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 $D^0{\bar{D}}^{\ast 0}$ 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${}^2$). 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 $B^{\ast }\to B\gamma$. Experimental search of these states will be very interesting.

Comments: 11 pages, 7 figures, 9 tables. The version to appear in EPJC