Charge-dependent nucleon-nucleon interaction at N$^3$LO in nuclear lattice effective field theory

TL;DR

This work develops a high-precision NN interaction on a lattice at N$^3$LO within nuclear lattice EFT (NLEFT), explicitly incorporating charge-independence and charge-symmetry breaking (CIB/CSB) through pion-mass splitting in OPEP, Coulomb forces, and dedicated CIB/CSB contact terms, along with the two-pion-exchange potential (TPEP). The authors implement a regulator and partial-wave decomposition, fit a comprehensive set of LECs to $np$, $pp$, and $nn$ scattering data, and extract phase shifts on the lattice via a radial basis and generalized eigenvalue problem, validating results against empirical data for $p\lesssim 200$ MeV and deuteron properties. They systematically study lattice-spacing and cutoff dependencies and assess the TPEP contribution, finding that TPEP effects can be largely absorbed by contact terms at low momentum. The resulting NN interaction provides a solid foundation for future high-precision, ab initio nuclear structure calculations with NLEFT, including light nuclei and nuclear clustering phenomena.

Abstract

The nuclear lattice effective field theory (NLEFT) is an efficient tool for solving nuclear many-body problems, which takes high-fidelity lattice chiral interactions as input and computes nuclear low-energy observables via quantum Monte Carlo techniques. In this work, we present the first next-to-next-to-next-to-leading order (N$^3$LO) chiral forces on the lattice with the isospin-breaking effects fully taken into account. We focus on both the charge-independence breaking (CIB) and charge-symmetry breaking (CSB) effects. Specifically, we include the isospin-breaking effect from the mass difference between the charged and neutral pions in the one-pion-exchange potential (OPEP), the Coulomb force for the $pp$ interaction and the contribution of two additional charge-dependent contact operators. We also explicitly incorporate the two-pion-exchange potentials which was mostly neglected in previous NLEFT calculations. With these improvements, we are able to accurately reproduce the $np$ and $pp$ scattering phase shifts up to relative momentum $p \sim 200$ MeV as well as the deuteron properties. The construction of these charge-dependent lattice nuclear forces establishes a solid foundation for future high-precision nuclear ab initio calculations within the NLEFT framework.

Figures (7)

• Figure 1: (Color online) Scattering phase shifts and mixing angles versus the relative momenta $P$ between two nucleons for the $np$ systems. The lattice spacing is set to $a = 0.99$ fm, and the momentum cutoff is set to $\Lambda = 350$ MeV. Notice that the TPEP is not included, which is consistent with the Monte Carlo simulations of the few- and many-body systems using NLEFT.
• Figure 2: (Color online) $pp$ and $nn$ scattering phase shifts for partial wave $^1S_0$. Notice that the $nn$ scattering phase shifts are not used in the fits, thus the results in right panel should be taken as a lattice prediction of the $nn$ phase shifts in partial wave $^1S_0$.
• Figure 3: (Color online) $np$ scattering phase shifts and mixing angles versus relative momentum $P$ between neutron and proton, calculated with a lattice spacing of $a = 1.97~{\rm fm}$. The momentum cutoff is fixed as $\Lambda = 350$ MeV.
• Figure 4: (Color online) $np$ phase shifts and mixing angles versus relative momentum $P$ between neutron and proton, calculated with a lattice spacing of $a = 1.64~{\rm fm}$. The momentum cutoff is fixed as $\Lambda = 350$ MeV.
• Figure 5: (Color online) $np$ phase shifts and mixing angles versus the relative momentum $P$ between neutron and proton, calculated with a lattice spacing of $a = 1.32~{\rm fm}$. The momentum cutoff is fixed as $\Lambda = 350$ MeV.