## Final Report Summary - NUCLEAREFT (Nuclear Physics from Quantum Chromodynamics)

The project NuclearEFT addresses one of the key challenge in nuclear physics, namely quantitative description of low-energy nuclear structure and dynamics based on Quantum Chromodynamics (QCD), the fundamental theory of the strong interactions. To achieve this goal we exploit the nonrelativistic nature of the problem, which allows one to describe nuclear dynamics in the framework of the Schroedinger equation for A nucleons, and employ chiral effective field theory (EFT) to derive nuclear forces and currents in a systematic and model-independent way in harmony with the symmetries of QCD. The project thus focuses on (i) the development of high-precision nuclear forces and (ii) advancing few-body methods to solve the A-body problem.

We have developed a new generation of nucleon-nucleon (NN) forces up to fifth order in the chiral expansion, which represents the state of the art in the field. We have formulated and validated a novel approach to estimating the theoretical uncertainty from the truncation of the chiral expansion, which is applicable to any observable and does not rely on cutoff variation. These developments open up new perspective for precision calculations in few- and many-nucleon systems and are especially relevant for ongoing efforts towards understanding the three-nucleon force (3NF), a current frontier in nuclear physics.

We put forward the theory of 3NF by completing the derivation of the fourth-order and most of the fifth-order contributions in chiral EFT. The resulting 3NF is being implemented by the recently formed Low Energy Nuclear Physics International Collaboration (LENPIC) to calculate the structure and reactions of light nuclei.

Several important accomplishments have been achieved in nuclear lattice simulations carried out within the Nuclear Lattice Effective Field Theory Collaboration. This method utilizes a discretized formulation of chiral EFT, in which nucleons are treated as point-like particles on a discrete Euclidean space-time lattice. It provides access to properties of nuclei and nuclear matter by performing Monte Carlo simulations. We have succeeded to perform the first ab initio calculation of the Hoyle state of 12C, which plays a crucial role in the 4He burning of stars heavier than our sun, and to unravel the structure of the low-lying states in 12C in terms of alpha-clusters. We have studied the robustness of the life-essential condition of the proximity of the Hoyle state to the triple-alpha threshold against variations of the quark mass and the fine structure constant. Shifts of the order of 2-3% were found to be not detrimental to the development of life. We have calculated the low-energy states of 16O and performed the first ab initio calculations of alpha-alpha scattering.

An important frontier in nuclear chiral dynamics is related to conceptual issues which concern nonperturbative renormalization of the Schrooedinger equation. Here, we proposed a new, renormalizable approach based on the manifestly Lorentz-invariant effective Lagrangian, which allowed us to completely remove the ultraviolet cutoff. We used this new method to calculate NN scattering observables, their quark mass dependence and electromagnetic form factors of 2H. Further, we have developed an alternative approach which unites the advantages of chiral EFT and dispersion relations. Both proposed methods are expected to bring advantages when extending these studies to scattering of strange baryons.

Other important achievements include, but are not limited to, the development of local NN interactions which allowed us, for the first time, to carry out Quantum Monte Carlo simulations for light nuclei and neutron matter within chiral EFT, establishing new approaches to chiral extrapolations based on resonance saturation and low-energy theorems, predictions for neutral pion photoproduction off 3H and 3He, theoretical studies of electroweak few-body reactions, pion production in NN collisions, nuclear parity violation and extensions of chiral EFT to higher energies.

We have developed a new generation of nucleon-nucleon (NN) forces up to fifth order in the chiral expansion, which represents the state of the art in the field. We have formulated and validated a novel approach to estimating the theoretical uncertainty from the truncation of the chiral expansion, which is applicable to any observable and does not rely on cutoff variation. These developments open up new perspective for precision calculations in few- and many-nucleon systems and are especially relevant for ongoing efforts towards understanding the three-nucleon force (3NF), a current frontier in nuclear physics.

We put forward the theory of 3NF by completing the derivation of the fourth-order and most of the fifth-order contributions in chiral EFT. The resulting 3NF is being implemented by the recently formed Low Energy Nuclear Physics International Collaboration (LENPIC) to calculate the structure and reactions of light nuclei.

Several important accomplishments have been achieved in nuclear lattice simulations carried out within the Nuclear Lattice Effective Field Theory Collaboration. This method utilizes a discretized formulation of chiral EFT, in which nucleons are treated as point-like particles on a discrete Euclidean space-time lattice. It provides access to properties of nuclei and nuclear matter by performing Monte Carlo simulations. We have succeeded to perform the first ab initio calculation of the Hoyle state of 12C, which plays a crucial role in the 4He burning of stars heavier than our sun, and to unravel the structure of the low-lying states in 12C in terms of alpha-clusters. We have studied the robustness of the life-essential condition of the proximity of the Hoyle state to the triple-alpha threshold against variations of the quark mass and the fine structure constant. Shifts of the order of 2-3% were found to be not detrimental to the development of life. We have calculated the low-energy states of 16O and performed the first ab initio calculations of alpha-alpha scattering.

An important frontier in nuclear chiral dynamics is related to conceptual issues which concern nonperturbative renormalization of the Schrooedinger equation. Here, we proposed a new, renormalizable approach based on the manifestly Lorentz-invariant effective Lagrangian, which allowed us to completely remove the ultraviolet cutoff. We used this new method to calculate NN scattering observables, their quark mass dependence and electromagnetic form factors of 2H. Further, we have developed an alternative approach which unites the advantages of chiral EFT and dispersion relations. Both proposed methods are expected to bring advantages when extending these studies to scattering of strange baryons.

Other important achievements include, but are not limited to, the development of local NN interactions which allowed us, for the first time, to carry out Quantum Monte Carlo simulations for light nuclei and neutron matter within chiral EFT, establishing new approaches to chiral extrapolations based on resonance saturation and low-energy theorems, predictions for neutral pion photoproduction off 3H and 3He, theoretical studies of electroweak few-body reactions, pion production in NN collisions, nuclear parity violation and extensions of chiral EFT to higher energies.