We present a method for efficiently finding solutions of Lüscher’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 $J^P=1^{-}$ and $1^{+}$ scattering in several coupled channels.

• Received 26 January 2020
• Accepted 11 May 2020

DOI:https://doi.org/10.1103/PhysRevD.101.114505

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Published by the American Physical Society