Investigation of the meson-meson interaction

Abstract

In the framework of the quark delocalization color screening model, we investigate the meson-meson interaction in the four-quark system with the three flavors $u, d$, and $s$. The calculation of the effective potentials of all the $S$-wave states shows that for most states the interaction between two vector mesons is attractive, the one between a pseudoscalar meson and a vector meson is repulsive or weakly attractive, and the one between two pseudoscalar mesons is always repulsive. However, there are still some exceptions. The interaction of the $IJ=00\phantom{\rule{4pt}{0ex}}\ensuremath{\pi}\ensuremath{\pi}$ channel is attractive, while the one of the $IJ=02\phantom{\rule{4pt}{0ex}}\ensuremath{\phi}\ensuremath{\phi}$ channel is repulsive. So it is difficult to use the $S$-wave $\ensuremath{\phi}\ensuremath{\phi}$ state to explain the $X(2239)$ at present calculation. The $S$-wave $\ensuremath{\rho}\ensuremath{\rho}$ states are more likely to be resonance states, which are worthy of investigating in future work. The study of the contribution of each interaction term shows that both the one-gluon exchange and the kinetic energy interaction are important in the interaction between two mesons. The study of the variation of the delocalization parameter indicates that the contribution of the kinetic energy relates to the intermediate-range attraction mechanism in the quark delocalization color screening model (QDCSM), which is achieved by the quark delocalization.