Relativistic-invariant formulation of the NREFT three-particle quantization condition

Abstract

A three-particle quantization condition on the lattice is written down in a manifestly relativistic-invariant form by using a generalization of the non-relativistic effective field theory (NREFT) approach. Inclusion of the higher partial waves is explicitly addressed. A partial diagonalization of the quantization condition into the various irreducible representations of the (little groups of the) octahedral group has been carried out both in the center-of-mass frame and in moving frames. Furthermore, producing synthetic data in a toy model, the relativistic invariance is explicitly demonstrated for the three-body bound state spectrum.

38 pages, 7 figures

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• Complex scaling in finite volume
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• Efficient few-body calculations in finite volume
• Form factors of the $\rho$ meson from effective field theory and the lattice
• Rediscovery of Numerical Lüscher's Formula from the Neural Network