Non-relativistic bound states in a finite volume

We derive general results for the mass shift of bound states with angular momentum ℓ≥1 in a periodic cubic box in two and three spatial dimensions. Our results have applications to lattice simulations of hadronic molecules, halo nuclei, and Feshbach molecules. The sign of the mass shift can be related to the symmetry properties of the state under consideration. We verify our analytical results with explicit numerical calculations. Moreover, we comment on the relations connecting the effective range parameter, the binding momentum of a given state and the asymptotic normalization coefficient of the corresponding wave function. We give explicit expressions for this relation in the shallow binding limit. - Highlights: ► We consider bound states with angular momentum in a cubic periodic box. ► We derive the mass shift of the states in two and three spatial dimensions. ► The sign of the shift is related to the symmetry properties of the states. ► Our results can be applied to lattice simulations of molecular states.