Abstract
Three-body states are critical to the dynamics of many hadronic resonances. We show that lattice QCD calculations have reached a stage where these states can be accurately resolved. We perform a calculation over a wide range of parameters and find all states below inelastic threshold agree with predictions from a state-of-the-art phenomenological formalism. This also illustrates the reliability of the formalism used to connect lattice QCD results to infinite volume physics. Our calculation is performed using three positively charged pions, with different lattice geometries and quark masses.
Highlights
It is important to understand hadron interactions in terms of quark-gluon dynamics as they emerge from QCD
As we increase η we find energies appearing below the inelastic threshold in irreps where, at smaller elongations, no energy levels exist
We make use of lattices elongated in a single spatial direction, and boosts along the same axis, to capture additional states below the inelastic threshold
Summary
Three-hadron systems present the hurdle in this quest, primarily for resonances with final state decays to three particles. One such example is the Roper resonance Nð1440Þ1=2þ which couples strongly to ππN. Jefferson Lab, ELSA, MAMI and other facilities have experimental programs dedicated to studying excited baryons [7,8,9] making the need for three body analyses critical. Another such example is the a1ð1260Þ resonance, which decays to ρπ and σπ intermediate states before its final state of three pions. E.g., GlueX at Jefferson Lab, searching for exotic states, there is a demand for theoretical determinations of the QCD spectrum below and in the region where such exotic states may lie
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