Efficient solution of the multi-channel L\"uscher determinant condition through eigenvalue decomposition
Abstract
We present a method for efficiently finding solutions of L\"uscher's quantisation 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 and scattering in several coupled channels.
Cite
@article{arxiv.2001.08474,
title = {Efficient solution of the multi-channel L\"uscher determinant condition through eigenvalue decomposition},
author = {Antoni J. Woss and David J. Wilson and Jozef J. Dudek},
journal= {arXiv preprint arXiv:2001.08474},
year = {2020}
}