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Abstract

Abstract About 18 years ago, the BABAR and the Belle Collaborations reported evidence for a new $$c\bar{c}$$ c c ¯ structure near $$3900~\textrm{MeV}$$ 3900 MeV in $$e^{+}e^{-} \rightarrow D\bar{D}$$ e + e - → D D ¯ , triggering debate over whether it represents a genuine hadronic state or arises from interference effects and the opening of the $$D^{*}\bar{D}$$ D ∗ D ¯ threshold. The issue remained unsettled until 2024, when BESIII, with an enlarged $$e^{+}e^{-} \rightarrow D\bar{D}$$ e + e - → D D ¯ sample, confirmed the presence of the G (3900) structure, reviving discussion of its nature. Although it has been proposed as a P -wave $$D\bar{D}^{*}$$ D D ¯ ∗ molecular state, no consensus has emerged, and interference effects remain a plausible explanation. In this Letter, we show that analyzing the $$e^{+}e^{-}\rightarrow D\bar{D}$$ e + e - → D 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.