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

TL;DR

This paper uses dispersive analysis to study gamma-gamma to D D-bar reactions, confirming a D D-bar bound state below threshold and clarifying the nature of the X(3860) resonance.

Contribution

It introduces a dispersive, model-independent approach to analyze D D-bar production, confirming a bound state and providing new insights into the X(3860) resonance.

Findings

Confirmed a D D-bar bound state below threshold at 3695 MeV.

Found no evidence of the broad X(3860) resonance as a pole.

Demonstrated consistency with experimental data and lattice predictions.

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.