More on volume dependence of spectral weight functions

Spectral weight functions are easily obtained from two-point correlation functions, and they might be used to distinguish single-particle from multiparticle states in a finite-volume lattice calculation, a problem crucial for many lattice QCD simulations. In previous studies, it has been shown that the spectral weight function for a broad resonance shares the typical volume dependence of a two-particle scattering state, i.e. proportional to 1/L3 in a large cubic box of size L, while the narrow resonance case requires further investigation. In this paper, a generalized formula is found for the spectral weight function which incorporates both the narrow and broad resonance cases. Within Luescher's formalism, it is shown that the volume dependence of the spectral weight function exhibits a single-particle behavior for an extremely narrow resonance and a two-particle behavior for a broad resonance. The corresponding formulas for both A1+ and T1- channels are derived. The potential application of these formulas in the extraction of resonance parameters are also discussed.