Efficient solution of the multichannel Lüscher determinant condition through eigenvalue decomposition
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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
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2470-0029
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Science and Technology Facilities Council (ST/R002452/1)
Science and Technology Facilities Council (ST/R00689X/1)
Science and Technology Facilities Council (ST/J005673/1)
Science and Technology Facilities Council (ST/K00333X/1)
Science and Technology Facilities Council (ST/L000636/1)
Science and Technology Facilities Council (ST/M007065/1)
STFC (ST/M007073/1)
Science and Technology Facilities Council (ST/P000673/1)
STFC (ST/T00049X/1)
STFC (ST/T000694/1)