Is X(3872) {\sl Really} a Molecular State?

Understand

After taking into account both the pion and sigma meson exchange potential, we have performed a dynamical calculation of the $D^0\bar{D}^{\ast0}$ system.

• The $\sigma$ meson exchange potential is repulsive from heavy quark symmetry and numerically important for a loosely bound system.
• Our analysis disfavors the interpretation of X(3872) as a loosely bound molecular state if we use the experimental $D^\ast D\pi$ coupling constant $g=0.59$ and a reasonable cutoff around 1 GeV, which is the typical hadronic scale.
• Bound state solutions with negative eigenvalues for the $D\bar{D}^\ast$ system exist only with either a very large coupling constant (two times of the experimental value) or a large cutoff ($\Lambda \sim 6$ GeV or $\beta \sim 6$ GeV$^2$).