Dispersive analysis of the γγ → DD¯ data and the confirmation of the DD¯ bound state

Abstract

In this paper, we present a data-driven analysis of the γγ → D+ D− and γγ → D0D¯ 0 reactions from threshold up to 4.0 GeV in the DD¯ 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 χc2(3930) state is described as a BreitWigner resonance. The resulting fits are consistent with the data on the invariant mass distribution of the e+e− → J/ψ DD¯ 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 DD¯ threshold at √sB = 3695(4) MeV, confirming the previous phenomenological and lattice predictions.