Criterion for the Existence of the $G(3900)$ Resonance

Abstract

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. The criterion illustrated by $G(3900)$ can be extended to other hadronic systems, offering a powerful tool to identify genuine resonances.