Spectrum of light nuclei in a finite volume

TL;DR

This paper investigates how finite volume effects influence light nuclei energies in lattice QCD calculations, using optimized stochastic variational methods and EFT extrapolations to understand boundary condition impacts.

Contribution

It introduces optimized computational techniques for few-body nuclear systems in finite volumes and evaluates the applicability of L"uscher formulas for multi-nucleon systems.

Findings

Finite volume effects significantly impact light nuclei energies.

L"uscher formulas are effective but have limitations for multi-nucleon systems.

Optimized stochastic variational method enables accurate finite volume calculations.

Abstract

Lattice quantum chromodynamics calculations of multi-baryon systems with physical quark masses would start a new age of ab initio predictions in nuclear physics. Performed on a finite grid, such calculations demand extrapolation of their finite volume numerical results to free-space physical quantities. Such extraction of the physical information can be carried out fitting effective field theories (EFTs) directly to the finite-volume results or utilizing the L\"uscher free-space formula or its generalizations for extrapolating the lattice data to infinite volume. To understand better the effect of periodic boundary conditions on the binding energy of few nucleon systems we explore here light nuclei with physical masses in a finite box and in free space. The stochastic variational method is used to solve the few-body systems. Substantial optimizations of the method are introduced to enable efficient calculations in a periodic box. With the optimized code, we perform accurate calculations of light nuclei $A \le 4$ within leading order pionless EFT. Using L\"uscher formula for the two-body system, and its generalization for 3- and 4-body systems, we examine the box effect and explore possible limitations of these formulas for the considered nuclear systems.