Characterization of resonances using finite size effects Original Research Article

We develop methods to extract resonance widths from finite volume spectra of image-dimensional quantum field theories. Our two methods are based on Lüscherʹs description of finite size corrections, and are dubbed the Breit–Wigner and the improved “mini-Hamiltonian” method, respectively. We establish a consistent framework for the finite volume description of sufficiently narrow resonances that takes into account the finite size corrections and mass shifts properly. Using predictions from form factor perturbation theory, we test the two methods against finite size data from truncated conformal space approach, and find excellent agreement which confirms both the theoretical framework and the numerical validity of the methods. Although our investigation is carried out in image dimensions, the extension to physical image space–time dimensions appears straightforward, given sufficiently accurate finite volume spectra.