About 18 years ago, the BABAR and the Belle Collaborations reported evidence for a new $c\bar{ c}$ structure near $3900~\mathrm{ MeV}$ in $e^{ +}e^{ -} \to D\bar{ D}$, triggering debate over whether it represents a genuine hadronic state or arises from interference effects and the opening of the $D^{ *}\bar{ D}$ threshold. The issue remained unsettled until 2024, when BESIII, with an enlarged $e^{ +}e^{ -} \to D\bar{ D}$ sample, confirmed the presence of the $G(3900)$ structure, reviving discussion of its nature. Although it has been proposed as a $P$-wave $D\bar{ D}^{ *}$ molecular state, no consensus has emerged, and interference effects remain a plausible explanation. In this Letter, we show that analyzing the $e^{ +}e^{ -}\to D\bar{ D}$ cross section as a function of the transverse momentum of the final-state $D$ meson reveals a prominent Jacobian peak. This feature cannot be generated by interference effects alone and thus provides direct evidence for the existence of $G(3900)$. Moreover, the peak position is highly sensitive to the actual mass of $G(3900)$, offering a precise determination method. Our results further disfavor the interpretation of $G(3900)$ as a $D\bar{ D}^{ *}$ molecular state, pointing instead to alternative internal structures. The criterion illustrated by $G(3900)$ can be extended to other hadronic systems, offering a powerful tool to identify genuine resonances.
Categories: hep-ph hep-ex