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arXiv · 2407.08721

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

Yuchuan Feng·Fernando Gil·Michael Döring·Raquel Molina·Maxim Mai·Vanamali Shastry·Adam Szczepaniak
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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.

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Yuchuan Feng, Fernando Gil, Michael Döring, Raquel Molina, Maxim Mai, Vanamali Shastry, Adam Szczepaniak. 2024-07-11. A unitary coupled-channel three-body amplitude with pions and kaons. https://arxiv.org/abs/2407.08721

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