Remarks on non-perturbative three--body dynamics and its application to the $KK\bar{K}$ system

Abstract

A formalism is discussed that allows for a straightforward treatment of the relativistic three-body problem while keeping the correct analytic structure. In particular it is demonstrated that sacrificing covariance for analyticity can be justified by the hierarchy of different contributions in the spirit of an effective field theory. For definiteness the formalism is applied to the $KK\bar{K}$ system allowing for the emergence of the $a_0(980)$ and the $f_0(980)$ as hadronic molecules. For simplicity all inelastic channels are switched off.

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• Pole position of the $a_1(1260)$ resonance in a three-body unitary framework
• A simple alternative to the Breit-Wigner distribution
• The charge and mass symmetry breaking in the $KK\bar{K}$ system
• Global Data-Driven Determination of Baryon Transition Form Factors
• Constraining the $DD{D}^{\ast }$ three-body bound state via the $Z_c(3900)$ pole
• Three-body final state interactions in $B^{+}\to D\bar{D}{K}^{+}$ decays
• Scattering Theory