Abstract
Strong three-body interactions above threshold govern the dynamics of many exotics and conventional excited mesons and baryons. Three-body finite-volume energies calculated from lattice QCD promise an ab-initio understanding of these systems. We calculate the three-$\pi^+$ spectrum unraveling the three-body dynamics that is tightly intertwined with the $S$-matrix principle of three-body unitarity and compare it with recent lattice QCD results. For this purpose, we develop a formalism for three-body systems in moving frames and apply it numerically.
Highlights
The dynamics of three-body systems above threshold play a key role in our understanding of strong forces
The ππN channels play a significant role for other excited baryons and their description needs a quantitative understanding of three-body dynamics
Often no correlations on low-energy constants (LECs) are quoted in the literature which leads to an uncontrolled overestimation of the prediction error
Summary
The dynamics of three-body systems above threshold play a key role in our understanding of strong forces. This leads to a discrete eigenvalue spectrum in contrast to the continuous spectral density of scattering states in the infinite volume These finite-volume effects are determined by hadron interactions and they offer a key to understanding these interactions arising from quark-gluon dynamics. We compare the results of a recently developed infinite-volume mapping technique [8] with new finite-volume energy eigenvalues [9] These data are calculated with multipion operators allowing for the reliable extraction of energy eigenvalues, above threshold and in different irreducible representation, providing, for the first time, access to three-body dynamics from first principles. One of the problems in the lattice QCD calculation of energies for channels where three-body states are relevant is the need for many-hadron type operators to reliably determine the spectrum, as demonstrated, e.g., in Ref. There is no reason to exclude the relative πþ-isobar D-wave which will turn out to be important
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