2022/08/22 by Andrew W. Jackura, Jackura, Andrew W. · 1 citation
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Phenomenology (hep-ph) #High-Energy Particle Collisions Research #Nuclear Theory (nucl-th) #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions
paper · pdf · doi:10.48550/arxiv.2208.10587
openalex publication_date 2022/08/22 · openalex created_date 2022/08/27 · openalex updated_date 2026/07/28
Two methodologies have been presented in the literature which connect relativistic three-particle scattering amplitudes with lattice QCD spectra -- the ``relativistic effective field theory'' approach and the ``finite-volume unitarity'' method. While both methods have been shown to be equivalent in various works, it has not been shown how to arrive at the relativistic effective field theory results directly from S matrix unitarity. In this work, we provide a simple proof of the relativistic effective field theory form of the scattering equations directly from unitarity. Motivated by the finite-volume unitarity approach, we then postulate a set of quantization conditions which relate the finite-volume energy spectra to the K matrices which drive the short-distance physics in the scattering equations, obtaining all previously known results for three identical particles. This work also presents new relations which provide a new pathway to generalize the results to arbitrary systems.