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

TL;DR

This study investigates whether the X(3872) particle can be explained as a molecular state of D mesons, finding that standard parameters do not support this interpretation, but B meson molecules are plausible and potentially stable.

Contribution

The paper provides a dynamical calculation including pion and sigma meson exchanges, challenging the molecular interpretation of X(3872) with realistic parameters and suggesting B meson molecules as candidates.

Findings

X(3872) unlikely to be a D meson molecule with standard coupling and cutoff

Bound states require unrealistically large coupling or cutoff values

B meson molecules could be loosely bound and stable, decaying radiatively

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 $\sigma$ 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.