Nodal mechanism for the suppressed DD̄ decay of ψ(4040) in the Bethe-Salpeter framework

A bstract The strong decay ψ (4040) → DD̄ D D ¯ is anomalously suppressed despite ample phase space, whereas the DD̄ D D ¯ ∗ and DₛD̄ₛ D s D ¯ s channels remain sizable. In this work, we study this suppression and the associated open-charm hierarchy in the framework of the instantaneous Bethe-Salpeter equation combined with the relativistic 3 P 0 model, with the pair-creation strength fixed independently from ψ (3770) → DD̄ D D ¯ . Within this framework, we show that the suppressed DD̄ D D ¯ mode can be understood as a consequence of node-induced cancellations in the relativistic decay amplitude. The DD̄ D D ¯ amplitude is strongly reduced because the corresponding overlap integral receives comparable positive and negative contributions from different momentum regions, whereas the DD̄ D D ¯ ∗ and DₛD̄ₛ D s D ¯ s channels do not undergo the same strong cancellation. This interpretation is further supported by the pronounced sensitivity of the DD̄ D D ¯ width to the initial mass, the charged-neutral D -meson mass splitting, and the dip structure in the mass dependence of the partial width. Our results provide a dynamical explanation of the suppressed DD̄ D D ¯ mode and the core open-charm hierarchy of ψ (4040) within a conventional 3 3 S 1 charmonium picture, while the precise value of the near-vanishing DD̄ D D ¯ width remains model dependent.