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

Abstract

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 $σ$ 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 $D^\ast Dπ$ 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 ($Λ\sim 6$ GeV or $β\sim 6$ GeV$^2$). In contrast, there probably exists a loosely bound S-wave $B\bar{B}^\ast$ molecular state. Once produced, such a molecular state would be rather stable since its dominant decay mode is the radiative decay through $B^\ast\to B γ$. Experimental search of these states will be very interesting.