Short range πJ/ψ-DDbar* interaction by the quark exchange diagram

Exotic hadrons reported in the heavy flavor sector have been one of the interesting topics in hadron and nuclear physics. Especially near the thresholds, the appearance of the hadron-hadron bound states, called hadronic molecules, is expected. On the other hand, an existence of thresholds induces the cusp structure which may be misinterpreted as a physical resonance.

The hadron interaction is an important ingredient in the hadron scattering.
Recently,  the Lattice QCD simulation by HALQCD indicates the importance of the πJ/ψ-DDbar* potential, given by the charm quark (hadron) exchange process, but the mechanism is not understood yet.
The D meson exchange potential can be considered. However, the interaction range is about 0.1 fm, which is smaller than the hadron size.

We introduce the Born-order quark exchange to describe the potential.
The meson-meson scattering is described,
where the meson wavefunctions and the quark interaction are given by the constituent quark model
In this study, the cross section and the energy dependent potential
for the πJ/ψ-DDbar* process are obtained.
We find that the hyperfine (spin-spin) and linear potential terms of the quark interaction plays an important role,
while the coulomb potential plays a minor role.