Dispersive analysis of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi>γ</mml:mi><mml:mi>γ</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>D</mml:mi><mml:mover accent="true"><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mrow></mml:mover></mml:math> data and the confirmation of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"><mml:mi>D</mml:mi><mml:mover accent="true"><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mrow></mml:mover></mml:math> bound state
Oleksandra Deineka, Igor Danilkin, Marc Vanderhaeghen
Abstract
In this paper, we present a data-driven analysis of the γ γ → D + D − and γ γ → D 0 D ¯ 0 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 c 2 ( 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 / ψ D 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.