Nuclear Theory from First Principles

Project Information

NuclearTheory

Grant agreement ID: 885150

DOI

10.3030/885150

EC signature date 27 November 2020

Start date 1 November 2021

End date 31 October 2027

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 2 499 206,00

EU contribution

€ 2 499 206,00

Coordinated by

RUHR-UNIVERSITAET BOCHUM
Germany

Periodic Reporting for period 2 - NuclearTheory (Nuclear Theory from First Principles)

Reporting period: 2023-05-01 to 2024-10-31

Summary of the context and overall objectives of the project

Nuclear physics aims to understand the origin and properties of complex structures such as atomic nuclei from Quantum Chromodynamics (QCD), the underlying quantum field theory of the strong interaction. It addresses some of the Big Science Questions including the origin of the elements, the limits of nuclear stability, the search for physics beyond the Standard Model, and the physics of neutron stars. Answering these key questions requires a reliable theory of nuclear structure and reactions. The currently most promising approach to this ambitious goal uses a systematically improvable low-energy approximation of QCD, called chiral effective field theory (EFT), to describe nuclear interactions in combination with ab initio methods for solving the many-body problem.

Recently, the PI and his group made a major breakthrough by using chiral EFT to develop high-precision two-nucleon interactions that describe all mutually compatible experimental data on neutron-proton and proton-proton scattering below the pion production threshold. This demonstrates that chiral EFT can be developed into a precision tool without compromising rigor and consistency.

In addition to the dominant pairwise interactions between protons and neutrons, three-nucleon forces (3NFs) are known to make important contributions to nuclear structure and dynamics. However, despite decades of intense research, 3NFs remain to be poorly understood and represent the main bottleneck for precision nuclear physics. This project aims at finally solving the long-standing 3NF challenge and development of accurate and precise nuclear interactions in the framework of chiral EFT, determined solely by the chiral symmetry of QCD and few-nucleon data. This milestone will be achieved through a combination of advanced and novel theoretical methods and groundbreaking computational techniques. The resulting Hamiltonian will be used in large-scale ab initio calculations of nuclear structure and reactions. In addition, a new EFT-based methodology will be developed to extend the emerging first-principles lattice-QCD calculations beyond the lightest nuclei. The ultimate goal of these studies is to establish a rigorous, fully microscopic and predictive approach to nuclear physics that is firmly rooted in the symmetries of QCD.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

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.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

The new methodology already developed in this project opens the way to derive consistently regularized 3NFs and nuclear currents beyond the leading contributions. We will complete the calculation of the sub-leading (i.e. fourth-order) contributions to the 3NF and study their implications by calculating nucleon-deuteron scattering and selected properties of light and medium-mass nuclei.

Based on the experience with the two-nucleon force, it is expected that an accurate description of the 3NF can only be achieved at fifth order of the EFT expansion. At this level of accuracy, the 3NF will depend on more than a dozen of LECs, which will have to be determined from experimental data on nucleon-deuteron scattering (and possibly from light nuclei). This computationally challenging task will be addressed using cutting edge innovative approaches such as eigenvector continuation and other reduced basis methods. These studies are expected to provide a solution to the long-standing 3NF challenge in nuclear physics by establishing the Hamiltonian that would simultaneously describe the existing two- and three-nucleon scattering data. We also plan to use the gradient flow formulation of chiral EFT to advance our understanding of the electroweak nuclear currents and reactions significantly beyond the state of the art. Together, these key developments have the potential to transform nuclear physics and can open up new perspectives for accurate and reliable description of nuclear structure and reactions.

Gradient flow method for the two-nucleon interaction mediated by pion exchange

State-of-the-art calculations of two- and three-nucleon scattering compared with experimental data