A unitary coupled-channel three-body amplitude with pions and kaons

TL;DR

This paper develops a three-body coupled-channel amplitude model incorporating pions and kaons, respecting unitarity, to improve the analysis of resonances and scattering processes in particle physics.

Contribution

It introduces a novel three-body coupled-channel framework with unequal masses and multiple isospin channels, including key resonances, for more accurate scattering amplitude calculations.

Findings

Inclusion of key resonances like $f_0(500)$ and $K^*(892)$ in the model.

Demonstration of numerical implementation with production amplitudes.

Discussion of methods for evaluating the amplitude at physical momenta.

Abstract

Three-body dynamics above threshold is required for the reliable extraction of many amplitudes and resonances from experiment and lattice QCD. The S-matrix principle of unitarity can be used to construct dynamical coupled-channel approaches in which three particles scatter off each other, re-arranging two-body subsystems by particle exchange. This paper reports the development of a three-body coupled-channel, amplitude including pions and kaons. The unequal-mass amplitude contains two-body S- and P-wave subsystems ("isobars") of all isospins, $I=0,\,1/2,\,1,\, 3/2, \, 2$, and it also allows for transitions within a given isobar. The $f_0(500)\, ("\sigma"),\,f_0(980),\,\rho(700), K_0^*(700)\,("\kappa")$, and $K^*(892)$ resonances are included, apart from repulsive isobars. Different methods to evaluate the amplitude for physical momenta are discussed. Production amplitudes for $a_1$ quantum numbers are shown as a proof of principle for the numerical implementation.