Efficient solution of the multichannel Lüscher determinant condition through eigenvalue decomposition
Antoni J. Woss, David J. Wilson, Jo Dudek
Abstract
We present a method for efficiently finding solutions of L\"uscher's quantization condition, the equation which relates two-particle scattering amplitudes to the discrete spectrum of states in a periodic spatial volume of finite extent such as that present in lattice QCD. The approach proposed is based on an eigenvalue decomposition in the space of coupled-channels and partial-waves, which proves to have several desirable and simplifying features that are of great benefit when considering problems beyond simple elastic scattering of spinless particles. We illustrate the method with a toy model of vector-vector scattering featuring a high density of solutions, and with an application to explicit lattice QCD energy level data describing ${J}^{P}={1}^{\ensuremath{-}}$ and ${1}^{+}$ scattering in several coupled channels.