A coupled-channel formalism for three-body final state interaction

From dispersion relation approach, a formalism that describes final state interaction among three particles in a coupled-channel system is presented. Different representations of coupled-channel three-body formalism for spinless particles in both initial and final states are derived.

Molecular state NΞ in the coupled-channel formalism

The relativistic six-quark equations for the molecule NΞ are found in the dispersion relation technique. The relativistic six-quark amplitudes of the hexaquark including the quarks of three flavors (u, d, s) are calculated. The pole of these amplitudes determines the mass of NΞ state M = 2252 MeV. The binding energy is equal to 3 MeV.

NEGATIVE PARITY TETRAQUARKS WITH THE OPEN CHARM

The relativistic four-quark equations are found in the framework of coupled-channel formalism. The dynamical mixing of the meson–meson states with the four-quark states is considered. The four-quark amplitudes of the negative parity tetraquarks including the quarks of three flavors (u, d, s) and the charmed quark are constructed. The poles of these amplitudes determine the masses of tetraquarks. The mass values of low-lying tetraquarks with the spin-parity JP = 0-, 1-, 2-, 3- are calculated.

S-WAVE BOTTOM TETRAQUARKS

The relativistic four-quark equations are found in the framework of coupled-channel formalism. The dynamical mixing of the meson–meson states with the four-quark states is considered. The four-quark amplitudes of the tetraquarks, including u, d, s, and bottom quarks, are constructed. The poles of these amplitudes determine the masses and widths of S-wave bottom tetraquarks.