Physicists Propose a Sharp Kinematic Test to Confirm the Elusive G(3900) Particle

Nearly two decades of uncertainty surrounding a mysterious particle-like structure near 3900 MeV may finally be drawing to a close. In 2007, the BABAR and Belle Collaborations reported the first hints of a new charm-quark pair structure in electron-positron collisions producing pairs of D mesons. From the beginning, physicists were divided: was this a genuine hadronic state, a new kind of matter built from a charm quark and a charm antiquark, or merely an artifact of quantum interference and the sudden opening of new decay channels? The question lingered unresolved until 2024, when the BESIII Collaboration, working with a vastly enlarged data sample of electron-positron annihilations into D meson pairs, confirmed the presence of the structure now called G(3900). Yet confirmation of its existence as a bump in a mass spectrum did not settle the deeper question of its nature, and a new theoretical study now proposes an elegant and potentially decisive experimental test.

The new analysis, published in The European Physical Journal C by Yin Huang and Xurong Chen, tackles the problem from a fresh angle. Rather than relying on the traditional method of fitting invariant mass spectra, the researchers focus on the transverse momentum of the final-state D mesons produced in electron-positron collisions. Their central insight is deceptively simple but theoretically powerful: if G(3900) is a real resonance, it must imprint a distinctive kinematic fingerprint on the angular distribution of its decay products, a fingerprint that no amount of interference between intermediate states can mimic. This fingerprint is known as a Jacobian peak, and its predicted position can be calculated with extraordinary precision from first principles.

The mathematics behind the proposal rests on the geometry of two-body decays. When a resonance of a given mass decays into a pair of D mesons, kinematics dictate that the transverse momentum of each meson cannot exceed a maximum value determined by the Källén function of the participating masses. When the cross section is re-expressed as a function of the transverse momentum rather than the emission angle, a characteristic singularity appears at this kinematic limit, producing a sharp enhancement called a Jacobian peak. For G(3900), the peak should appear at approximately 520.995 MeV for neutral D meson pairs and 504.018 MeV for charged pairs. Crucially, the position of this peak depends only on the mass of the parent resonance, not on the details of any theoretical model used to describe the production amplitudes.

This model independence is precisely what makes the proposal so compelling. The authors demonstrate that when G(3900) is treated as a genuine resonance alongside the known charmonium states psi(3686), psi(3770), psi(4040), and psi(4160), the calculated transverse momentum distribution displays a clear Jacobian peak at the predicted location. When the G(3900) contribution is removed and the observed enhancement is instead attributed entirely to interference effects and the opening of the D D* threshold, the peak vanishes completely. Because interference between intermediate states cannot produce this kinematic singularity, the presence or absence of the peak in experimental data would constitute direct evidence for or against the existence of G(3900) as a bona fide hadronic state.

The theoretical framework underpinning the study combines an effective Lagrangian approach with loop calculations that account for the opening of the D D* threshold. The coupling constants for the charmonium states are fixed from known decay widths, while other parameters are fitted to the existing body of electron-positron collision data. The authors performed a series of fits using different model assumptions, including scenarios with and without G(3900), and found that all of them describe the measured invariant mass spectra reasonably well. This degeneracy explains why nearly twenty years of fitting mass spectra have failed to settle the debate: the two-body invariant mass distribution alone simply does not contain enough information to discriminate between a genuine resonance and cleverly arranged interference effects.

Intriguingly, the analysis also sheds new light on the internal structure of G(3900). Its measured mass of about 3872.5 MeV sits remarkably close to the D D* threshold, prompting several theoretical groups to interpret it as a P-wave molecular state composed of a D meson and a D* meson bound together. The new study explores this possibility but finds that different, equally reasonable fits lead to contradictory conclusions about the molecular interpretation. In one favored fit, the ratio of the G(3900) decay width into D meson pairs to its width into electron-positron pairs appears incompatible with a molecular assignment, while in another equally successful fit the numbers permit it. The authors emphasize that this ambiguity in classification does not undermine the Jacobian peak criterion, which remains valid regardless of the particle’s ultimate structural identity.

The experimental prospects for testing the prediction appear highly favorable. The authors estimate that the predicted Jacobian peaks have characteristic widths of roughly 14 MeV at a normalized cross section value of 3, narrowing to about 5 MeV at a value of 6, features that are easily resolvable by modern detectors. The momentum resolution of the BESIII detector is approximately 0.5 percent at momenta around 1 GeV, corresponding to uncertainties of only about 2.6 MeV at the relevant transverse momenta. Combined with the beam-energy spread of roughly 1.5 MeV, the total experimental uncertainty amounts to about 3 MeV, far smaller than the width of the predicted peak. Moreover, BESIII has already accumulated large datasets of electron-positron collisions producing D meson pairs, providing ample statistics, and the estimated signal-to-background ratio in the most favorable region reaches approximately 110.

The authors also identify an important caveat that itself constitutes a valuable experimental probe. If the production amplitude for the process carries a purely angular dependence proportional to the cosine of the emission angle, the Jacobian peak could be dynamically suppressed, because the squared amplitude would vanish exactly at the kinematic limit. Measuring the differential cross section at a scattering angle of 90 degrees would therefore provide an important consistency check: a vanishing cross section at that angle would indicate suppression of the peak without negating the underlying kinematic structure. This subtlety underscores the care required in interpreting the proposed measurement, but it does not diminish the power of the criterion when applied with full awareness of the angular dynamics.

Beyond its immediate implications for G(3900), the Jacobian peak method offers a broadly applicable tool for hadron spectroscopy. The field has been flooded in recent years with candidate exotic states whose reality is debated, from tetraquarks to hadronic molecules, and many of these controversies stem from the same fundamental limitation: interference effects can mimic resonance signals in invariant mass spectra. A model-independent observable whose position is fixed purely by the mass of the hypothesized parent state provides exactly the kind of clean discriminator the field needs. The authors suggest that the same transverse momentum analysis can be extended to other hadronic systems, potentially resolving long-standing disputes about the existence of various resonance candidates across the light, strange, charm, and bottom sectors.

The study represents a convergence of precision experiment and incisive theoretical reasoning at a moment when the particle physics community is actively re-examining the census of hadronic matter. With BESIII’s confirmation of the G(3900) structure having reignited interest in the 3.9 GeV region, and with the proposed Jacobian peak test requiring no new instrumentation beyond what existing datasets already permit, the coming analysis of transverse momentum distributions may soon deliver one of the cleanest verdicts in modern hadron physics. Whether G(3900) emerges as a genuine new state of matter or fades into the machinery of quantum interference, the criterion developed by Huang and Chen is poised to become a standard instrument in the ongoing effort to map the true spectrum of strongly interacting particles.

Subject of Research: Criterion for establishing the existence of the G(3900) hadronic resonance through transverse momentum distributions in electron-positron collisions

Article Title: Criterion for the existence of the G(3900) resonance

Article References: Huang, Y., & Chen, X. (2026). Criterion for the existence of the G(3900) resonance. The European Physical Journal C, 86(10), Article 1161. https://doi.org/10.1140/epjc/s10052-026-16432-2

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16432-2

Keywords: G(3900), BESIII, charmonium, D meson, Jacobian peak, hadron spectroscopy, resonance, electron-positron annihilation, D D* threshold, molecular state, quantum interference, particle physics