techniques commonly applied to nuclear interactions violate the chiral symmetry, a key ingredient of the theory and a fundamental feature of QCD. This problem is also relevant for exchange currents and limits the accuracy of chiral EFT applications to electroweak nuclear reactions.
To solve this problem, we have developed a new methodology by merging chiral EFT with the smoothing technique known as the gradient flow. For this purpose, the pion field is extended by introducing, in addition to space-time coordinates, the artificial flow "time". Its evolution in the flow time is governed by a variant of the heat equation, which is written in a way that is consistent with chiral and gauge symmetries of the Standard Model. The flow time acts as a cutoff and allows one to gradually remove short-distance pion-nucleon dynamics without violating any symmetries. This new methodology has already been successfully applied to derive, for the first time, consistently regularized subleading long-range contributions to the 3NF.
We have also addressed important conceptual issues of chiral EFT, performed ab initio calculations of nuclear structure and reactions, developed a new methodology to tame the computational limitations of Monte Carlo nuclear lattice simulations caused by the fermion sign problem and established a novel technique to facilitate the interplay between chiral EFT and lattice QCD.
