Efficient solution of the multi-channel Lüscher determinant condition through eigenvalue decomposition
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 prop...
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| creator | Woss, Antoni J Wilson, David J Dudek, Jozef J |
| description | 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 \(J^P=1^-\) and \(1^+\) scattering in several coupled channels. |
| doi_str_mv | 10.48550/arxiv.2001.08474 |
| format | Article |
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| subjects | Channels Decomposition Eigenvalues Elastic scattering Energy levels Quantum chromodynamics |
| title | Efficient solution of the multi-channel Lüscher determinant condition through eigenvalue decomposition |
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