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

Abstract

In this paper, we present a data-driven analysis of the γγ → D + D − and γγ → D 0 D0 reactions from threshold up to 4.0 GeV in the D 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 χ 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 − → J/ψD 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 D threshold at √ s B = 3695(4) MeV, confirming the previous phenomenological and lattice predictions.

Hadron Spectroscopy with Lattice QCD

“…Coupled D D − D s Ds scattering with I = 0 rendered the expected charmonium resonances χ c0 (2P ) and χ c2 (2P ), as well as two unconventional scalar states just below D D and D s Ds thresholds [77]. The D D bound state was not claimed by experiment, but predicted in [78] and found in the analysis of experimental data for example in [79]. The state slightly below D s Ds shares similar features as experimental X(3915) as it lies just below D s Ds and has a very small/negligible coupling to D D. Future lattice simulations should aim to go beyond several simplifications of this study listed in Section 5 of [77].…”