Spectra and Scattering of Light Lattice Nuclei from Effective Field Theory

TL;DR

This paper employs effective field theory to predict properties of light nuclei from lattice QCD data at unphysical pion masses, establishing correlations and analyzing structural changes.

Contribution

It introduces a method to connect lattice QCD results at unphysical pion masses with nuclear properties using effective field theory, including predictions and correlation analyses.

Findings

Predicted neutron-deuteron scattering lengths at two pion masses.

Calculated alpha-particle binding energies at those pion masses.

Established correlations similar to Phillips and Tjon lines.

Abstract

An effective field theory is used to describe light nuclei, calculated from quantum chromodynamics on a lattice at unphysically large pion masses. The theory is calibrated at leading order to two available data sets on two- and three-body nuclei for two pion masses. At those pion masses we predict the quartet and doublet neutron-deuteron scattering lengths, and the alpha-particle binding energy. For $m_\pi=510~$MeV we obtain, respectively, $^4a_{\rm nD}=2.3\pm 1.3~$fm, $^2a_{\rm nD}=2.2\pm 2.1~$fm, and $B_{\alpha}^{}=35\pm 22~$MeV, while for $m_\pi=805~$MeV $^4a_{\rm nD}=1.6\pm 1.3~$fm, $^2a_{\rm nD}=0.62\pm 1.0~$fm, and $B_{\alpha}^{}=94\pm 45~$MeV are found. Phillips- and Tjon-like correlations to the triton binding energy are established. Higher-order effects on the respective correlation bands are found insensitive to the pion mass. As a benchmark, we present results for the physical pion mass, using experimental two-body scattering lengths and the triton binding energy as input. Hints of subtle changes in the structure of the triton and alpha particle are discussed.