3-body quantization condition in a unitary formalism

Abstract

Unitarity identifies all power-law finite-volume effects and is, therefore, the crucial S-matrix principle for a mapping between experimental results and those of Lattice QCD calculations. In this contribution we review how 3-body unitarity constrains the form of the 3-body scattering amplitude parametrized by the tower of isobars. The result is discretized and projected to the irreducible representations of the cubic group, leading to a fully relativistic 3-body quantization condition. The latter is used to deduce the finite-volume excited level spectrum of the ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ system, which agrees nicely with the available lattice results by the NPLQCD collaboration.

Talk presented at the 36th Annual International Symposium on Lattice Field Theory, 22-28 July 2018, Michigan State University, East Lansing, Michigan, USA

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