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We study the coupling of a tetraquark system to an exchanged meson-mesonchannel, using a pure gluonic theory based four-quark potential {\em matrix}model which is known to fit well a large number of data points for latticesimulations of different geometries of a four-quark system. We find that ifthis minimal-area-based potential matrix replaces the earlier used simpleGaussian form for the gluon field overlap factor $f$ in its off-diagonal terms,the resulting $T$-matrix and phase shifts develop an angle dependence whosepartial wave analysis reveals $D$ wave and higher angular momentum componentsin it. In addition to the obvious implications of this result for themeson-meson scattering, this new feature indicates the possibility of orbitalexcitations influencing properties of meson-meson molecules through apolarization potential. We have used a formalism of the resonating groupmethod, treated kinetic energy and overlap matrices on model of the potentialmatrix, but decoupled the resulting complicated integral equations through theBorn approximation. In this exploratory study we have used a quadraticconfinement and not included the spin-dependence; we also used theapproximation of equal constituent quark masses.

Dynamical effects of QCD in $q^2 \bar{q}^{2}$ systems