We studied meson-meson interactions using the ’t Hooft model, which represents QCD in $1+1$ dimensions and assumes a large number of colors $\left(N_c\right)$. 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 “$\sigma$”-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 $q\overline{q}q\overline{q}$ systems.

• Received 16 September 2003

DOI:https://doi.org/10.1103/PhysRevC.69.035209