Characterization of resonances using finite size effects

TL;DR

This paper introduces two novel methods to extract resonance widths from finite volume spectra in 1+1 dimensional quantum field theories, validated through numerical tests and with potential extension to higher dimensions.

Contribution

It develops a consistent framework for analyzing narrow resonances in finite volume, combining Luscher's corrections with new methods validated by numerical data.

Findings

Excellent agreement between methods and data confirms validity.

Framework accurately accounts for finite size effects and mass shifts.

Potential for extension to 3+1 dimensions with accurate spectra.

Abstract

We develop methods to extract resonance widths from finite volume spectra of 1+1 dimensional quantum field theories. Our two methods are based on Luscher's 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 1+1 dimensions, the extension to physical (3+1) space-time dimensions appears straightforward, given sufficiently accurate finite volume spectra.