Hadron-hadron potentials coupled to quark degrees of freedom for X(3872)

To study the internal structure of the exotic hadron $X(3872)$, considering the coupled-channel potential between quarks and hadrons is necessary because $X(3872)$ is regarded as a mixture state of $c\bar{c}$ and $D^0{\bar{D}}^{\ast 0}$. In this work, we construct the hadron-hadron potentials coupled to the quark channel and study the properties of the $D^0{\bar{D}}^{\ast 0}$ potentials for $X(3872)$. In particular, we compare various local approximations by focusing on the scattering phase shifts.