Spectrum of light nuclei in a finite volume

Lattice quantum chromodynamics calculations of multibaryon 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 Lüscher 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≤4 within leading-order pionless EFT. Using Lüscher formula for the two-body system, and its generalization for three- and four-body systems, we examine the box effect and explore possible limitations of these formulas for the considered nuclear systems.