Meson-meson interactions and resonances in the ’t Hooft model

Abstract

We studied meson-meson interactions using the 't Hooft model, which represents QCD in 1 + 1 dimensions and assumes a large number of colors ͑N c ͒. The dominant interactions in this large N c limit are generated by quark exchange. Our results show that QCD in 1 + 1 dimensions allows the realization of a constituent-type quark model for the mesons and generates a scalar ""-like meson-meson resonance, whose effective coupling and mass are determined by the underlying QCD dynamics. These results suggest an interpretation of the lightest scalar mesons as qqqq systems.

Meson-meson scattering in two-dimensional QCD

“…Therefore, we will simply suppress those meson exchange diagrams, and concentrate on the contact interaction diagrams to search for the exotic states. The numerical studies reveal that we do not observe any Breit-Wigner resonance, in contradiction with what is found in [18]. Nevertheless, we do observe the near-threshold enhancement in the contact interaction amplitude in some scattering channels.…”

“…We remark that the meson-meson scattering has already been analyzed within the 't Hooft model by Batiz, Pena and Stadler more than a decade ago [18]. Those authors claim to discover a Breit-Wigner peak, which is interpreted as the a σ-like tetraquark state.…”

“…[20]. We end this section by commenting on the preceding calculation of meson-meson scattering by Batiz et al [18]. One of the problems is that their Feynman rules seems not to distinguish the outgoing quark and the incoming quark for a meson vertex.…”

“…Notice diagrams with crossed gluons will be suppressed by 1/N c , therefore the rainbow approximation becomes exact in the large N c limit. The Dyson-Schwinger equation then reads [16,18]…”

“…Those authors claim to discover a Breit-Wigner peak, which is interpreted as the a σ-like tetraquark state. Unfortunately, the authors of [18] appear to neglect some important class of Feynman diagrams also of the order 1/N c , and consequently, their expressions are in fact gauge-dependent and sensitive to the infrared regulator. Therefore, we feel obligated to revisit the meson-meson scattering in the 't Hooft model from more consistent approach, and consider all possible types of flavor textured possessed by the incident and outgoing mesons.…”