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

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 $f_0(500)("\sigma "),f_0(980),\rho (700),K_0^{\ast }(700)("\kappa ")$, and $K^{\ast }(892)$ 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.

Comments: 27 pages, 11 figures, version accepted for publication