$X(3915)$ as a $D_s \bar D_s$ bound state

Abstract

We suggest that the observed properties of the charmoniumlike resonance $X(3915)$ can possibly be explained if it is an $S-$wave molecular bound state of $D_s \bar D_s$ meson pair with binding energy about 18\,MeV. In particular, the decays of $X(3915)$ to pairs of non-strange $D$ mesons are suppressed and proceed at a rate comparable to that of the decay $X(3915) \to \omega J/\psi$, whose branching fraction can be as large as about 0.3. Other major types of decay of $X(3915)$ with a comparable (or slightly smaller) rate are the transition $X(3915) \to \eta \eta_c$ and the decays into light hadrons due to the annihilation of the $c \bar c$ quark pair. The existence of a bound state should lead to an enhancement in the spectrum of the invariant mass for the $D_s \bar D_s$ near threshold in $B$ decays, e.g. in $B \to K D_s \bar D_s$ which enhancement can be tested experimentally.