Dispersive analysis of the $\gamma \gamma \to D\bar{D}$ data and the confirmation of the $D\bar{D}$ bound state

Abstract

In this paper, we present a data-driven analysis of the $\gamma \gamma \to D^{+}{D}^{-}$ and $\gamma \gamma \to D^0{\bar{D}}^0$ reactions from threshold up to 4.0 GeV in the $D\bar{D}$ invariant mass. For the $S$-wave contribution, we adopt a partial-wave dispersive representation, which is solved using the $N/D$ ansatz. The left-hand cuts are accounted for using the model-independent conformal expansion. The $D$-wave ${\chi }_{c2}(3930)$ state is described as a Breit-Wigner resonance. The resulting fits are consistent with the data on the invariant mass distribution of the $e^{+}{e}^{-}\to J/\psi D\bar{D}$ process. Performing an analytic continuation to the complex $s$-plane, we find no evidence of a pole corresponding to the broad resonance $X(3860)$ reported by the Belle Collaboration. Instead, we find a clear bound state below the $D\bar{D}$ threshold at $\sqrt{s_B}=3695(4)$ MeV, confirming the previous phenomenological and lattice predictions.

Comments: 8 pages, 4 figures